{"id":51363,"date":"2024-07-10T23:18:19","date_gmt":"2024-07-10T15:18:19","guid":{"rendered":"https:\/\/swarma.org\/?p=51363"},"modified":"2024-07-10T23:18:19","modified_gmt":"2024-07-10T15:18:19","slug":"%e5%85%a8%e7%bd%91%e6%9c%80%e5%85%a8%e6%80%bb%e7%bb%93%ef%bc%81%e5%9b%a0%e6%9e%9c%e6%b6%8c%e7%8e%b0%e6%a0%b8%e5%bf%83%e6%8c%87%e6%a0%87%e6%9c%89%e6%95%88%e4%bf%a1%e6%81%af%ef%bd%9c","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=51363","title":{"rendered":"\u5168\u7f51\u6700\u5168\u603b\u7ed3\uff01\u56e0\u679c\u6d8c\u73b0\u6838\u5fc3\u6307\u6807\u201c\u6709\u6548\u4fe1\u606f\u201d\uff5c\u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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\u767e\u79d1\u5730\u5740\uff1a<\/span>https:\/\/wiki.swarma.org\/index.php\/\u6709\u6548\u4fe1\u606f<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n

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\u6709\u6548\u4fe1\u606f<\/span>\uff08Effective Information\uff0c\u7b80\u79f0EI\uff09<\/span>\u662f\u56e0\u679c\u6d8c\u73b0<\/span>\uff08Causal Emergence\uff09<\/span>\u7406\u8bba\u4e2d\u7684\u4e00\u4e2a\u6838\u5fc3\u6982\u5ff5\uff0c\u5b83\u53ef\u4ee5\u7528\u6765\u8861\u91cf\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u52a8\u529b\u5b66\u7684\u56e0\u679c\u6548\u5e94\u7684\u5f3a\u5ea6\u3002\u8fd9\u91cc\uff0c\u56e0\u679c\u6548\u5e94\u662f\u6307\u628a\u52a8\u529b\u5b66\u770b\u505a\u4e00\u4e2a\u9ed1\u7bb1\uff0c\u90a3\u4e48\u4e0d\u540c\u7684\u8f93\u5165\u5206\u5e03\u5c31\u4f1a\u5bfc\u81f4\u4e0d\u540c\u7684\u8f93\u51fa\u5206\u5e03\uff0c\u4e8c\u8005\u4e4b\u95f4\u8054\u7cfb\u7684\u7d27\u5bc6\u7a0b\u5ea6\u5c31\u662f\u56e0\u679c\u6548\u5e94\u3002\u6709\u6548\u4fe1\u606f\u901a\u5e38\u53ef\u4ee5\u5206\u89e3\u4e3a\u4e24\u4e2a\u90e8\u5206\uff1a\u786e\u5b9a\u6027<\/span>\uff08Determinism\uff09<\/span>\u548c\u7b80\u5e76\u6027<\/span>\uff08Degeneracy\uff09<\/span>\u3002\u786e\u5b9a\u6027\u662f\u6307\uff0c\u5728\u52a8\u529b\u5b66\u7684\u4f5c\u7528\u4e0b\uff0c\u6211\u4eec\u6839\u636e\u7cfb\u7edf\u524d\u4e00\u65f6\u523b\u7684\u72b6\u6001\u4f1a\u4ee5\u591a\u5927\u7a0b\u5ea6\u9884\u6d4b\u5b83\u4e0b\u4e00\u65f6\u523b\u72b6\u6001\uff1b\u7b80\u5e76\u6027\u662f\u6307\uff1a\u6211\u4eec\u80fd\u591f\u4ee5\u591a\u5927\u7a0b\u5ea6\u4ece\u4e0b\u4e00\u65f6\u523b\u7684\u72b6\u6001\u9884\u6d4b\u4e0a\u4e00\u65f6\u523b\u7684\u72b6\u6001\u3002\u5982\u679c\u786e\u5b9a\u6027\u8d8a\u5927\uff0c\u6216\u7b80\u5e76\u6027\u8d8a\u5c0f\uff0c\u5219\u7cfb\u7edf\u7684\u6709\u6548\u4fe1\u606f\u5c31\u4f1a\u8d8a\u5927\u3002\u5728\u672c\u9875\u4e2d\uff0c\u6240\u6709\u7684<\/span><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-math>log<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u90fd\u8868\u793a\u4ee52\u4e3a\u5e95\u7684\u5bf9\u6570\u8fd0\u7b97\u3002<\/span><\/section>\n

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1. \u5386\u53f2\u6e0a\u6e90<\/span><\/strong><\/p>\n

2. \u7b80\u4ecb<\/span><\/strong><\/p>\n

3. Do\u5f62\u5f0f\u53ca\u89e3\u91ca<\/span><\/strong><\/p>\n

3.1 \u5f62\u5f0f\u5b9a\u4e49<\/span><\/section>\n
3.2 \u4e3a\u4ec0\u4e48\u8981\u4f7f\u7528do\u7b97\u5b50\uff1f<\/span><\/section>\n
3.3 \u4e3a\u4ec0\u4e48\u5e72\u9884\u6210\u5747\u5300\u5206\u5e03\uff1f<\/span><\/section>\n

4. \u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u6709\u6548\u4fe1\u606f<\/span><\/strong><\/p>\n

4.1 \u9a6c\u5c14\u79d1\u592b\u94fe\u7b80\u4ecb<\/span><\/p>\n

4.2 \u9a6c\u5c14\u79d1\u592b\u94fe\u7684EI<\/span><\/p>\n

4.3 \u9a6c\u5c14\u79d1\u592b\u94feEI\u7684\u5411\u91cf\u5f62\u5f0f<\/span><\/p>\n

4.4 \u5f52\u4e00\u5316<\/span><\/p>\n

4.5 \u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027<\/span><\/p>\n

4.5.1 EI\u7684\u5206\u89e3<\/span><\/p>\n

4.5.2 \u786e\u5b9a\u6027\u4e0e\u7b80\u5e76\u6027<\/span><\/p>\n

4.5.3 \u4e3e\u4f8b<\/span><\/p>\n

4.5.4 \u5f52\u4e00\u5316\u7684\u786e\u5b9a\u6027\u4e0e\u7b80\u5e76\u6027<\/span><\/p>\n

4.6 EI\u7684\u51fd\u6570\u6027\u8d28<\/span><\/p>\n

4.6.1 \u5b9a\u4e49\u57df<\/span><\/section>\n
4.6.2 \u4e00\u9636\u5bfc\u6570\u53ca\u6781\u503c\u70b9<\/span><\/section>\n
4.6.3 \u4e8c\u9636\u5bfc\u6570\u4e0e\u51f8\u6027<\/span><\/section>\n
4.6.4 \u6700\u5c0f\u503c<\/span><\/section>\n
4.6.5 \u6700\u5927\u503c<\/span><\/section>\n

4.7 \u6700\u7b80\u9a6c\u5c14\u79d1\u592b\u94fe\u4e0b\u7684\u89e3\u6790\u89e3<\/span><\/p>\n

4.8 \u56e0\u679c\u6d8c\u73b0<\/span><\/p>\n

4.9 \u8ba1\u7b97EI\u7684\u6e90\u4ee3\u7801<\/span><\/p>\n

5. \u8fde\u7eed\u53d8\u91cf\u7684EI<\/span><\/strong><\/p>\n

5.1 \u968f\u673a\u51fd\u6570\u6620\u5c04<\/span><\/section>\n
5.1.1 \u4e00\u7ef4\u51fd\u6570\u6620\u5c04<\/span><\/section>\n

5.1.2 \u9ad8\u7ef4\u60c5\u51b5<\/span><\/p>\n

5.2 \u7ef4\u5ea6\u5e73\u5747\u7684EI<\/span><\/section>\n
5.3 \u968f\u673a\u8fed\u4ee3\u7cfb\u7edf<\/span><\/section>\n
5.4 \u524d\u9988\u795e\u7ecf\u7f51\u7edc<\/span><\/section>\n
5.5 \u8fde\u7eed\u7cfb\u7edfEI\u7684\u6e90\u4ee3\u7801<\/span><\/section>\n

6. EI\u4e0e\u5176\u4ed6\u76f8\u5173\u4e3b\u9898<\/span><\/strong>
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6.1 EI\u4e0e\u6574\u5408\u4fe1\u606f\u8bba<\/span><\/section>\n
6.1.1 EI\u4e0e\u03a6<\/span><\/section>\n
6.1.2 \u533a\u522b<\/span><\/section>\n
6.2 EI\u4e0e\u5176\u5b83\u56e0\u679c\u5ea6\u91cf\u6307\u6807<\/span><\/section>\n
6.2.1 \u56e0\u679c\u5143\u8bed\u7684\u5b9a\u4e49<\/span><\/section>\n
6.2.2 \u56e0\u679c\u5143\u8bed\u4e0e\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027<\/span><\/section>\n
6.2.3 \u56e0\u679c\u5ea6\u91cf\u6307\u6807\u7684\u56e0\u679c\u5143\u8bed\u8868\u793a<\/span><\/section>\n
6.3 EI\u4e0e\u52a8\u529b\u5b66\u53ef\u9006\u6027<\/span><\/section>\n
6.4 EI\u4e0eJS\u6563\u5ea6<\/span><\/section>\n
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\u6709\u6548\u4fe1\u606f<\/span>\uff08effective informaion\uff0cEI\uff09<\/span>\u8fd9\u4e2a\u6982\u5ff5\u6700\u65e9\u7531Giulio Tononi\u7b49\u4eba\u57282003\u5e74\u63d0\u51fa[1]\uff0c\u4f5c\u4e3a\u6574\u5408\u4fe1\u606f\u8bba\u4e2d\u7684\u4e00\u4e2a\u5173\u952e\u6307\u6807\u3002\u5f53\u4e00\u4e2a\u7cfb\u7edf\u5404\u4e2a\u7ec4\u5206\u4e4b\u95f4\u5177\u6709\u5f88\u5f3a\u7684\u56e0\u679c\u5173\u8054\u7684\u65f6\u5019\uff0c\u53ef\u4ee5\u8bf4\u8fd9\u4e2a\u7cfb\u7edf\u4fbf\u5177\u5907\u5f88\u9ad8\u7684\u6574\u5408\u7a0b\u5ea6\uff0c\u800c\u6709\u6548\u4fe1\u606f\uff1aEI\uff0c\u4fbf\u662f\u7528\u6765\u5ea6\u91cf\u8fd9\u79cd\u56e0\u679c\u5173\u8054\u7a0b\u5ea6\u7684\u5173\u952e\u6307\u6807\u3002<\/span><\/section>\n

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\u5230\u4e862013\u5e74\uff0cGiulio Tononi\u7684\u5b66\u751fErik Hoel\u7b49\u4eba\u5c06\u6709\u6548\u4fe1\u606f\u8fd9\u4e2a\u6982\u5ff5\u8fdb\u4e00\u6b65\u63d0\u70bc\u51fa\u6765\uff0c\u4ece\u800c\u5b9a\u91cf\u5730\u523b\u753b\u6d8c\u73b0\uff0c\u4e8e\u662f\u63d0\u51fa\u4e86\u56e0\u679c\u6d8c\u73b0\u7406\u8bba[2]\u3002\u5728\u8fd9\u4e2a\u7406\u8bba\u4e2d\uff0cHoel\u4f7f\u7528\u4e86Judea Pearl\u7684do\u7b97\u5b50\u6765\u6539\u9020\u4e00\u822c\u7684\u4e92\u4fe1\u606f\u6307\u6807[3]\uff0c\u8fd9\u4f7f\u5f97EI\u672c\u8d28\u4e0a\u4e0e\u4e92\u4fe1\u606f\u4e0d\u540c\u3002\u4e92\u4fe1\u606f\u5ea6\u91cf\u7684\u662f\u76f8\u5173\u6027\uff0c\u800c\u6709\u6548\u4fe1\u606f\u56e0\u4e3a\u5f15\u5165\u4e86do\u7b97\u5b50\uff0c\u4ece\u800c\u53ef\u4ee5\u5ea6\u91cf\u56e0\u679c\u6027\u3002\u5728\u8fd9\u4e00\u6587\u7ae0\u4e2d\uff0c\u4f5c\u8005\u4eec\u540c\u65f6\u63d0\u51fa\u4e86\u5f52\u4e00\u5316\u7684\u6709\u6548\u4fe1\u606f\u6307\u6807Eff\u3002<\/span><\/section>\n

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2. \u7b80\u4ecb<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>E<\/span><\/mi>I<\/span><\/mi>(<\/span><\/mo>P<\/span><\/mi>)<\/span><\/mo>\u2261<\/span><\/mo>I<\/span><\/mi>(<\/span><\/mo>Y<\/span><\/mi>;<\/span><\/mo>X<\/span><\/mi>|<\/span><\/mo><\/mrow>d<\/span><\/mi>o<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi>\u223c<\/span><\/mo>U<\/span><\/mi>)<\/span><\/mo>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u7b2c\u4e00\u4e2a\u77e9\u9635<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-math>P<\/span><\/mi>1<\/span><\/sub><\/mn><\/msub><\/mjx-assistive-mml><\/mjx-container>\u7684EI\u6bd4\u7b2c\u4e8c\u4e2a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-math>P<\/span><\/mi>2<\/span><\/sub><\/mn><\/msub><\/mjx-assistive-mml><\/mjx-container>\u7684\u9ad8\uff0c\u8fd9\u662f\u56e0\u4e3a\u8fd9\u4e00\u6982\u7387\u8f6c\u79fb\u662f\u4e00\u4e2a\u5b8c\u5168\u786e\u5b9a\u6027\u7684\u8f6c\u79fb\uff0c\u4e5f\u5c31\u662f\u4ece\u67d0\u4e00\u4e2a\u72b6\u6001\u51fa\u53d1\uff0c\u5b83\u4f1a\u4ee5100%\u7684\u6982\u7387\u8f6c\u79fb\u5230\u53e6\u5916\u67d0\u4e00\u4e2a\u72b6\u6001\u3002\u7136\u800c\uff0c\u5e76\u4e0d\u662f\u6240\u6709\u7684\u786e\u5b9a\u6027\u8f6c\u79fb\u7684\u77e9\u9635\u90fd\u4f1a\u5bf9\u5e94\u8f83\u5927\u7684EI\uff0c\u6bd4\u5982<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-math>P<\/span><\/mi>3<\/span><\/mn><\/msub><\/mjx-assistive-mml><\/mjx-container>\u8fd9\u4e2a\u77e9\u9635\uff0c\u867d\u7136\u5b83\u7684\u8f6c\u79fb\u6982\u7387\u4e5f\u90fd\u662f100%\u62160\uff0c\u4f46\u662f\u56e0\u4e3a\u6240\u6709\u540e\u9762\u4e09\u79cd\u72b6\u6001\u90fd\u4f1a\u8f6c\u79fb\u5230\u7b2c1\u4e2a\u72b6\u6001\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u65e0\u6cd5\u533a\u5206\u5b83\u4e0a\u4e00\u65f6\u523b\u662f\u5904\u4e8e\u4f55\u79cd\u72b6\u6001\u7684\u3002\u8fd9\u79cd\u60c5\u5b83\u7684EI\u4e5f\u4f1a\u6bd4\u8f83\u4f4e\uff0c\u6211\u4eec\u79f0\u8fd9\u79cd\u60c5\u51b5\u5b58\u5728\u7740\u7b80\u5e76\u6027\u3002\u4e8e\u662f\uff0c\u5982\u679c\u4e00\u4e2a\u8f6c\u79fb\u77e9\u9635\u5177\u6709\u8f83\u9ad8\u7684\u786e\u5b9a\u6027\u548c\u8f83\u4f4e\u7684\u7b80\u5e76\u6027\uff0c\u5219\u5b83\u7684EI\u5c31\u4f1a\u5f88\u9ad8\u3002\u8fdb\u4e00\u6b65\uff0c\u5b58\u5728\u5982\u4e0b\u5bf9EI\u7684\u5206\u89e3\uff1a<\/span><\/section>\n

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<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>E<\/span><\/mi>I<\/span><\/mi>=<\/span><\/mo>D<\/span><\/mi>e<\/span><\/mi>t<\/span><\/mi>\u2212<\/span><\/mo>D<\/span><\/mi>e<\/span><\/mi>g<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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\u8fd9\u91cc\uff0cDet\u662f\u5bf9\u786e\u5b9a\u6027<\/span>\uff08Determinism\uff09<\/span>\u7684\u7f29\u5199\uff0c\u800cDeg\u662f\u5bf9\u7b80\u5e76\u6027<\/span>\uff08Degeneracy\uff09<\/span>\u7684\u7f29\u5199\uff0cEI\u662f\u4e8c\u8005\u4e4b\u5dee\u3002\u5728\u4e0a\u9762\u7684\u8868\u683c\u4e2d\uff0c\u6211\u4eec\u5c06\u77e9\u9635\u6240\u5bf9\u5e94\u7684Det\u548cDeg\u6570\u503c\u4e5f\u90fd\u5217\u5728\u4e86\u4e0b\u9762\u3002<\/span><\/section>\n

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\u7b2c\u4e00\u4e2a\u8f6c\u79fb\u6982\u7387\u77e9\u9635\u662f\u4e00\u4e2a\u6392\u5217\u77e9\u9635<\/span>\uff08Permutation\uff09<\/span>\uff0c\u5b83\u662f\u53ef\u9006\u7684\uff0c\u56e0\u6b64\u786e\u5b9a\u6027\u6700\u9ad8\uff0c\u6ca1\u6709\u7b80\u5e76\u6027\uff0c\u56e0\u800cEI\u6700\u5927\uff1b\u7b2c\u4e8c\u4e2a\u77e9\u9635\u7684\u524d\u4e09\u4e2a\u72b6\u6001\u90fd\u4f1a\u4ee51\/3\u7684\u6982\u7387\u8df3\u8f6c\u5230\u5f7c\u6b64\uff0c\u56e0\u6b64\u786e\u5b9a\u6027\u7a0b\u5ea6\u6700\u4f4e\uff0c\u800c\u7b80\u5e76\u6027\u4e5f\u5f88\u4f4e\uff0cEI\u662f0.81\uff1b\u7b2c\u4e09\u4e2a\u77e9\u9635\u867d\u7136\u4e5f\u662f\u975e0\u53731\u7684\u8f6c\u79fb\u6982\u7387\uff0c\u56e0\u800c\u786e\u5b9a\u6027\u6700\u9ad8\uff0c\u4f46\u662f\u7531\u4e8e\u540e\u4e09\u4e2a\u72b6\u6001\u90fd\u8df3\u8f6c\u52301\uff0c\u56e0\u6b64\uff0c\u4ece1\u72b6\u6001\u4e0d\u80fd\u63a8\u77e5\u5b83\u6765\u81ea\u4e8e\u54ea\u4e2a\u72b6\u6001\uff0c\u56e0\u6b64\u7b80\u5e76\u6027\u6700\u9ad8\uff0c\u6700\u7ec8\u7684EI\u4e0e\u7b2c\u4e8c\u4e2a\u76f8\u540c\uff0c\u4ecd\u7136\u662f0.81\u3002<\/span><\/section>\n

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\u5c3d\u7ba1\u5728\u539f\u59cb\u6587\u732e\u4e2d[2]\uff0c\u6709\u6548\u4fe1\u606f\u5927\u591a\u5e94\u7528\u4e8e\u79bb\u6563\u72b6\u6001\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\uff0c\u4f46\u662f\uff0c\u5f20\u6c5f\u3001\u5218\u51ef\u5a01\u3001\u6768\u660e\u54f2\u7b49\u4eba\u5c06EI\u7684\u5b9a\u4e49\u6269\u5c55\u5230\u4e86\u66f4\u4e00\u822c\u7684\u8fde\u7eed\u53d8\u91cf\u7684\u60c5\u5f62[5][6][7]\u3002\u8fd9\u4e00\u6269\u5145\u7684\u57fa\u672c\u601d\u60f3\u662f\u4eceEI\u7684\u539f\u59cb\u5b9a\u4e49\u51fa\u53d1\uff0c\u5c06\u56e0\u53d8\u91cfx\u5e72\u9884\u4e3a\u4e00\u4e2a\u8db3\u591f\u5927\u7684\u6709\u754c\u533a\u95f4\uff0c\u5373<\/span><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-math>[<\/span><\/mo>\u2212<\/span><\/mo>L<\/span><\/mi>2<\/span><\/mn><\/mfrac>,<\/span><\/mo>L<\/span><\/mi>2<\/span><\/mn><\/mfrac>]<\/span><\/mo>n<\/span><\/mi><\/msup><\/mjx-assistive-mml><\/mjx-container>\u4e0a\u7684\u5747\u5300\u5206\u5e03\uff0c\u7136\u540e\u518d\u5047\u8bbe\u56e0\u679c\u673a\u5236\u4e3a\u4e00\u79cd\u6ee1\u8db3\u9ad8\u65af\u5206\u5e03\u7684\u6761\u4ef6\u6982\u7387\uff0c\u5176\u5747\u503c\u4e3a\u786e\u5b9a\u503c\u6620\u5c04<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u534f\u65b9\u5dee\u77e9\u9635\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03a3<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4ece\u800c\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u518d\u5ea6\u91cf\u56e0\u679c\u53d8\u91cf\u4e4b\u95f4\u7684\u6709\u6548\u4fe1\u606f\u3002\u8fd9\u91cc\u7684\u56e0\u679c\u673a\u5236\u662f\u7531\u6620\u5c04<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u548c\u534f\u65b9\u5dee\u77e9\u9635\u5171\u540c\u51b3\u5b9a\u7684\uff0c\u4e5f\u5c31\u662f\u6761\u4ef6\u6982\u7387<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>P<\/span><\/mi>r<\/span><\/mi>(<\/span><\/mo>y<\/span><\/mi>|<\/span><\/mo><\/mrow>x<\/span><\/mi>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u6765\u51b3\u5b9a\u7684\u3002<\/span><\/section>\n

\u4e0b\u9762\uff0c\u6211\u4eec\u5c06\u8fdb\u884c\u66f4\u8be6\u7ec6\u5730\u8bb2\u89e3\u3002<\/span><\/section>\n


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3. Do\u5f62\u5f0f\u53ca\u89e3\u91ca<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u539f\u59cb\u7684\u6709\u6548\u4fe1\u606f\u662f\u5b9a\u4e49\u5728\u79bb\u6563\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u4e0a\u7684\u3002\u7136\u800c\uff0c\u4e3a\u4e86\u80fd\u591f\u66f4\u5e7f\u6cdb\u5730\u5e94\u7528\uff0c\u5728\u8fd9\u91cc\u6211\u4eec\u63a2\u8ba8\u6709\u6548\u4fe1\u606f\u7684\u66f4\u4e00\u822c\u7684\u5f62\u5f0f\u3002<\/span><\/section>\n

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3.1 \u5f62\u5f0f\u5b9a\u4e49<\/span><\/strong><\/span><\/h2>\n

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\u8003\u8651\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\uff1a<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>Y<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5206\u522b\u4ee3\u8868\u56e0\u53d8\u91cf<\/span>\uff08Cause Variable\uff09<\/span>\u548c\u679c\u53d8\u91cf<\/span>\uff08Effect Variable\uff09<\/span>\uff0c\u5e76\u4e14\u5047\u5b9a\u5b83\u4eec\u7684\u53d6\u503c\u533a\u95f4\u5206\u522b\u662f<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>X<\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>Y<\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u3002\u5219<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5230<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>Y<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u6709\u6548\u4fe1\u606fEI\u7684\u5b9a\u4e49\u4e3a\uff1a<\/span><\/section>\n

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<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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\u8fd9\u91cc\uff0c<\/span><\/sub><\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4ee3\u8868\u5bf9<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5b9e\u65bddo\u5e72\u9884<\/span> (\u6216\u79f0do\u64cd\u4f5c\uff0c\u82f1\u6587\u662fdo-operator\uff09<\/span>\uff0c\u4f7f\u5176\u670d\u4ece<\/span><\/sub><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u4e0a\u7684\u5747\u5300\u5206\u5e03<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-math>U<\/span><\/mi>(<\/sub><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mo>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4e5f\u5373\u662f\u6700\u5927\u71b5\u5206\u5e03\u3002<\/span><\/sub><\/span><\/mo><\/mover><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u4e0e<\/span><\/sub><\/span><\/mo><\/mover><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u5206\u522b\u4ee3\u8868\u5728\u7ecf\u8fc7<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-math>d<\/span><\/mi>o<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5e72\u9884\u540e\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>Y<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u53d8\u91cf\uff0c\u5176\u4e2d\uff0c<\/span><\/section>\n

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<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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\u4e5f\u5c31\u662f\uff0c\u7ecf\u8fc7\u5e72\u9884\u540e\u7684\u53d8\u91cf<\/span><\/sub><\/span><\/mo><\/mover><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/mo><\/mover><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u4e0e\u5e72\u9884\u524d\u7684\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e4b\u95f4\u7684\u6700\u5927\u533a\u522b\u5c31\u5728\u4e8e\u5206\u5e03\u4e0d\u540c\uff1a<\/span><\/sub><\/span><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mo><\/mover><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u670d\u4ece<\/span><\/sub><\/span><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u4e0a\u7684\u5747\u5300\u5206\u5e03\uff0c\u800c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5219\u53ef\u80fd\u662f\u4efb\u610f\u7684\u5206\u5e03\u3002\u8fd9\u91cc<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-math>#<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi><\/mrow>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4ee3\u8868\u96c6\u5408<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>X<\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u7684\u57fa\u6570\u3002\u5bf9\u4e8e\u6709\u9650\u5143\u7d20\u96c6\u5408\u6765\u8bf4\uff0c\u8fd9\u5c31\u662f\u96c6\u5408\u4e2d\u5143\u7d20\u7684\u4e2a\u6570\u3002<\/span><\/section>\n

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\u6309\u7167Judea Pearl\u7684\u7406\u8bba\uff0cdo\u7b97\u5b50\u5b9e\u9645\u4e0a\u662f\u5207\u65ad\u4e86\u6240\u6709\u6307\u5411<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u53d8\u91cf\u7684\u56e0\u679c\u7bad\u5934\uff0c\u540c\u65f6\u4fdd\u6301\u5176\u5b83\u56e0\u7d20\uff0c\u7279\u522b\u662f\u4ece<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5230<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>Y<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u56e0\u679c\u673a\u5236\u4fdd\u6301\u4e0d\u53d8\u3002\u6240\u8c13\u7684\u56e0\u679c\u673a\u5236\u662f\u6307\u5728\u7ed9\u5b9a<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u53d6\u503c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>x<\/span><\/mi>\u2208<\/sub><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u7684\u60c5\u51b5\u4e0b\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>Y<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5728<\/sub><\/span>\u4e0a\u53d6\u4efb\u610f\u503c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>y<\/span><\/mi>\u2208<\/sub><\/span><\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u7684\u6761\u4ef6\u6982\u7387\uff1a<\/span><\/section>\n

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<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi>\u2261<\/span><\/mo>P<\/span><\/mi>r<\/span><\/mi>(<\/span><\/mo>Y<\/span><\/mi>=<\/span><\/mo>y<\/span><\/mi>|<\/span><\/mo><\/mrow>X<\/span><\/mi>=<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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\u5728\u5e72\u9884\u4e2d\uff0c\u6211\u4eec\u8981\u59cb\u7ec8\u4fdd\u6301\u5219\u8fd9\u4e2a\u56e0\u679c\u673a\u5236<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>f<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4fdd\u6301\u4e0d\u53d8\u3002\u5f53\u6ca1\u6709\u5176\u5b83\u53d8\u91cf\u5f71\u54cd\u7684\u65f6\u5019\uff0c\u8fd9\u5c31\u4f1a\u5bfc\u81f4\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>Y<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u6982\u7387\u5206\u5e03\u4f1a\u8ddf\u7740\u53d1\u751f\u53d8\u5316\uff0c\u5373\u88ab\u95f4\u63a5\u5e72\u9884\u6210\u4e3a\uff1a<\/span><\/section>\n

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<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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<\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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\u5176\u4e2d\uff0c<\/span><\/sub><\/span><\/mo><\/mover><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/mo><\/mover><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u5219\u4ee3\u8868\uff1a\u5728\u4fdd\u6301\u56e0\u679c\u673a\u5236<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>f<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e0d\u53d8\u7684\u60c5\u51b5\u4e0b\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>Y<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u53d8\u91cf\u88ab<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684do\u5e72\u9884\u6240\u95f4\u63a5\u6539\u53d8\u4e86\u7684Y\u53d8\u91cf\uff0c\u8fd9\u79cd\u53d8\u5316\u4e3b\u8981\u4f53\u73b0\u5728\u6982\u7387\u5206\u5e03\u7684\u53d8\u5316\u4e0a\u3002<\/span><\/section>\n

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\u56e0\u6b64\uff0c\u6240\u8c13\u4e00\u4e2a\u56e0\u679c\u673a\u5236<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>f<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u6709\u6548\u4fe1\u606fEI\uff0c\u5c31\u662f\u88ab\u5e72\u9884\u540e\u7684\u56e0\u53d8\u91cf<\/span><\/sub><\/span><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mo><\/mover><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u548c\u679c\u53d8\u91cf<\/span><\/sub><\/span><\/mo><\/mover><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/mo><\/mover><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u4e4b\u95f4\u7684\u4e92\u4fe1\u606f\u3002<\/span><\/section>\n

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3.2 \u4e3a\u4ec0\u4e48\u8981\u4f7f\u7528do\u7b97\u5b50\uff1f<\/span><\/strong><\/span><\/h2>\n

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\u4e0d\u96be\u770b\u51fa\uff0c\u5c3d\u7ba1EI\u672c\u8d28\u4e0a\u5c31\u662f\u4e92\u4fe1\u606f\uff0c\u4f46\u662f\u4e0e\u4f20\u7edf\u4fe1\u606f\u8bba\u4e2d\u7684\u4e92\u4fe1\u606f\u4e0d\u540c\uff0c\u6709\u6548\u4fe1\u606fEI\u5728\u5b9a\u4e49\u4e2d\u5305\u542b\u4e86do\u64cd\u4f5c\uff0c\u5373\u5bf9\u8f93\u5165\u53d8\u91cf\u505a\u4e86\u4e00\u4e2a\u5e72\u9884\u64cd\u4f5c\u3002\u4e3a\u4ec0\u4e48\u8981\u5f15\u5165\u8fd9\u4e00\u64cd\u4f5c\u5462\uff1f<\/span><\/section>\n

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\u6839\u636eJudea Pearl\u7684\u56e0\u679c\u9636\u68af\u7406\u8bba[3]\uff0c\u56e0\u679c\u63a8\u65ad\u5305\u542b\u4e86\u4e09\u4e2a\u5c42\u6b21\uff0c\u5206\u522b\u662f\uff1a\u5173\u8054\u3001\u5e72\u9884\u548c\u53cd\u4e8b\u5b9e\u3002\u9636\u68af\u5c42\u7ea7\u8d8a\u9ad8\uff0c\u56e0\u679c\u7279\u5f81\u8d8a\u660e\u663e\u3002\u76f4\u63a5\u5bf9\u89c2\u6d4b\u6570\u636e\u4f30\u6d4b\u4e92\u4fe1\u606f\uff0c\u4fbf\u662f\u5728\u5ea6\u91cf\u5173\u8054\u7a0b\u5ea6\uff1b\u800c\u5982\u679c\u6211\u4eec\u80fd\u5bf9\u53d8\u91cf\u505a\u5e72\u9884\u64cd\u4f5c\uff0c\u5373\u8bbe\u5b9a\u53d8\u91cf\u4e3a\u67d0\u4e2a\u503c\u6216\u670d\u4ece\u67d0\u4e2a\u5206\u5e03\uff0c\u4fbf\u4e0a\u5347\u5230\u4e86\u5e72\u9884\u7684\u5c42\u7ea7\u3002\u5728EI\u7684\u5b9a\u4e49\u4e2d\u5f15\u5165\u4e86<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-math>d<\/span><\/mi>o<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u64cd\u4f5c\uff0c\u5219\u4f7f\u5f97EI\u80fd\u591f\u6bd4\u4e92\u4fe1\u606f\u66f4\u80fd\u4f53\u73b0\u56e0\u679c\u7279\u5f81\u3002<\/span><\/section>\n

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\u800c\u4ece\u5b9e\u9645\u610f\u4e49\u4e0a\u6765\u8bb2\uff0c\u5728EI\u7684\u8ba1\u7b97\u4e2d\u5f15\u5165do\u7b97\u5b50\uff0c\u5219\u53ef\u4ee5\u628a\u6570\u636e\u548c\u52a8\u529b\u5b66\u5206\u5f00\uff0c\u4ece\u800c\u6d88\u9664\u6570\u636e\u5206\u5e03<\/span>\uff08\u5373<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u5206\u5e03\uff09<\/span>\u5bf9EI\u5ea6\u91cf\u6240\u5e26\u6765\u7684\u5f71\u54cd\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5728\u4e00\u822c\u7684\u56e0\u679c\u56fe\u4e0a\uff0cdo\u7b97\u5b50\u662f\u4e00\u79cd\u6d88\u9664\u6307\u5411\u88ab\u5e72\u9884\u53d8\u91cf\u6240\u6709\u7684\u56e0\u679c\u7bad\u5934\u7684\u64cd\u4f5c\uff0c\u8fd9\u79cd\u64cd\u4f5c\u53ef\u4ee5\u907f\u514d\u6df7\u6742\u56e0\u5b50\u9020\u6210\u7684\u865a\u5047\u5173\u8054\u3002\u56e0\u6b64\uff0cEI\u5b9a\u4e49\u4e2d\u7684do\u7b97\u5b50\u4e5f\u53ef\u4ee5\u6d88\u9664\u6240\u6709\u6307\u5411\u56e0\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u56e0\u679c\u7bad\u5934\uff0c\u5305\u62ec\u5176\u5b83\u53d8\u91cf<\/span>\uff08\u5305\u62ec\u4e0d\u53ef\u89c2\u6d4b\u7684\u53d8\u91cf\uff09<\/span>\u5bf9<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u5f71\u54cd\uff0c\u4ece\u800c\u4f7f\u5f97EI\u66f4\u80fd\u591f\u523b\u753b\u52a8\u529b\u5b66\u672c\u8eab\u7684\u7279\u6027\u3002<\/span><\/section>\n

do\u7b97\u5b50\u7684\u5f15\u5165\u8ba9EI\u8fd9\u4e2a\u6307\u6807\u4e0e\u5176\u4ed6\u4fe1\u606f\u5ea6\u91cf\u6307\u6807\u622a\u7136\u4e0d\u540c\uff0c\u5173\u952e\u5728\u4e8e\u5b83\u662f\u4e14\u4ec5\u662f\u56e0\u679c\u673a\u5236\u7684\u51fd\u6570\uff0c\u4e00\u65b9\u9762\u8fd9\u4e00\u7279\u6027\u4f7f\u5f97\u5b83\u6bd4\u5176\u4ed6\u6307\u6807<\/span>\uff08\u6bd4\u5982\u8f6c\u79fb\u71b5\uff09<\/span>\u66f4\u80fd\u6293\u4f4f\u56e0\u679c\u6982\u5ff5\u7684\u672c\u8d28\uff0c\u53e6\u4e00\u65b9\u9762\u5b83\u9700\u8981\u6211\u4eec\u80fd\u591f\u5df2\u77e5\u6216\u83b7\u53d6\u5230\u56e0\u679c\u673a\u5236\uff0c\u8fd9\u5728\u53ea\u6709\u89c2\u6d4b\u6570\u636e\u7684\u60c5\u51b5\u4e0b\u5b58\u5728\u4e00\u5b9a\u7684\u56f0\u96be\u3002<\/span><\/section>\n

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3.3 \u4e3a\u4ec0\u4e48\u5e72\u9884\u6210\u5747\u5300\u5206\u5e03\uff1f<\/span><\/strong><\/span><\/h2>\n

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\u5728Erik Hoel\u7684\u539f\u59cb\u5b9a\u4e49\u4e2d\uff0cdo\u64cd\u4f5c\u662f\u5c06\u56e0\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5e72\u9884\u6210\u4e86\u5728\u5176\u5b9a\u4e49\u57df<\/span><\/sub><\/span><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u4e0a\u7684\u5747\u5300\u5206\u5e03<\/span>\uff08\u4e5f\u5c31\u662f\u6700\u5927\u71b5\u5206\u5e03\uff09<\/span>[2][10]\u3002\u90a3\u4e48\uff0c \u4e3a\u4ec0\u4e48\u8981\u5e72\u9884\u6210\u5747\u5300\u5206\u5e03\u5462\uff1f\u5176\u5b83\u5206\u5e03\u662f\u5426\u4e5f\u53ef\u4ee5\uff1f<\/span><\/section>\n

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\u9996\u5148\uff0c\u6839\u636e\u4e0a\u4e00\u5c0f\u8282\u7684\u8bba\u8ff0\uff0cdo\u64cd\u4f5c\u7684\u5b9e\u8d28\u662f\u5e0c\u671b\u8ba9EI\u80fd\u591f\u66f4\u6e05\u6670\u5730\u523b\u753b\u56e0\u679c\u673a\u5236<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>f<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u6027\u8d28\uff0c\u56e0\u6b64\uff0c\u9700\u8981\u5207\u65ad\u56e0\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e0e\u5176\u5b83\u53d8\u91cf\u7684\u8054\u7cfb\uff0c\u5e76\u6539\u53d8\u5176\u5206\u5e03\uff0c\u8ba9EI\u5ea6\u91cf\u4e0e<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u5206\u5e03\u65e0\u5173\u3002<\/span><\/section>\n

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\u800c\u4e4b\u6240\u4ee5\u8981\u628a\u8f93\u5165\u53d8\u91cf\u5e72\u9884\u4e3a\u5747\u5300\u5206\u5e03\uff0c\u5176\u5b9e\u5c31\u662f\u8981\u66f4\u597d\u5730\u523b\u753b\u56e0\u679c\u673a\u5236\u7684\u7279\u6027\u3002<\/span><\/section>\n

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\u8fd9\u662f\u56e0\u4e3a\uff0c\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>X<\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>Y<\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u90fd\u662f\u6709\u9650\u53ef\u6570\u96c6\u5408\u7684\u65f6\u5019\uff0c\u56e0\u679c\u673a\u5236<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>f<\/span><\/mi>\u2261<\/span><\/mo>P<\/span><\/mi>r<\/span><\/mi>(<\/span><\/mo>Y<\/span><\/mi>=<\/span><\/mo>y<\/span><\/mi>|<\/span><\/mo><\/mrow>X<\/span><\/mi>=<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u5c31\u6210\u4e3a\u4e86\u4e00\u4e2a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-math>#<\/span><\/mi>(<\/span><\/mo><\/sub><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mi><\/mrow>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u884c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-math>#<\/span><\/mi>(<\/span><\/mo><\/sub><\/span><\/mi><\/mrow>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u5217\u7684\u77e9\u9635\uff0c\u6211\u4eec\u53ef\u4ee5\u5c55\u5f00EI\u7684\u5b9a\u4e49\uff1a<\/span><\/section>\n

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\uff081\uff09<\/span><\/p>\n

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\u4e0d\u96be\u770b\u51fa\uff0c\u6700\u540e\u5f97\u5230\u7684\u7b49\u5f0f\u544a\u8bc9\u6211\u4eec\uff0cEI\u5b9e\u9645\u4e0a\u7531\u4e24\u9879\u6784\u6210\uff0c\u7b2c\u4e00\u9879\u662f\u56e0\u679c\u673a\u5236\u77e9\u9635\u6bcf\u4e00\u884c\u7684\u8d1f\u71b5\u7684\u5e73\u5747\u503c\uff0c\u7b2c\u4e8c\u9879\u5219\u662f\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>Y<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u71b5\u3002\u5728\u7b2c\u4e00\u9879\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u6982\u7387\u5206\u5e03<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>P<\/span><\/mi>r<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi>=<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u5b9e\u9645\u4e0a\u8d77\u5230\u4e86\u5bf9\u6bcf\u4e00\u884c\u7684\u71b5\u6c42\u5e73\u5747\u65f6\u5019\u7684\u6743\u91cd\u7684\u4f5c\u7528\u3002\u53ea\u6709\u5f53\u6211\u4eec\u5c06\u8be5\u6743\u91cd\u53d6\u4e3a\u540c\u6837\u7684\u6570\u503c\u7684\u65f6\u5019\uff0c\u624d\u80fd\u591f\u5e73\u7b49\u5730\u5bf9\u5f85\u56e0\u679c\u673a\u5236\u77e9\u9635\u4e2d\u7684\u6bcf\u4e00\u4e2a\u884c\uff0c\u8fd9\u65f6\u5c31\u6070\u597d\u662f\u5c06<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>X<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5e72\u9884\u6210\u5747\u5300\u5206\u5e03\u7684\u65f6\u5019\u3002<\/span><\/section>\n

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\u5982\u679c\u4e0d\u662f\u5747\u5300\u5206\u5e03\uff0c\u4e5f\u5c31\u610f\u5473\u7740\u67d0\u4e9b\u884c\u7684\u71b5\u5c31\u4f1a\u88ab\u4e58\u4ee5\u4e00\u4e2a\u8f83\u5927\u7684\u6743\u91cd\uff0c\u6709\u7684\u884c\u5c31\u4f1a\u88ab\u8d4b\u4e88\u4e00\u4e2a\u8f83\u5c0f\u7684\u6743\u91cd\uff0c\u8fd9\u79cd\u6743\u91cd\u4ee3\u8868\u4e86\u67d0\u79cd\u201c\u504f\u89c1\u201d\uff0c\u56e0\u6b64\u4e5f\u5c31\u4e0d\u80fd\u505a\u5230\u8ba9EI\u80fd\u591f\u53cd\u6620\u56e0\u679c\u673a\u5236\u7684\u5929\u7136\u5c5e\u6027\u4e86\u3002<\/span><\/section>\n

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4. \u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u6709\u6548\u4fe1\u606f<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


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4.1 \u9a6c\u5c14\u79d1\u592b\u94fe\u7b80\u4ecb<\/span><\/strong><\/span><\/strong><\/h2>\n

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\u5728\u672c\u5c0f\u8282\u4e2d\uff0c\u6240\u6709\u7684\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u6982\u7387\u77e9\u9635\u90fd\u8868\u793a\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>P<\/mi><\/mjx-assistive-mml><\/mjx-container>\u3002N\u4e3a\u603b\u7684\u72b6\u6001\u6570\u91cf\u3002<\/span><\/span><\/section>\n

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\u6700\u65e9\uff0cErik Hoel\u7b49\u4eba\u662f\u5728\u79bb\u6563\u72b6\u6001\u7684\u9a6c\u5c14\u79d1\u592b\u52a8\u529b\u5b66\uff0c\u5373\u9a6c\u5c14\u79d1\u592b\u94fe\u4e0a\u63d0\u51fa\u6709\u6548\u4fe1\u606f\u8fd9\u4e00\u5ea6\u91cf\u56e0\u679c\u6027\u7684\u6307\u6807\u7684\u3002\u56e0\u6b64\uff0c\u8fd9\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u4ecb\u7ecd\u6709\u6548\u4fe1\u606f\u5728\u9a6c\u5c14\u79d1\u592b\u94fe\u4e0a\u7684\u7279\u6b8a\u5f62\u5f0f\u3002<\/span><\/section>\n

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\u6240\u8c13\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u662f\u6307\u72b6\u6001\u79bb\u6563\u3001\u65f6\u95f4\u79bb\u6563\u7684\u4e00\u79cd\u5e73\u7a33\u968f\u673a\u8fc7\u7a0b\uff0c\u5b83\u7684\u52a8\u529b\u5b66\u4e00\u822c\u90fd\u53ef\u4ee5\u7528\u6240\u8c13\u7684\u8f6c\u79fb\u6982\u7387\u77e9\u9635<\/span> (Transitional Probability Matrix)<\/span>\uff0c\u7b80\u79f0TPM\u6765\u8868\u793a\uff0c\u6709\u65f6\u4e5f\u53eb\u505a\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u6216\u72b6\u6001\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u6216\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\u3002<\/span><\/section>\n

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\u5177\u4f53\u6765\u8bb2\uff0c\u9a6c\u5c14\u79d1\u592b\u94fe\u5305\u542b\u4e00\u7ec4\u968f\u673a\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>X<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5b83\u5728\u72b6\u6001\u7a7a\u95f4<\/sub><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span>=<\/span><\/mo>{<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>2<\/span><\/mn>,<\/span><\/mo>\u22ef<\/span><\/mo>,<\/span><\/mo>N<\/span><\/mi>}<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4e0a\u53d6\u503c\uff0c\u5176\u4e2d<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>t<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5f80\u5f80\u8868\u793a\u65f6\u95f4\u3002\u6240\u8c13\u7684\u8f6c\u79fb\u6982\u7387\u77e9\u9635\u662f\u6307\u4e00\u4e2a\u6982\u7387\u77e9\u9635\uff0c\u5176\u4e2d\u7b2c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>i<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u884c\uff0c\u7b2c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>j<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5217\u5143\u7d20\uff1a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>p<\/span><\/mi>i<\/span><\/sub><\/mi>j<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u4e86\u7cfb\u7edf\u5728\u4efb\u610f\u65f6\u523b<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>t<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5728<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>i<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u72b6\u6001\u7684\u6761\u4ef6\u4e0b\uff0c\u5728<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math>t<\/span><\/mi>+<\/span><\/mo>1<\/span><\/mn><\/mjx-assistive-mml><\/mjx-container>\u65f6\u523b\u8df3\u8f6c\u5230<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>j<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u72b6\u6001\u7684\u6982\u7387\u3002\u540c\u65f6\uff0c\u6bcf\u4e00\u884c\u6ee1\u8db3\u5f52\u4e00\u5316\u6761\u4ef6\uff1a<\/span><\/section>\n

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<\/mjx-c><\/mjx-mi><\/mjx-over><\/mjx-c><\/mjx-mo><\/mjx-base><\/mjx-row><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-under><\/mjx-row><\/mjx-munder><\/mjx-box><\/mjx-munderover><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mo><\/munderover><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
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<\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\u53ef\u4ee5\u770b\u4f5c\u662f\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u52a8\u529b\u5b66\uff0c\u8fd9\u662f\u56e0\u4e3a\uff0c\u4efb\u610f\u65f6\u523b<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math>t<\/span><\/mi>+<\/span><\/mo>1<\/span><\/mn><\/mjx-assistive-mml><\/mjx-container>\u4e0a\u7684\u72b6\u6001\u6982\u7387\u5206\u5e03\uff0c\u5373<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-math>P<\/span><\/mi>r<\/span><\/mi>(X<\/span><\/mi>t+1<\/span><\/sub><\/mi><\/span><\/mo>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u53ef\u4ee5\u88ab\u4e0a\u4e00\u65f6\u523b\u7684\u72b6\u6001\u6982\u7387\u5206\u5e03\uff0c\u5373<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-math>P<\/span><\/mi>r<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi>t<\/span><\/mi><\/msub>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u548c\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\u6240\u552f\u4e00\u786e\u5b9a\uff0c\u5e76\u6ee1\u8db3\u5173\u7cfb\uff1a<\/span><\/section>\n

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<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-over><\/mjx-c><\/mjx-mo><\/mjx-base><\/mjx-row><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-under><\/mjx-row><\/mjx-munder><\/mjx-box><\/mjx-munderover><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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<\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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\u8fd9\u91cc\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>i<\/span><\/mi>,<\/span><\/mo>j<\/span><\/mi>\u2208<\/sub><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u90fd\u662f<\/sub><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u4e2d\u7684\u4efb\u610f\u72b6\u6001\uff0c\u4e14<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-math>N<\/span><\/mi>=<\/span><\/mo>#<\/span><\/mi>(<\/sub><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mo>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u5373<\/sub><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u4e2d\u7684\u603b\u72b6\u6001\u6570\u3002<\/span><\/section>\n

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\u4e0b\u8868\u5c55\u793a\u7684\u662f\u4e09\u4e2a\u4e0d\u540c\u7684\u8f6c\u79fb\u6982\u7387\u77e9\u9635\uff0c\u4ee5\u53ca\u5b83\u4eec\u7684EI\u6570\u503c\uff1a<\/span><\/section>\n

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\u9a6c\u5c14\u79d1\u592b\u94fe\u793a\u4f8b<\/span><\/strong><\/section>\n

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\u8fd9\u4e09\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u72b6\u6001\u7a7a\u95f4\u90fd\u662f<\/span><\/sub><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mi><\/mrow>=<\/span><\/mo>{<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>2<\/span><\/mn>,<\/span><\/mo>3<\/span><\/mn>,<\/span><\/mo>4<\/span><\/mn>}<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u56e0\u6b64\u5b83\u4eec\u7684TPM\u7684\u5927\u5c0f\u90fd\u662f<\/span><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math>4<\/span><\/mn>\u00d7<\/span><\/mo>4<\/span><\/mn><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/section>\n

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4.2 \u9a6c\u5c14\u79d1\u592b\u94fe\u7684EI<\/span><\/strong><\/span><\/h2>\n

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\u5728\u9a6c\u5c14\u79d1\u592b\u94fe\u4e2d\uff0c\u4efb\u610f\u65f6\u523b\u7684\u72b6\u6001\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>X<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u90fd\u53ef\u4ee5\u770b\u4f5c\u662f\u539f\u56e0\uff0c\u800c\u4e0b\u4e00\u65f6\u523b\u7684\u72b6\u6001\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>X<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u5c31\u53ef\u4ee5\u770b\u4f5c\u662f\u7ed3\u679c\uff0c\u8fd9\u6837\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\u5c31\u662f\u5b83\u7684\u56e0\u679c\u673a\u5236\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6709\u6548\u4fe1\u606f\u7684\u5b9a\u4e49\u5957\u7528\u5230\u9a6c\u5c14\u79d1\u592b\u94fe\u4e0a\u6765\u3002<\/span><\/section>\n

<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-tstrut><\/mjx-mtd><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-tstrut><\/mjx-mtd><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-over><\/mjx-c><\/mjx-mo><\/mjx-base><\/mjx-row><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-under><\/mjx-row><\/mjx-munder><\/mjx-box><\/mjx-munderover><\/mjx-c><\/mjx-mi><\/mjx-over><\/mjx-c><\/mjx-mo><\/mjx-base><\/mjx-row><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-under><\/mjx-row><\/mjx-munder><\/mjx-box><\/mjx-munderover><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-tstrut><\/mjx-mtd><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-over><\/mjx-c><\/mjx-mo><\/mjx-base><\/mjx-row><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-under><\/mjx-row><\/mjx-munder><\/mjx-box><\/mjx-munderover><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-tstrut><\/mjx-mtd><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mi><\/mjx-over><\/mjx-c><\/mjx-mo><\/mjx-base><\/mjx-row><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-under><\/mjx-row><\/mjx-munder><\/mjx-box><\/mjx-munderover><\/mjx-c><\/mjx-mi><\/mjx-over><\/mjx-c><\/mjx-mo><\/mjx-base><\/mjx-row><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-under><\/mjx-row><\/mjx-munder><\/mjx-box><\/mjx-munderover><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-spacer><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-munderover><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-itable><\/mjx-table><\/mjx-mtable><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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\u5176\u4e2d<\/span><\/sub><\/span><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5206\u522b\u4e3a\u628at\u65f6\u523b\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>X<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u5e72\u9884\u4e3a\u5747\u5300\u5206\u5e03\u540e\uff0c\u524d\u540e\u4e24\u4e2a\u65f6\u523b\u7684\u72b6\u6001\u3002<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi>i<\/span><\/sub><\/mi>j<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u7b2ci\u4e2a\u72b6\u6001\u8f6c\u79fb\u5230\u7b2cj\u4e2a\u72b6\u6001\u7684\u8f6c\u79fb\u6982\u7387\u3002\u4ece\u8fd9\u4e2a\u5f0f\u5b50\uff0c\u4e0d\u96be\u770b\u51fa\uff0cEI\u4ec5\u4ec5\u662f\u6982\u7387\u8f6c\u79fb\u77e9\u9635<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>P<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u51fd\u6570\u3002<\/span><\/section>\n

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4.3 \u9a6c\u5c14\u79d1\u592b\u94feEI\u7684\u5411\u91cf\u5f62\u5f0f<\/span><\/strong><\/span><\/h2>\n

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\u6211\u4eec\u4e5f\u53ef\u4ee5\u5c06\u8f6c\u79fb\u6982\u7387\u77e9\u9635<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>P<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5199\u6210<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>N<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e2a\u884c\u5411\u91cf\u62fc\u63a5\u800c\u6210\u7684\u5f62\u5f0f\uff0c\u5373\uff1a<\/span><\/section>\n

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<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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\u5176\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u77e9\u9635<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>P<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u7b2c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>i<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e2a\u884c\u5411\u91cf\uff0c\u4e14\u6ee1\u8db3\u6761\u4ef6\u6982\u7387\u7684\u5f52\u4e00\u5316\u6761\u4ef6\uff1a<\/span><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math>|<\/span><\/mo>|<\/span><\/mo><\/mrow>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub>|<\/span><\/mo><\/mrow>|<\/span><\/mo><\/mrow>1<\/span><\/sub><\/mn><\/msub>=<\/span><\/mo>1<\/span><\/mn><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u91cc\u7684<\/span><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-math>|<\/span><\/mo>|<\/span><\/mo><\/mrow>\u22c5<\/span><\/mo>|<\/span><\/mo><\/mrow>|<\/span><\/mo>1<\/span><\/sub><\/mn><\/msub><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u5411\u91cf\u76841\u8303\u6570\u3002\u90a3\u4e48EI\u53ef\u4ee5\u5199\u6210\u5982\u4e0b\u7684\u5f62\u5f0f\uff1a<\/span><\/section>\n

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  (2)<\/span><\/section>\n

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\u5c06\u77e9\u9635\u6bcf\u5217\u6c42\u5747\u503c\uff0c\u53ef\u5f97\u5230\u5e73\u5747\u8f6c\u79fb\u5411\u91cf<\/span><\/sub><\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>D<\/span><\/mi><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>K<\/span><\/sub><\/span><\/mi>L<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u4fbf\u662f\u4e24\u4e2a\u5206\u5e03\u7684KL\u6563\u5ea6\u3002\u56e0\u6b64\uff0cEI\u662f\u8f6c\u79fb\u77e9\u9635\u6bcf\u4e2a\u884c\u8f6c\u79fb\u5411\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u4e0e\u5e73\u5747\u8f6c\u79fb\u5411\u91cf<\/span><\/sub><\/span><\/mi><\/mover><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u7684KL\u6563\u5ea6\u7684\u5747\u503c\u3002<\/span><\/section>\n

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\u9488\u5bf9\u4e0a\u9762\u6240\u5217\u7684\u4e09\u4e2a\u72b6\u6001\u8f6c\u79fb\u77e9\u9635\uff0c\u6211\u4eec\u53ef\u4ee5\u5206\u522b\u6c42\u51fa\u5b83\u4eec\u7684EI\u4e3a\uff1a2\u6bd4\u7279\u30011\u6bd4\u7279\u548c0\u6bd4\u7279\u3002\u7531\u6b64\u53ef\u89c1\uff0c\u5982\u679c\u8f6c\u79fb\u6982\u7387\u77e9\u9635\u4e2d\u51fa\u73b0\u66f4\u591a\u76840\u62161\uff0c\u4e5f\u5c31\u662f\u884c\u5411\u91cf\u591a\u662f\u72ec\u70ed\u5411\u91cf<\/span>\uff08\u4e5f\u53eb\u505aone-hot\u5411\u91cf\uff0c\u5373\u67d0\u4e00\u4e2a\u4f4d\u7f6e\u4e3a1\uff0c\u5176\u5b83\u4f4d\u7f6e\u4e3a0\u7684\u5411\u91cf\uff09<\/span>\uff0c\u5219EI\u503c\u5c31\u4f1a\u66f4\u5927\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u5728\u72b6\u6001\u8f6c\u79fb\u7684\u8fc7\u7a0b\u4e2d\uff0c\u4ece\u67d0\u4e00\u65f6\u523b\u5230\u4e0b\u4e00\u65f6\u523b\u7684\u8df3\u8f6c\u8d8a\u786e\u5b9a\uff0c\u5219EI\u503c\u5c31\u4f1a\u503e\u5411\u4e8e\u8d8a\u9ad8\u3002\u4f46\u662f\uff0c\u8fd9\u4e2a\u89c2\u5bdf\u5e76\u4e0d\u5341\u5206\u7cbe\u786e\uff0c\u66f4\u7cbe\u786e\u7684\u7ed3\u8bba\u7531\u540e\u9762\u7684\u5c0f\u8282\u7ed9\u51fa\u3002<\/span><\/section>\n

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4.4 \u5f52\u4e00\u5316<\/span><\/strong><\/span><\/h2>\n

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\u663e\u7136\uff0cEI\u7684\u5927\u5c0f\u548c\u72b6\u6001\u7a7a\u95f4\u5927\u5c0f\u6709\u5173\uff0c\u8fd9\u4e00\u6027\u8d28\u5728\u6211\u4eec\u6bd4\u8f83\u4e0d\u540c\u5c3a\u5ea6\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u65f6\u5019\u975e\u5e38\u4e0d\u65b9\u4fbf\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u5c3d\u53ef\u80fd\u4e0d\u53d7\u5c3a\u5ea6\u6548\u5e94\u5f71\u54cd\u7684\u56e0\u679c\u6548\u5e94\u5ea6\u91cf\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u6709\u6548\u4fe1\u606fEI\u505a\u4e00\u4e2a\u5f52\u4e00\u5316\u5904\u7406\uff0c\u5f97\u5230\u548c\u7cfb\u7edf\u5c3a\u5bf8\u65e0\u5173\u7684\u4e00\u4e2a\u91cf\u5316\u6307\u6807\u3002<\/span><\/section>\n

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\u6839\u636eErik Hoel\u548cTononi\u7b49\u4eba\u7684\u5de5\u4f5c\uff0c\u8981\u7528\u5747\u5300\u5206\u5e03\u5373\u6700\u5927\u71b5\u5206\u5e03\u4e0b\u7684\u71b5\u503c\uff0c\u5373<\/span><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>log<\/span><\/mi>\u2061<\/span><\/mo>N<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u6765\u505a\u5206\u6bcd\u5bf9EI\u8fdb\u884c\u5f52\u4e00\u5316\uff0c\u8fd9\u91cc\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>N<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u72b6\u6001\u7a7a\u95f4<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>X<\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u4e2d\u7684\u72b6\u6001\u7684\u6570\u91cf[2]\u3002\u90a3\u4e48\u5f52\u4e00\u5316\u540e\u7684EI\u4fbf\u7b49\u4e8e\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
<\/section>\n
<\/mi><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/section>\n
\u8fdb\u4e00\u6b65\u5b9a\u4e49\u5f52\u4e00\u5316\u6307\u6807\u4e5f\u79f0\u4e3a\u6709\u6548\u6027<\/span>\uff08effectiveness\uff09<\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u7136\u800c\uff0c\u5728\u5904\u7406\u8fde\u7eed\u72b6\u6001\u53d8\u91cf\u7684\u65f6\u5019\uff0c\u8fd9\u79cd\u4f7f\u7528\u72b6\u6001\u7a7a\u95f4\u4e2d\u72b6\u6001\u6570\u91cf\u7684\u5bf9\u6570\u503c\u8fdb\u884c\u5f52\u4e00\u5316\u7684\u5904\u7406\u65b9\u5f0f\u5e76\u4e0d\u662f\u975e\u5e38\u5408\u9002\uff0c\u56e0\u4e3a\u8fd9\u4e00\u72b6\u6001\u6570\u5f80\u5f80\u53d7\u5230\u53d8\u91cf\u7684\u7ef4\u5ea6\u548c\u5b9e\u6570\u5206\u8fa8\u7387\u7684\u5f71\u54cd\u3002<\/span><\/section>\n

<\/span><\/section>\n

4.5 \u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027<\/span><\/strong><\/span><\/h2>\n


<\/span><\/strong><\/h3>\n

4.5.1 EI\u7684\u5206\u89e3<\/span><\/strong><\/h3>\n

<\/span><\/section>\n
\u6839\u636e\u516c\u5f0f1\uff0c\u6211\u4eec\u53d1\u73b0\uff0cEI\u5b9e\u9645\u4e0a\u53ef\u4ee5\u88ab\u5206\u89e3\u4e3a\u4e24\u9879\uff0c\u5373\uff1a<\/span><\/section>\n

<\/span><\/section>\n

<\/p>\n


<\/span><\/section>\n
\u540c\u6837\uff0c\u5728\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u60c5\u666f\u4e0b\uff0cEI\u4e5f\u53ef\u4ee5\u505a\u8fd9\u6837\u7684\u5206\u89e3\uff1a<\/span><\/section>\n

<\/span><\/section>\n
 \uff08tow_terms\uff09<\/span><\/span><\/section>\n

<\/span><\/section>\n
\u5176\u4e2d\uff0c\u7b2c\u4e00\u9879\uff1a<\/sub><\/span>\u4e3a\u6bcf\u4e2a\u884c\u5411\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u7684\u8d1f\u71b5\u7684\u5e73\u5747\u503c\uff0c\u5b83\u523b\u753b\u4e86\u6574\u4e2a\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u77e9\u9635\u7684\u786e\u5b9a\u6027<\/span>\uff08determinism\uff09<\/span>\uff1b<\/span><\/section>\n

<\/span><\/section>\n
\u7b2c\u4e8c\u9879\uff1a<\/span><\/sub><\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u5e73\u5747\u884c\u5411\u91cf\u7684\u71b5\uff0c\u5176\u4e2d<\/span><\/sub><\/span><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u6240\u6709N\u4e2a\u884c\u5411\u91cf\u7684\u5e73\u5747\u884c\u5411\u91cf\uff0c\u5b83\u523b\u753b\u4e86\u6574\u4e2a\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u77e9\u9635\u7684\u975e\u7b80\u5e76\u6027\u6216\u975e\u9000\u5316\u6027<\/span> (non-degeneracy)<\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n

4.5.2 \u786e\u5b9a\u6027\u4e0e\u7b80\u5e76\u6027<\/span><\/strong><\/h3>\n

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\u7136\u800c\u4e0a\u8ff0\u5b9a\u4e49\u4e2d\u7684\u786e\u5b9a\u6027\u9879\u548c\u975e\u7b80\u5e76\u6027\u90fd\u662f\u8d1f\u6570\uff0c\u4e3a\u6b64\uff0c\u6211\u4eec\u91cd\u65b0\u5b9a\u4e49\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u8f6c\u79fb\u77e9\u9635P\u7684\u786e\u5b9a\u6027\u4e3a\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/p>\n

<\/mo><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/section>\n
\u8fd9\u4e00\u9879\u662f\u4e00\u4e2a\u5e73\u5747\u7684\u8d1f\u71b5\uff0c\u4e3a\u4e86\u9632\u6b62\u5176\u4e3a\u8d1f\u6570\uff0c\u6240\u4ee5\u52a0\u4e0a\u4e86<\/span><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>log<\/span><\/mi>\u2061<\/span><\/mo>N<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>[2]\u3002Determinism\u80fd\u523b\u753b\u6574\u4e2a\u8f6c\u79fb\u77e9\u9635\u7684\u786e\u5b9a\u6027\uff1a\u4e5f\u5c31\u662f\u8bf4\u5982\u679c\u6211\u4eec\u77e5\u9053\u4e86\u7cfb\u7edf\u5f53\u524d\u65f6\u523b\u6240\u5904\u7684\u72b6\u6001\uff0c\u5219\u6211\u4eec\u80fd\u591f\u63a8\u65ad\u51fa\u7cfb\u7edf\u5728\u4e0b\u4e00\u65f6\u523b\u6240\u5904\u7684\u72b6\u6001\u7684\u7a0b\u5ea6\u3002\u4e3a\u4ec0\u4e48\u8fd9\u4e48\u8bf4\u5462\uff1f\u8fd9\u662f\u56e0\u4e3a\u786e\u5b9a\u6027\u8fd9\u4e00\u9879\u662f\u6240\u6709\u884c\u5411\u91cf\u71b5\u7684\u5e73\u5747\u503c\uff0c\u518d\u53d6\u4e00\u4e2a\u8d1f\u53f7\u3002\u6211\u4eec\u77e5\u9053\uff0c\u5f53\u4e00\u4e2a\u5411\u91cf\u66f4\u9760\u8fd1\u5747\u5300\u5206\u5e03\u7684\u65f6\u5019\uff0c\u5b83\u7684\u71b5\u5c31\u8d8a\u5927\uff0c\u76f8\u53cd\uff0c\u5982\u679c\u4e00\u4e2a\u5411\u91cf\u8d8a\u9760\u8fd1\u4e00\u4e2a\u201c\u72ec\u70ed\u201d<\/span>\uff08one-hot\uff09<\/span>\u7684\u5411\u91cf\uff0c\u4e5f\u5c31\u662f\u8fd9\u4e2a\u5411\u91cf\u4e2d\u53ea\u6709\u4e00\u4e2a1\uff0c\u5176\u5b83\u5143\u7d20\u90fd\u662f0\uff0c\u90a3\u4e48\u5b83\u7684\u71b5\u5c31\u8d8a\u5c0f\u3002\u6211\u4eec\u77e5\u9053\uff0c\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u7684\u4e00\u4e2a\u884c\u5411\u91cf\u7684\u542b\u4e49\u5c31\u4ee3\u8868\u7cfb\u7edf\u4ece\u5f53\u524d\u72b6\u6001\u8f6c\u79fb\u5230\u5404\u4e2a\u4e0d\u540c\u72b6\u6001\u7684\u6982\u7387\u5927\u5c0f\u3002\u90a3\u4e48\uff0c\u5f53\u5e73\u5747\u7684\u884c\u5411\u91cf\u8d1f\u71b5\u5927\u7684\u65f6\u5019\uff0c\u4e5f\u5c31\u662f\u8fd9\u4e2a\u884c\u5411\u91cf\u7684\u67d0\u4e00\u4e2a\u5355\u5143\u6982\u7387\u4e3a1\uff0c\u5176\u5b83\u4e3a0\uff0c\u8fd9\u5c31\u610f\u5473\u7740\u7cfb\u7edf\u80fd\u591f\u786e\u5b9a\u5730\u8f6c\u79fb\u52301\u5bf9\u5e94\u7684\u72b6\u6001\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u6211\u4eec\u5b9a\u4e49\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u8f6c\u79fb\u77e9\u9635P\u7684\u7b80\u5e76\u6027\u4e3a\uff1a<\/span><\/section>\n

<\/section>\n

<\/p>\n

<\/mo><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/section>\n
\u8fd9\u4e00\u9879\u4e3a\u7b80\u5e76\u6027\u6216\u53eb\u9000\u5316\u6027\uff0c\u4e3a\u4e86\u9632\u6b62\u5176\u4e3a\u8d1f\u6570\uff0c\u6240\u4ee5\u52a0\u4e0a\u4e86<\/span><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>log<\/span><\/mi>\u2061<\/span><\/mo>N<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>[2]\u3002\u8fd9\u91cc\u7684\u201c\u7b80\u5e76\u6027\u201d\u7684\u542b\u4e49\u662f\uff1a\u5982\u679c\u77e5\u9053\u4e86\u7cfb\u7edf\u7684\u5f53\u524d\u72b6\u6001\uff0c\u80fd\u4e0d\u80fd\u53cd\u63a8\u7cfb\u7edf\u5728\u4e0a\u4e00\u65f6\u523b\u7684\u72b6\u6001\u7684\u80fd\u529b\uff0c\u5982\u679c\u53ef\u4ee5\u63a8\u65ad\uff0c\u5219\u8fd9\u4e2a\u9a6c\u5c14\u79d1\u592b\u77e9\u9635\u7684\u7b80\u5e76\u6027\u5c31\u4f1a\u6bd4\u8f83\u4f4e\uff0c\u4e5f\u5c31\u662f\u975e\u7b80\u5e76\u7684\uff1b\u800c\u5982\u679c\u5f88\u96be\u63a8\u65ad\uff0c\u5219\u9a6c\u5c14\u79d1\u592b\u77e9\u9635\u5c31\u662f\u7b80\u5e76\u7684\uff0c\u4e5f\u5373\u9000\u5316\u7684\u3002\u4e3a\u4ec0\u4e48\u201c\u7b80\u5e76\u6027\u201d\u53ef\u4ee5\u7528\u5e73\u5747\u884c\u5411\u91cf\u5206\u5e03\u7684\u8d1f\u71b5\u6765\u523b\u753b\u5462\uff1f\u8fd9\u662f\u56e0\u4e3a\uff0c\u9996\u5148\uff0c\u5f53\u6240\u6709\u7684P\u4e2d\u7684\u884c\u5411\u91cf\u90fd\u662f\u5f7c\u6b64\u72ec\u7acb\u7684\u72ec\u70ed\u5411\u91cf\uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u5e73\u5747\u5206\u5e03\u5c31\u4f1a\u975e\u5e38\u63a5\u8fd1\u4e8e\u4e00\u4e2a\u5747\u5300\u5206\u5e03\uff0c\u5373<\/span><\/sub><\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u4e2a\u65f6\u5019\uff0c\u5b83\u7684Shannon\u71b5\u6700\u5927\uff0c\u5373<\/span><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>log<\/span><\/mi>\u2061<\/span><\/mo>N<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u3002\u800c\u5728\u6b64\u65f6\uff0c\u8fd9\u4e2a\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u77e9\u9635\u662f\u4e00\u4e2a\u53ef\u9006\u77e9\u9635<\/span>\uff08\u7531\u5f7c\u6b64\u72ec\u7acb\u7684\u201c\u72ec\u70ed\u201d\u5411\u91cf\u5f62\u6210\u7684\u5168\u4f53\u5f7c\u6b64\u7ebf\u6027\u65e0\u5173\uff0c\u56e0\u6b64\u77e9\u9635\u6ee1\u79e9\uff0c\u56e0\u6b64\u662f\u53ef\u9006\u7684\uff09<\/span>\u3002\u8fd9\u4e5f\u5c31\u610f\u5473\u7740\uff0c\u6211\u4eec\u4ece\u7cfb\u7edf\u5f53\u524d\u7684\u72b6\u6001\uff0c\u662f\u53ef\u4ee5\u63a8\u65ad\u51fa\u7cfb\u7edf\u7684\u4e0a\u4e00\u65f6\u523b\u7684\u72b6\u6001\u7684\uff0c\u6240\u4ee5\u8fd9\u4e2a\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u77e9\u9635\u662f\u975e\u7b80\u5e76\u7684\uff0c\u8ba1\u7b97\u51fa\u7684\u7b80\u5e76\u5ea6\u6070\u6070\u4e5f\u4e3a0\uff1b<\/span><\/section>\n

<\/span><\/section>\n
\u5176\u6b21\uff0c\u5f53P\u4e2d\u7684\u884c\u5411\u91cf\u90fd\u662f\u76f8\u540c\u7684\u72ec\u70ed\u5411\u91cf\u7684\u65f6\u5019\uff0c\u5219\u5e73\u5747\u5411\u91cf\u4e5f\u662f\u4e00\u4e2a\u72ec\u70ed\u7684\u5411\u91cf\uff0c\u800c\u8fd9\u79cd\u5411\u91cf\u7684\u71b5\u662f\u6700\u5c0f\u7684\u3002\u5728\u6b64\u65f6\uff0c\u7531\u4e8e\u6240\u6709\u7684\u4e0a\u4e00\u65f6\u523b\u72b6\u6001\u90fd\u4f1a\u8f6c\u79fb\u5230\u884c\u5411\u91cf\u4e2d1\u5bf9\u5e94\u7684\u72b6\u6001\uff0c\u56e0\u6b64\u6211\u4eec\u4e5f\u5c31\u5f88\u96be\u63a8\u65ad\u51fa\u5f53\u524d\u8fd9\u4e2a\u72b6\u6001\u662f\u7531\u54ea\u4e00\u4e2a\u4e0a\u4e00\u6b65\u7684\u72b6\u6001\u8f6c\u79fb\u8fc7\u6765\u7684\u3002\u56e0\u6b64\uff0c\u8fd9\u79cd\u60c5\u5f62\u4e0b\u7684\u9a6c\u5c14\u79d1\u592b\u77e9\u9635\u662f\u7b80\u5e76\u7684<\/span>\uff08\u6216\u9000\u5316\u7684\uff09<\/span>\uff0c\u8ba1\u7b97\u51fa\u6765\u7684\u7b80\u5e76\u5ea6\u5219\u6070\u6070\u662f<\/span><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>log<\/span><\/mi>\u2061<\/span><\/mo>N<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5bf9\u4e8e\u66f4\u4e00\u822c\u7684\u60c5\u51b5\uff0c\u5982\u679cP\u4e2d\u7684\u884c\u5411\u91cf\u9760\u8fd1\u4e00\u4e2a\u5f7c\u6b64\u72ec\u7acb\u7684\u72ec\u70ed\u884c\u5411\u91cf\u6784\u6210\u7684\u77e9\u9635\uff0c\u5219P\u5c31\u8d8a\u975e\u7b80\u5e76\uff0c\u76f8\u53cd\uff0c\u5982\u679c\u884c\u5411\u91cf\u5f7c\u6b64\u76f8\u540c\u4e14\u9760\u8fd1\u540c\u4e00\u4e2a\u72ec\u70ed\u5411\u91cf\uff0c\u5219P\u5c31\u8d8a\u7b80\u5e76\u3002<\/span><\/section>\n


<\/span><\/h3>\n

4.5.3 \u4e3e\u4f8b<\/span><\/strong><\/h3>\n

<\/span><\/section>\n
\u4e0b\u9762\uff0c\u6211\u4eec\u4ee5\u4e09\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\u4e3a\u4f8b\uff0c\u6765\u8003\u5bdf\u5b83\u4eec\u7684\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027<\/span><\/section>\n

<\/section>\n

\u9a6c\u5c14\u79d1\u592b\u94fe\u793a\u4f8b<\/span><\/strong><\/p>\n

<\/p>\n


<\/span><\/section>\n
\u7b2c\u4e00\u4e2a\u8f6c\u79fb\u6982\u7387\u77e9\u9635\u662f\u4e00\u4e2a\u7f6e\u6362\u6392\u5217\u77e9\u9635<\/span>\uff08Permutation\uff09<\/span>\uff0c\u5b83\u662f\u53ef\u9006\u7684\uff0c\u56e0\u6b64\u786e\u5b9a\u6027\u6700\u9ad8\uff0c\u6ca1\u6709\u7b80\u5e76\u6027\uff0c\u56e0\u800cEI\u6700\u5927\uff1b\u7b2c\u4e8c\u4e2a\u77e9\u9635\u7684\u524d\u4e09\u4e2a\u72b6\u6001\u90fd\u4f1a\u4ee51\/3\u7684\u6982\u7387\u8df3\u8f6c\u5230\u5f7c\u6b64\uff0c\u56e0\u6b64\u786e\u5b9a\u6027\u7a0b\u5ea6\u6700\u4f4e\uff0c\u800c\u975e\u7b80\u5e76\uff0cEI\u662f0.81\uff1b\u7b2c\u4e09\u4e2a\u77e9\u9635\u867d\u7136\u4e5f\u662f\u786e\u5b9a\u6027\u7684\u77e9\u9635\uff0c\u56e0\u800c\u786e\u5b9a\u6027\u6700\u9ad8\uff0c\u4f46\u662f\u7531\u4e8e\u540e\u4e09\u4e2a\u72b6\u6001\u90fd\u8df3\u8f6c\u52301\uff0c\u56e0\u6b64\uff0c\u4ece1\u72b6\u6001\u4e0d\u80fd\u63a8\u77e5\u5b83\u6765\u81ea\u4e8e\u54ea\u4e2a\u72b6\u6001\uff0c\u56e0\u6b64\u7b80\u5e76\u6027\u6700\u9ad8\uff0c\u6700\u7ec8\u7684EI\u4e0e\u7b2c\u4e8c\u4e2a\u76f8\u540c\uff0c\u4ecd\u7136\u662f0.81\u3002<\/span><\/section>\n


<\/span><\/h3>\n

4.5.4 \u5f52\u4e00\u5316\u7684\u786e\u5b9a\u6027\u4e0e\u7b80\u5e76\u6027<\/span><\/strong><\/h3>\n

<\/span><\/section>\n
\u5728Erik Hoel\u7b49\u4eba\u7684\u539f\u59cb\u8bba\u6587\u4e2d[2]\uff0c\u4f5c\u8005\u4eec\u5b9a\u4e49\u7684\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027\u662f\u4ee5\u5f52\u4e00\u5316\u7684\u5f62\u5f0f\u5448\u73b0\u7684\uff0c\u4e5f\u5c31\u662f\u5c06\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027\u9664\u4ee5\u4e86\u4e00\u4e2a\u4e0e\u7cfb\u7edf\u5c3a\u5ea6\u6709\u5173\u7684\u91cf\u3002\u4e3a\u4e86\u533a\u5206\uff0c\u6211\u4eec\u5c06\u5f52\u4e00\u5316\u7684\u5bf9\u5e94\u91cf\u79f0\u4e3a\u786e\u5b9a\u6027\u7cfb\u6570\u548c\u7b80\u5e76\u6027\u7cfb\u6570\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5177\u4f53\u5730\uff0cErik Hoel\u7b49\u4eba\u5c06\u5f52\u4e00\u5316\u540e\u7684\u6709\u6548\u4fe1\u606f\uff0c\u5373Eff\u8fdb\u884c\u5206\u89e3\uff0c\u5206\u522b\u5bf9\u5e94\u786e\u5b9a\u6027\u7cfb\u6570<\/span>\uff08determinism coefficient\uff09<\/span>\u548c\u7b80\u5e76\u6027\u7cfb\u6570<\/span>\uff08degeneracy coefficient\uff09<\/span>\u3002<\/span><\/section>\n

<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>E<\/span><\/mi>f<\/span><\/mi>f<\/span><\/mi>=<\/span><\/mo>D<\/span><\/mi>e<\/span><\/mi>t<\/span><\/mi>e<\/span><\/mi>r<\/span><\/mi>m<\/span><\/mi>i<\/span><\/mi>n<\/span><\/mi>i<\/span><\/mi>s<\/span><\/mi>m<\/span><\/mi> <\/span><\/mtext>C<\/span><\/mi>o<\/span><\/mi>e<\/span><\/mi>f<\/span><\/mi>f<\/span><\/mi>i<\/span><\/mi>c<\/span><\/mi>i<\/span><\/mi>e<\/span><\/mi>n<\/span><\/mi>t<\/span><\/mi>\u2212<\/span><\/mo>D<\/span><\/mi>e<\/span><\/mi>g<\/span><\/mi>e<\/span><\/mi>n<\/span><\/mi>e<\/span><\/mi>r<\/span><\/mi>a<\/span><\/mi>c<\/span><\/mi>y<\/span><\/mi> <\/span><\/mtext>C<\/span><\/mi>o<\/span><\/mi>e<\/span><\/mi>f<\/span><\/mi>f<\/span><\/mi>i<\/span><\/mi>c<\/span><\/mi>i<\/span><\/mi>e<\/span><\/mi>n<\/span><\/mi>t<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/section>\n
\u8fd9\u4e24\u9879\u7684\u5b9a\u4e49\u5206\u522b\u662f\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-tstrut><\/mjx-mtd><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-tstrut><\/mjx-mtd><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-base><\/mjx-row><\/mjx-c><\/mjx-mi><\/mjx-under><\/mjx-row><\/mjx-munder><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-texatom><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-itable><\/mjx-table><\/mjx-mtable><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mtd><\/mi><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/p>\n


<\/span><\/section>\n
\u603b\u4e4b\uff0c\u786e\u5b9a\u6027\u6307\u7684\u662f\uff0c\u5df2\u77e5\u5f53\u524d\u65f6\u523b\u72b6\u6001\u6982\u7387\u5206\u5e03\uff0c\u5bf9\u672a\u6765\u53ef\u80fd\u72b6\u6001\u7684\u5224\u65ad\u6709\u591a\u5927\u7684\u628a\u63e1\uff1b\u800c\u7b80\u5e76\u6027\u6307\u7684\u662f\uff0c\u5df2\u77e5\u5f53\u524d\u7684\u72b6\u6001\uff0c\u8ffd\u6eaf\u5386\u53f2\uff0c\u6211\u4eec\u80fd\u6709\u591a\u5927\u786e\u5b9a\u6027\u505a\u51fa\u5224\u65ad\u3002\u5982\u679c\u6709\u72b6\u6001\u5728\u52a8\u529b\u5b66\u8fc7\u7a0b\u4e2d\u53d1\u751f\u7b80\u5e76\uff0c\u6211\u4eec\u56de\u6eaf\u5386\u53f2\u65f6\u80fd\u8fd0\u7528\u7684\u4fe1\u606f\u5c31\u4f1a\u53d8\u5c11\u3002\u5f53\u4e00\u4e2a\u7cfb\u7edf\u80cc\u540e\u7684\u52a8\u529b\u5b66\u786e\u5b9a\u6027\u9ad8\uff0c\u540c\u65f6\u7b80\u5e76\u6027\u4f4e\u65f6\uff0c\u8bf4\u660e\u8fd9\u662f\u4e00\u4e2a\u5177\u6709\u660e\u663e\u56e0\u679c\u6548\u5e94\u7684\u52a8\u529b\u5b66\u3002<\/span><\/section>\n

<\/span><\/section>\n

4.6 EI\u7684\u51fd\u6570\u6027\u8d28<\/span><\/strong><\/span><\/h2>\n

<\/span><\/section>\n
\u7531\u516c\u5f0f2\u53ef\u4ee5\u770b\u51fa\uff0c\u5728\u6982\u7387\u8f6c\u79fb\u77e9\u9635P\u4e0a\uff0cEI\u662f\u5173\u4e8e\u77e9\u9635\u4e2d\u6bcf\u4e00\u4e2a\u5143\u7d20<\/span>\uff08\u4ece\u67d0\u4e00\u72b6\u6001\u5230\u53e6\u4e00\u72b6\u6001\u7684\u6761\u4ef6\u6982\u7387\uff09<\/span>\u7684\u51fd\u6570\uff0c\u4e8e\u662f\u6211\u4eec\u81ea\u7136\u4f1a\u95ee\uff1a\u8fd9\u6837\u4e00\u4e2a\u51fd\u6570\u5177\u6709\u54ea\u4e9b\u6570\u5b66\u6027\u8d28\uff1f\u5982\u5b83\u6709\u6ca1\u6709\u6781\u503c\u70b9\uff1f\u6781\u503c\u70b9\u5728\u54ea\u91cc\uff1f\u51f8\u6027\u5982\u4f55\uff1f\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u53c8\u662f\u591a\u5c11\uff1f<\/span><\/section>\n

<\/span><\/section>\n

4.6.1 \u5b9a\u4e49\u57df<\/span><\/strong><\/h3>\n

<\/span><\/section>\n
\u5728\u79bb\u6563\u72b6\u6001\u548c\u79bb\u6563\u65f6\u95f4\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u4e0a\uff0cEI\u7684\u5b9a\u4e49\u57df\u663e\u7136\u662f\u6982\u7387\u8f6c\u79fb\u77e9\u9635P\u3002P\u662f\u4e00\u4e2a\u7531<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>N<\/span><\/mi>\u00d7<\/span><\/mo>N<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e2a\u5143\u7d20\u6784\u6210\u7684\u77e9\u9635\uff0c\u5176\u4e2d\u6bcf\u4e00\u4e2a\u5143\u7d20<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-math>p<\/span><\/mi>i<\/span><\/sub><\/mi>j<\/span><\/sub><\/mi><\/mrow><\/msub>\u2208<\/span><\/mo>[<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo>1<\/span><\/mn>]<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4ee3\u8868\u4e00\u4e2a\u6982\u7387\u503c\uff0c\u540c\u65f6\u5bf9\u4e8e\u4efb\u610f\u7684\u884c\uff0c\u8fd9\u7ec4\u6982\u7387\u503c\u9700\u8981\u6ee1\u8db3\u5f52\u4e00\u5316\u6761\u4ef6\uff0c\u4e5f\u5c31\u662f\u5bf9\u4e8e\u4efb\u610f\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>\u2200<\/span><\/mi>i<\/span><\/sub><\/mi>\u2208<\/span><\/mo>[<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>N<\/span><\/mi>]<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>:<\/span><\/section>\n

<\/span><\/section>\n
 \uff083\uff09<\/span><\/section>\n

<\/span><\/section>\n
\u56e0\u6b64EI\u7684\u5b9a\u4e49\u57df\uff0c\u4e5f\u5c31\u662fP\u7684\u53ef\u80fd\u7a7a\u95f4\u5e76\u4e0d\u662f\u5168\u90e8<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>N<\/span><\/mi>\u00d7<\/span><\/mo>N<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u7684\u5b9e\u6570\u7a7a\u95f4<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math>R<\/span><\/mi><\/mrow><\/mi><\/msup><\/mrow><\/msup><\/mjx-assistive-mml><\/mjx-container>N<\/span><\/sup><\/mi><\/msup><\/mrow><\/msup><\/mjx-assistive-mml><\/mjx-container><\/mn><\/msup><\/mrow><\/msup><\/mjx-assistive-mml><\/mjx-container>2<\/sup><\/span><\/sup><\/span><\/mn><\/msup><\/mrow><\/msup><\/mjx-assistive-mml><\/mjx-container><\/mn><\/msup><\/mrow><\/msup><\/mjx-assistive-mml><\/mjx-container><\/mn><\/msup><\/mrow><\/msup><\/mjx-assistive-mml><\/mjx-container>\uff0c\u7531\u4e8e\u5f52\u4e00\u5316\u6761\u4ef63\u7684\u5b58\u5728\uff0c\u4f7f\u5f97\u8be5\u5b9a\u4e49\u57df\u6210\u4e3a\u4e00\u4e2a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>N<\/span><\/mi>\u00d7<\/span><\/mo>N<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u5b9e\u6570\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u5b50\u7a7a\u95f4\u3002\u5982\u4f55\u8868\u8fbe\u8fd9\u4e2a\u5b50\u7a7a\u95f4\u5462\uff1f<\/span><\/section>\n

<\/span><\/section>\n
\u9996\u5148\uff0c\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u884c\u5411\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u6765\u8bf4\uff0c\u5b83\u7684\u53d6\u503c\u8303\u56f4\u7a7a\u95f4\u4e3aN\u7ef4\u5b9e\u6570\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u8d85\u6b63\u591a\u9762\u4f53\u3002\u4f8b\u5982\uff0c\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math>N<\/span><\/mi>=<\/span><\/mo>2<\/span><\/mn><\/mjx-assistive-mml><\/mjx-container>\u7684\u65f6\u5019\uff0c\u8be5\u7a7a\u95f4\u4e3a\u4e00\u6761\u76f4\u7ebf\uff1a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-math>p<\/span><\/mi><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>i<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>1<\/span><\/sub><\/span><\/mn><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msub>+<\/span><\/mo>p<\/span><\/mi><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>i<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>2<\/span><\/sub><\/span><\/mn><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msub>=<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>\u2200<\/span><\/mi>i<\/span><\/sub><\/mi>\u2208<\/span><\/mo>{<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>2<\/span><\/mn>}<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u3002\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math>N<\/span><\/mi>=<\/span><\/mo>3<\/span><\/mn><\/mjx-assistive-mml><\/mjx-container>\u7684\u65f6\u5019\uff0c\u8be5\u7a7a\u95f4\u4e3a\u4e00\u5f20\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u5e73\u9762\uff1a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-math>p<\/span><\/mi><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>i<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>1<\/span><\/sub><\/span><\/mn><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msub>+<\/span><\/mo>p<\/span><\/mi><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>i<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>2<\/span><\/sub><\/span><\/mn><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msub>+<\/span><\/mo>p<\/span><\/mi><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>i<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>3<\/span><\/sub><\/span><\/mn><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msub>=<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>\u2200<\/span><\/mi>i<\/span><\/sub><\/mi>\u2208<\/span><\/mo>{<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>2<\/span><\/mn>,<\/span><\/mo>3<\/span><\/mn>}<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u3002\u8fd9\u4e24\u4e2a\u7a7a\u95f4\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/span><\/section>\n

<\/span><\/section>\n

<\/p>\n


<\/span><\/section>\n
\u5728\u4e00\u822c\u60c5\u51b5\uff0c\u6211\u4eec\u5c06N\u7ef4\u7a7a\u95f4\u4e0b\u7684\u884c\u5411\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u7684\u53d6\u503c\u8303\u56f4\u7a7a\u95f4\u5b9a\u4e49\u4e3a<\/sub><\/span>\uff0c\u5219N\u4e2a\u8fd9\u6837\u7684\u7a7a\u95f4\u7684\u7b1b\u5361\u5c14\u79ef\u5373\u4e3aEI\u7684\u5b9a\u4e49\u57df\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>D<\/span><\/mi>o<\/span><\/mi>m<\/span><\/mi>(<\/span><\/mo>E<\/span><\/mi>I<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>\u0394<\/span><\/mi>\u00d7<\/span><\/mo>\u0394<\/span><\/mi>\u22ef<\/span><\/mo>\u00d7<\/span><\/mo>\u0394<\/span><\/mi>=<\/span><\/mo>\u0394<\/span><\/mi>N<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n


<\/span><\/h3>\n

4.6.2 \u4e00\u9636\u5bfc\u6570\u53ca\u6781\u503c\u70b9<\/span><\/strong><\/h3>\n

<\/span><\/section>\n
\u5bf9\u516c\u5f0f2\u6c42<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>p<\/span><\/mi>i<\/span><\/sub><\/mi>j<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u7684\u4e00\u9636\u5bfc\u6570\uff0c\u5e76\u6ce8\u610f\u5230\u5f52\u4e00\u5316\u6761\u4ef6<\/span><\/sub><\/span><\/mn><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5219\u5c31\u53ef\u4ee5\u5f97\u5230\uff1a<\/span><\/section>\n

<\/span><\/section>\n
\uff083\uff09<\/span><\/section>\n
\u5176\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi>i<\/span><\/sub><\/mi>j<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793aP\u4e2d\u7b2ci\u884c\u7b2cj\u5217\u7684\u6761\u4ef6\u6982\u7387\uff0c\u56e0\u4e3aP\u6bcf\u4e00\u884c\u6709\u5f52\u4e00\u5316\u7ea6\u675f\u6761\u4ef62\uff0c\u6240\u4ee5EI\u51fd\u6570\u672c\u8eab\u6709<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>N<\/span><\/mi>(<\/span><\/mo>N<\/span><\/mi>\u2212<\/span><\/mo>1<\/span><\/mn>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e2a\u81ea\u7531\u53d8\u5143\uff0c\u6211\u4eec\u53ef\u4ee5\u53d6<\/span><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>1<\/span><\/mn>\u2264<\/span><\/mo>i<\/span><\/mi>\u2264<\/span><\/mo>N<\/span><\/mi>,<\/span><\/mo>1<\/span><\/mn>\u2264<\/span><\/mo>j<\/span><\/mi>\u2264<\/span><\/mo>N<\/span><\/mi>\u2212<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>i<\/span><\/sub><\/span><\/mi>N<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u7b2ci\u884c\u7b2cN\u5217\u7684\u6761\u4ef6\u6982\u7387\uff0c<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5219\u5206\u522b\u8868\u793a\u7b2cj\u5217\u548c\u7b2cN\u5217\u6761\u4ef6\u6982\u7387\u7684\u5747\u503c\u3002\u4e0d\u96be\u770b\u51fa\uff0c\u8be5\u5bfc\u6570\u6709\u5b9a\u4e49\u7684\u524d\u63d0\u662f\u5bf9\u4e8e\u9009\u5b9a\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>i<\/span><\/mi>,<\/span><\/mo>j<\/span><\/mi>\u2208<\/span><\/mo>[<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>N<\/span><\/mi>]<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/sub><\/mi><\/mfrac><\/mjx-assistive-mml><\/mjx-container>\u90fd\u5927\u4e8e0\uff0c\u53ea\u6709\u6ee1\u8db3\u8fd9\u4e2a\u6761\u4ef6\uff0c\u5219EI\u5728<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>p<\/span><\/mi>i<\/span><\/mi>j<\/span><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u9644\u8fd1\u662f\u53ef\u5bfc\u7684\u3002\u5426\u5219\uff0c\u5982\u679c\u6709\u4e00\u9879\u4e3a0\uff0c\u5219\u5bfc\u6570\u4e0d\u5b58\u5728\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4ee4\u5f0f3\u7b49\u4e8e0\uff0c\u53ef\u4ee5\u6c42\u5f97\u6781\u503c\u70b9\uff1a\u5373\u5bf9\u4e8e\u4efb\u610f\u7684<\/span><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>1<\/span><\/mn>\u2264<\/span><\/mo>i<\/span><\/mi>\u2264<\/span><\/mo>N<\/span><\/mi>,<\/span><\/mo>1<\/span><\/mn>\u2264<\/span><\/mo>j<\/span><\/mi>\u2264<\/span><\/mo>N<\/span><\/mi>\u2212<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u90fd\u6709\u4e0b\u5f0f\u7684\u6210\u7acb\uff0c<\/span><\/section>\n

<\/span><\/section>\n

<\/p>\n


<\/span><\/section>\n
\u4e0d\u96be\u8ba1\u7b97\u51fa\uff0c\u6b64\u65f6<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>E<\/span><\/mi>I<\/span><\/mi>=<\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5373EI\u8fbe\u5230\u4e86\u6781\u503c\u70b9\u3002\u6839\u636eEI\u7684\u4e8c\u9636\u5bfc\u6570\u4e0d\u96be\u5224\u65ad\u51fa\uff0c\u8fd9\u662f\u6781\u5c0f\u503c\u70b9\u3002\u6362\u4e2a\u89d2\u5ea6\u6765\u770b\u8fd9\u4e2a\u516c\u5f0f\uff0c\u8fd9\u610f\u5473\u7740EI\u7684\u6781\u5c0f\u503c\u70b9\u6709\u5f88\u591a\u4e2a\uff0c\u53ea\u8981\u8f6c\u79fb\u6982\u7387\u77e9\u9635\u6240\u6709\u884c\u5411\u91cf\u5b8c\u5168\u4e00\u81f4\uff0c\u65e0\u8bba\u8be5\u884c\u5411\u91cf\u672c\u8eab\u662f\u600e\u6837\u7684\u5206\u5e03\uff0cEI\u90fd\u4f1a\u7b49\u4e8e0\u3002<\/span><\/section>\n

<\/span><\/section>\n

4.6.3 \u4e8c\u9636\u5bfc\u6570\u4e0e\u51f8\u6027<\/span><\/strong><\/h3>\n

<\/span><\/section>\n
\u8fdb\u4e00\u6b65\u5730\uff0c\u4e3a\u4e86\u6c42\u5f97EI\u51fd\u6570\u7684\u51f8\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u6c42\u51faEI\u8fd9\u4e2a\u51fd\u6570\u7684\u4e8c\u9636\u5bfc\u6570<\/sub>\uff0c\u5176\u4e2d<\/span><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>1<\/span><\/mn>\u2264<\/span><\/mo>s<\/span><\/mi>\u2264<\/span><\/mo>N<\/span><\/mi>,<\/span><\/mo>1<\/span><\/mn>\u2264<\/span><\/mo>t<\/span><\/mi>\u2264<\/span><\/mo>N<\/span><\/mi>\u2212<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u9996\u5148\u6211\u4eec\u9700\u8981\u5f15\u5165\u4e00\u4e2a\u51fd\u6570\u7b26\u53f7<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b4<\/span><\/mi>i<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>j<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-tstrut><\/mjx-mtd><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-c><\/mjx-mn><\/mjx-tstrut><\/mjx-mtd><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-itable><\/mjx-table><\/mjx-mtable><\/mjx-mo><\/mjx-mrow><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
<\/section>\n
<\/mo><\/mtd><\/mtr><\/mtable><\/mo><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/section>\n
\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u6765\u63a8\u5bfcEI\u7684\u4e8c\u9636\u5bfc\u6570\uff0c\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>i<\/span><\/mi>=<\/span><\/mo>s<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\uff0c<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-tstrut><\/mjx-mtd><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-tstrut><\/mjx-mtd><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-nstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-spacer><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-munderover><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-spacer><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-munderover><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-tstrut><\/mjx-mtd><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-nstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-munder><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-munder><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-itable><\/mjx-table><\/mjx-mtable><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/msup><\/mrow><\/mfrac><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/p>\n

<\/mo><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/section>\n
\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>i<\/span><\/mi>\u2260<\/span><\/mo>s<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\uff0c<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/msup><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/p>\n

<\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
\u7efc\u4e0a\uff0cEI\u7684\u4e8c\u9636\u5bfc\u6570\u4e3a\uff0c<\/span><\/section>\n

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<\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/msup><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/p>\n

<\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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\u5e76\u4e14\uff0c\u4e8c\u9636\u5bfc\u6570\u5728<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>i<\/span><\/mi>=<\/span><\/mo>s<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u65f6\u5019\u4e3a\u6b63\uff0c\u5728<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>i<\/span><\/mi>\u2260<\/span><\/mo>s<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\u4e3a\u8d1f\u3002\u56e0\u6b64EI\u65e2\u4e0d\u662f\u51f8\u7684\u4e5f\u4e0d\u662f\u51f9\u7684\u3002<\/span><\/section>\n


<\/span><\/h3>\n

4.6.4 \u6700\u5c0f\u503c<\/span><\/strong><\/h3>\n

<\/span><\/section>\n
\u524d\u9762\u5df2\u7ecf\u6839\u636eEI\u7684\u4e00\u9636\u5bfc\u6570\u8ba8\u8bba\u4e86\u5b83\u7684\u6781\u503c\u95ee\u9898\u3002\u5373EI\u4f1a\u5728\u6240\u6709\u884c\u5411\u91cf\u90fd\u662f\u540c\u4e00\u4e2a\u5411\u91cf\u7684\u65f6\u5019\u8fbe\u5230\u6781\u5c0f\u503c0\u3002\u90a3\u4e48\uff0c\u8fd9\u4e2a\u6781\u5c0f\u503c\u662f\u4e0d\u662f\u6700\u5c0f\u7684\u5462\uff1f<\/span><\/section>\n

<\/span><\/section>\n
\u6211\u4eec\u77e5\u9053\uff0c\u6839\u636e\u516c\u5f0f2\uff0cEI\u672c\u8d28\u4e0a\u662f\u4e00\u79cdKL\u6563\u5ea6\uff0c\u800cKL\u6563\u5ea6\u90fd\u662f\u975e\u8d1f\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>E<\/span><\/mi>I<\/span><\/mi>\u2265<\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
\u8fd9\u4e2a\u4e0d\u7b49\u5f0f\u7684\u7b49\u53f7\u5728<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u5bf9\u6240\u6709\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>i<\/span><\/mi>,<\/span><\/mo>j<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u90fd\u6210\u7acb\u7684\u65f6\u5019\u80fd\u591f\u53d6\u5230\u3002\u56e0\u6b64\uff0c0\u662fEI\u7684\u6700\u5c0f\u503c\uff0c\u4e14<\/sub>\u662f\u5b83\u7684\u6700\u5c0f\u503c\u70b9\uff0c\u5373\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>E<\/span><\/mi>I<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>m<\/span><\/sub><\/span><\/mi>i<\/span><\/sub><\/span><\/mi>n<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub>=<\/span><\/mo>0.<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n


<\/span><\/h3>\n

4.6.5 \u6700\u5927\u503c<\/span><\/strong><\/h3>\n

<\/span><\/section>\n
\u901a\u8fc7\u524d\u9762\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027\u7ae0\u8282\u7684\u8ba8\u8bba\uff0c\u6211\u4eec\u77e5\u9053EI\u53ef\u4ee5\u62c6\u6210\u4e24\u90e8\u5206\uff0c<\/span><\/section>\n

<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
<\/section>\n
<\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/section>\n
\u5176\u4e2d\u71b5\u7684\u5b9a\u4e49\u662f<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u5206\u5f00\u6765\u770b\uff0c\u524d\u4e00\u9879\u5f0f\u5b50\u6700\u5927\u503c\u4e3a0\uff0c\u5373\uff1a<\/span><\/section>\n

<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
<\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u2212<\/span><\/mo>H<\/span><\/mi>(<\/span><\/mo>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo>\u2264<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/section>\n
\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u6ca1\u6709\u4e0d\u786e\u5b9a\u6027\u7684\u72ec\u70ed\u5411\u91cf\u65f6\uff0c\u8be5\u5f0f\u5b50\u7684\u7b49\u53f7\u6210\u7acb\u3002\u6240\u4ee5\uff0c\u5f53\u5bf9\u6240\u6709\u7684i\u90fd\u6709<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>P<\/span><\/mi>i<\/span><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u72ec\u70ed\u53d8\u91cf\u65f6\uff0c\u6709<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u2212<\/span><\/mo>\u27e8<\/span><\/mo>H<\/span><\/mi>(<\/span><\/mo>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo>\u27e9<\/span><\/mo>=<\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/section>\n
\u6210\u7acb\u3002\u53e6\u4e00\u8fb9\uff0cP\u4e2d\u6240\u6709\u884c\u5411\u91cf\u7684\u5e73\u5747\u5411\u91cf\u7684\u71b5\u4e5f\u6709\u4e00\u4e2a\u4e0d\u7b49\u5f0f\u6210\u7acb\uff0c<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/p>\n

<\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/section>\n
\u5176\u4e2d\u7b49\u4e8e\u53f7\u5728\u6ee1\u8db3 <\/sub>\u6761\u4ef6\u65f6\u6210\u7acb\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>E<\/span><\/mi>I<\/span><\/mi>\u2264<\/span><\/mo>0<\/span><\/mn>+<\/span><\/mo>log<\/span><\/mi>\u2061<\/span><\/mo>N<\/span><\/mi>=<\/span><\/mo>log<\/span><\/mi>\u2061<\/span><\/mo>N<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/section>\n
\u5f53\u8fd9\u4e24\u4e2a\u5f0f\u5b50\u7684\u7b49\u53f7\u540c\u65f6\u6210\u7acb\u65f6\uff0c\u5373<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u72ec\u70ed\u5411\u91cf\uff0c\u540c\u65f6<\/sub>\u4e3a\u5747\u5300\u5206\u5e03\u65f6<\/span>\uff08\u6b64\u65f6\u5fc5\u7136\u8981\u6c42<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>P<\/span><\/mi>i<\/span><\/sub><\/span><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u5f7c\u6b64\u5782\u76f4\uff0c\u4e5f\u5c31\u662fP\u662f\u4e00\u4e2a\u6392\u5217\u7f6e\u6362\u77e9\u9635\uff09<\/span>\uff0cEI\u4f1a\u8fbe\u5230\u6700\u5927\u503c\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>E<\/span><\/mi>I<\/span><\/mi>m<\/span><\/sub><\/mi>a<\/span><\/sub><\/mi>x<\/span><\/sub><\/mi><\/mrow><\/msub>=<\/span><\/mo>log<\/span><\/mi>\u2061<\/span><\/mo>N<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

4.7 \u6700\u7b80\u9a6c\u5c14\u79d1\u592b\u94fe\u4e0b\u7684\u89e3\u6790\u89e3<\/span><\/strong><\/span><\/h2>\n

<\/span><\/section>\n
\u6211\u4eec\u8003\u8651\u4e00\u4e2a\u6700\u7b80\u5355\u76842*2\u9a6c\u5c14\u79d1\u592b\u94fe\u77e9\u9635\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-tstrut><\/mjx-mtd><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-tstrut><\/mjx-mtd><\/mjx-c><\/mjx-mi><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-itable><\/mjx-table><\/mjx-mtable><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
<\/section>\n
<\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

<\/section>\n
\u5176\u4e2d <\/span><\/mjx-c><\/mjx-mi><\/mjx-math>p<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container> \u548c <\/span><\/mjx-c><\/mjx-mi><\/mjx-math>q<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container> \u4e3a\u53d6\u503c <\/span><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-math>[<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo>1<\/span><\/mn>]<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container> \u7684\u53c2\u6570\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8fd9\u4e2a\u53c2\u6570\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>p<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>q<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u8f6c\u79fb\u6982\u7387\u77e9\u9635\u7684EI\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u89e3\u6790\u89e3\u8ba1\u7b97\uff1a<\/span><\/section>\n

<\/span><\/section>\n

<\/p>\n


<\/span><\/section>\n
\u4e0b\u56fe\u5c55\u793a\u4e86\u4e0d\u540c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>p<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container> \u548c <\/span><\/mjx-c><\/mjx-mi><\/mjx-math>q<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u53d6\u503c\u7684 EI \u7684\u53d8\u5316\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u7531\u8fd9\u5f20\u56fe\u4e0d\u96be\u770b\u51fa\uff0c\u5f53p+q=1\u7684\u65f6\u5019\uff0c\u4e5f\u5c31\u662f\u6240\u6709\u884c\u5411\u91cf\u90fd\u76f8\u540c\u7684\u60c5\u5f62\uff0cEI\u53d6\u5f97\u6700\u5c0f\u503c0\u3002\u5426\u5219\uff0c\u968f\u7740p,q\u6cbf\u7740\u5782\u76f4\u4e8ep+q=1\u7684\u65b9\u5411\u589e\u5927\uff0cEI\u5f00\u59cb\u53d8\u5927\uff0c\u800c\u6700\u5927\u503c\u4e3a1.<\/span><\/section>\n


<\/span><\/h2>\n

4.8 \u56e0\u679c\u6d8c\u73b0<\/span><\/strong><\/span><\/h2>\n

<\/span><\/section>\n
\u6709\u4e86\u6709\u6548\u4fe1\u606f\u8fd9\u4e00\u5ea6\u91cf\u6307\u6807\u540e\uff0c\u6211\u4eec\u4fbf\u53ef\u4ee5\u8ba8\u8bba\u9a6c\u5c14\u79d1\u592b\u94fe\u4e0a\u7684\u56e0\u679c\u6d8c\u73b0\u4e86\u3002\u5bf9\u4e8e\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u94fe\uff0c\u89c2\u5bdf\u8005\u53ef\u4ee5\u5efa\u7acb\u591a\u5c3a\u5ea6\u89c6\u89d2\u53bb\u89c2\u6d4b\uff0c\u533a\u5206\u51fa\u5fae\u89c2\u548c\u5b8f\u89c2\u3002\u9996\u5148\uff0c\u539f\u59cb\u7684\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635P\u5373\u5b9a\u4e49\u4e86\u5fae\u89c2\u52a8\u529b\u5b66\uff1b\u5176\u6b21\uff0c\u7ecf\u8fc7\u5bf9\u5fae\u89c2\u6001\u7684\u7c97\u7c92\u5316\u6620\u5c04<\/span>\uff08coarse-graining\uff09<\/span>\u540e<\/span>\uff08\u901a\u5e38\u53cd\u6620\u4e3a\u5bf9\u5fae\u89c2\u72b6\u6001\u7684\u5206\u7ec4\uff09<\/span>\uff0c\u89c2\u5bdf\u8005\u53ef\u4ee5\u5f97\u5230\u5bf9\u5e94\u7684\u5b8f\u89c2\u72b6\u6001<\/span>\uff08\u5373\u5206\u7ec4\uff09<\/span>\uff0c\u8fd9\u4e9b\u5b8f\u89c2\u72b6\u6001\u5f7c\u6b64\u4e4b\u95f4\u7684\u6982\u7387\u8f6c\u79fb\u53ef\u4ee5\u7528\u5b8f\u89c2\u7684\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635P’\u6765\u523b\u753b\u3002\u5bf9\u4e24\u4e2a\u52a8\u529b\u5b66\u5206\u522b\u53ef\u4ee5\u8ba1\u7b97EI\uff0c\u5982\u679c\u5b8f\u89c2\u7684EI\u5927\u4e8e\u5fae\u89c2EI\uff0c\u6211\u4eec\u8bf4\u8be5\u7cfb\u7edf\u53d1\u751f\u4e86\u56e0\u679c\u6d8c\u73b0\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u53ef\u4ee5\u5b9a\u4e49\u4e00\u4e2a\u65b0\u7684\u6307\u6807\u76f4\u63a5\u5ea6\u91cf\u56e0\u679c\u6d8c\u73b0\u7684\u7a0b\u5ea6\uff1a<\/span><\/section>\n

<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
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\u8fd9\u91cc<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>P<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u5fae\u89c2\u72b6\u6001\u7684\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635\uff0c\u7ef4\u5ea6\u4e3a\uff1a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>N<\/span><\/mi>\u00d7<\/span><\/mo>N<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u91ccN\u4e3a\u5fae\u89c2\u7684\u72b6\u6001\u6570\uff1b\u800c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-math>P<\/span><\/mi>\u2032<\/span><\/mo><\/msup><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u5bf9<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>P<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u505a\u7c97\u7c92\u5316\u64cd\u4f5c\u4e4b\u540e\u5f97\u5230\u7684\u5b8f\u89c2\u6001\u7684\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635\uff0c\u7ef4\u5ea6\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>M<\/span><\/mi>\u00d7<\/span><\/mo>M<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5176\u4e2d<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>M<\/span><\/mi><<\/span><\/mo>N<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u5b8f\u89c2\u72b6\u6001\u6570\u3002<\/span><\/section>\n

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\u5173\u4e8e\u5982\u4f55\u5bf9\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u5b9e\u65bd\u7c97\u7c92\u5316\u7684\u65b9\u6cd5\uff0c\u5f80\u5f80\u4f53\u73b0\u4e3a\u4e24\u6b65\uff1a1\u3001\u5bf9\u5fae\u89c2\u72b6\u6001\u505a\u5f52\u5e76\uff0c\u5c06N\u4e2a\u5fae\u89c2\u6001\uff0c\u5f52\u5e76\u4e3aM\u4e2a\u5b8f\u89c2\u6001\uff1b2\u3001\u5bf9\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u77e9\u9635\u505a\u7ea6\u7b80\u3002\u5173\u4e8e\u5177\u4f53\u7684\u7c97\u7c92\u5316\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u65b9\u6cd5\uff0c\u8bf7\u53c2\u8003\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u7c97\u7c92\u5316\u3002<\/span><\/section>\n

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\u5373\u5b58\u5728\u77400.19\u6bd4\u7279\u7684\u56e0\u679c\u6d8c\u73b0\u3002<\/span><\/section>\n

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\u6709\u65f6\uff0c\u6211\u4eec\u4e5f\u4f1a\u6839\u636e\u5f52\u4e00\u5316\u7684EI\u6765\u8ba1\u7b97\u56e0\u679c\u6d8c\u73b0\u5ea6\u91cf\uff0c\u5373\uff1a<\/span><\/section>\n

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4.9 \u8ba1\u7b97EI\u7684\u6e90\u4ee3\u7801<\/span><\/strong><\/span><\/h2>\n

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\u8fd9\u662f\u8ba1\u7b97\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u7684Python\u6e90\u4ee3\u7801\u3002\u8f93\u5165tpm\u4e3a\u4e00\u4e2a\u6ee1\u8db3\u884c\u5f52\u4e00\u5316\u6761\u4ef6\u7684\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635\uff0c\u8fd4\u56de\u7684ei_all\u4e3a\u5176EI\u503c\uff0ceff\u4e3a\u6709\u6548\u6027\uff0cdet\uff0cdeg\u5206\u522b\u4e3a\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027\uff0cdet_c\uff0cdeg_c\u5206\u522b\u4e3a\u786e\u5b9a\u6027\u7cfb\u6570\u548c\u7b80\u5e76\u6027\u7cfb\u6570\u3002<\/span><\/section>\n

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    def<\/span> tpm_ei(tpm, log_base = 2):<\/span><\/span><\/code>    '''<\/span><\/span><\/code>    tpm<\/span>: \u8f93\u5165\u7684\u6982\u7387\u8f6c\u79fb\u77e9\u9635\uff0c\u53ef\u4ee5\u662f\u975e\u65b9\u9635<\/span><\/span><\/code>    log_base\uff1a\u5bf9\u6570\u7684\u5e95<\/span><\/span><\/code>
    <\/span><\/code>    ei_all\uff1aEI\u7684\u503c<\/span><\/span><\/code>    det\uff1aEI\u4e2d\u786e\u5b9a\u6027\u7684\u90e8\u5206<\/span><\/span><\/code>    deg\uff1aEI\u4e2d\u7b80\u5e76\u6027\u7684\u90e8\u5206<\/span><\/span><\/code>    eff\uff1a\u6709\u6548\u6027<\/span><\/span><\/code>    det_c\uff1a\u786e\u5b9a\u6027\u7cfb\u6570<\/span><\/span><\/code>    deg_c\uff1a\u7b80\u5e76\u6027\u7cfb\u6570<\/span><\/span><\/code>    '''<\/span><\/span><\/code>    # marginal distribution of y given x ~ Unifrom Dist<\/span><\/span><\/code>    puy<\/span> = tpm.mean(axis=0)<\/span><\/span><\/code>    m,n<\/span> = tpm.shape<\/span><\/span><\/code>    if<\/span> m > n:<\/span><\/span><\/code>        q<\/span> = n<\/span><\/span><\/code>    else<\/span>:<\/span><\/span><\/code>        q<\/span> = m<\/span><\/span><\/code>    <\/span><\/span><\/code>    # replace 0 to a positive number to avoid log error<\/span><\/span><\/code>    eps<\/span> = 0.5<\/span><\/span><\/code>    tpm_e<\/span> = np.where(tpm==0, eps, tpm)<\/span><\/span><\/code>    puy_e<\/span> = np.where(puy==0, eps, puy)<\/span><\/span><\/code>    <\/span><\/span><\/code>    # calculate EI of specific x<\/span><\/span><\/code>    ei_x<\/span> = (np.log2(tpm_e \/ puy_e) \/ np.log2(log_base)  * tpm).sum(axis=1)<\/span><\/span><\/code>    <\/span><\/span><\/code>    # calculate det and deg<\/span><\/span><\/code>    det<\/span> = np.log2(n) + (tpm * np.log2(tpm_e)).sum(axis=1).mean(axis=0)<\/span><\/span><\/code>    deg<\/span> = np.log2(n) + (puy * np.log2(puy_e)).sum()<\/span><\/span><\/code>    <\/span><\/code>    det<\/span> = det \/ np.log2(log_base)<\/span><\/span><\/code>    deg<\/span> = deg \/ np.log2(log_base)<\/span><\/span><\/code>
    <\/span><\/code>    det_c<\/span> = det \/ np.log2(q) * np.log2(log_base)<\/span><\/span><\/code>    deg_c<\/span> = deg \/ np.log2(q) * np.log2(log_base)<\/span><\/span><\/code>    # calculate total EI<\/span><\/span><\/code>    ei_all<\/span> = ei_x.mean()<\/span><\/span><\/code>    eff<\/span> = ei_all \/ np.log2(q) * np.log2(log_base)<\/span><\/span><\/code>    return<\/span> ei_all,det,deg,eff,det_c,deg_c<\/span><\/span><\/code>
    <\/span><\/code>tpm_ei(mi_states)<\/span><\/span><\/code><\/pre>\n<\/section>\n

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    5. \u8fde\u7eed\u53d8\u91cf\u7684 EI<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n
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    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

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    \u8fd9\u79cd\u6269\u5c55\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u8fde\u7eed\u7a7a\u95f4\u4e2d\u7684\u56e0\u679c\u673a\u5236\u7b80\u5316\u4e3a\u4e00\u4e2a\u786e\u5b9a\u6027\u7684\u51fd\u6570\u6620\u5c04<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>f<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u518d\u52a0\u4e0a\u4e00\u4e2a\u566a\u58f0\u968f\u673a\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03be<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u3002\u800c\u4e14\uff0c\u5728\u4e0b\u9762\u5217\u4e3e\u7684\u60c5\u5f62\u4e2d\uff0c<\/span><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5373\u6ee1\u8db3\u9ad8\u65af\u5206\u5e03\uff0c\u8fd9\u6837\u4fbf\u53ef\u6c42\u5f97EI\u7684\u89e3\u6790\u8868\u8fbe\u5f0f\u3002\u5bf9\u4e8e\u66f4\u4e00\u822c\u7684\u60c5\u51b5\uff0c\u5c1a\u6ca1\u6709\u6587\u732e\u8fdb\u884c\u8ba8\u8bba\u3002<\/span><\/section>\n

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    5.1 \u968f\u673a\u51fd\u6570\u6620\u5c04<\/span><\/strong><\/span><\/h2>\n

    <\/span><\/section>\n
    \u6700\u521dErik Hoel\u8003\u8651\u5230\u4e86\u8fd9\u4e00\u70b9\uff0c\u63d0\u51fa\u4e86\u56e0\u679c\u51e0\u4f55[4]\u6846\u67b6\uff0c\u5b83\u4e0d\u4ec5\u7387\u5148\u8ba8\u8bba\u4e86\u968f\u673a\u51fd\u6570\u6620\u5c04\u7684EI\u8ba1\u7b97\u95ee\u9898\uff0c\u540c\u65f6\u8fd8\u5f15\u5165\u4e86\u5e72\u9884\u566a\u97f3\u548c\u56e0\u679c\u51e0\u4f55\u7684\u6982\u5ff5\uff0c\u5e76\u5b9a\u4e49\u4e86EI\u7684\u5c40\u90e8\u5f62\u5f0f\uff0c\u5e76\u5c06\u8fd9\u79cd\u5f62\u5f0f\u4e0e\u4fe1\u606f\u51e0\u4f55\u8fdb\u884c\u4e86\u5bf9\u7167\u548c\u7c7b\u6bd4\u3002\u4e0b\u9762\uff0c\u6211\u4eec\u5206\u522b\u4ece\u4e00\u7ef4\u51fd\u6570\u6620\u5c04\u3001\u591a\u7ef4\u51fd\u6570\u6620\u5c04\uff0c\u548cEI\u7684\u5c40\u90e8\u5f62\u5f0f\u6765\u5206\u522b\u8fdb\u884c\u8ba8\u8bba\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    5.1.1 \u4e00\u7ef4\u51fd\u6570\u6620\u5c04<\/span><\/strong><\/h3>\n

    <\/span><\/section>\n
    \u9996\u5148\uff0c\u6211\u4eec\u8003\u8651\u6700\u7b80\u5355\u7684\u60c5\u51b5\uff1a<\/span><\/section>\n

    <\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/p>\n
    <\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u5176\u4e2d\uff0c<\/span><\/sub><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u90fd\u662f\u4e00\u7ef4\u5b9e\u6570\u53d8\u91cf\u3002\u6309\u7167\u6709\u6548\u4fe1\u606f\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u53d8\u91cfx\u8fdb\u884c\u5e72\u9884\uff0c\u4f7f\u5176\u6ee1\u8db3\u5728\u5176\u5b9a\u4e49\u57df\u7a7a\u95f4\u4e0a\u670d\u4ece\u5747\u5300\u5206\u5e03\u3002\u5982\u679cx\u7684\u5b9a\u4e49\u57df\u4e3a\u4e00\u4e2a\u56fa\u5b9a\u7684\u533a\u95f4\uff0c\u5982[a,b]\uff0c\u5176\u4e2da,b\u90fd\u662f\u5b9e\u6570\uff0c\u90a3\u4e48x\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u5c31\u662f<\/span><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>1<\/span><\/mn>\/<\/span><\/mo><\/mrow>(<\/span><\/mo>b<\/span><\/mi>\u2212<\/span><\/mo>a<\/span><\/mi>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u3002\u7136\u800c\uff0c\u5f53x\u7684\u5b9a\u4e49\u57df\u4e3a\u5168\u4f53\u5b9e\u6570\u7684\u65f6\u5019\uff0c\u533a\u95f4\u6210\u4e3a\u4e86\u65e0\u7a77\u5927\uff0c\u800cx\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u5c31\u6210\u4e3a\u4e86\u65e0\u7a77\u5c0f\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u5047\u8bbex\u7684\u5b9a\u4e49\u57df\u4e0d\u662f\u6574\u4e2a\u5b9e\u6570\u7a7a\u95f4\uff0c\u800c\u662f\u4e00\u4e2a\u8db3\u591f\u5927\u7684\u533a\u57df\uff1a<\/span><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-math>[<\/span><\/mo>\u2212<\/span><\/mo>L<\/span><\/mi>\/<\/span><\/mo><\/mrow>2<\/span><\/mn>,<\/span><\/mo>L<\/span><\/mi>\/<\/span><\/mo><\/mrow>2<\/span><\/mn>]<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5176\u4e2dL\u4e3a\u8be5\u533a\u95f4\u7684\u5927\u5c0f\u3002\u8fd9\u6837\uff0c\u8be5\u533a\u57df\u4e0a\u7684\u5747\u5300\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a<\/span><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-math>1<\/span><\/mn>\/<\/span><\/mo><\/mrow>L<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u3002\u6211\u4eec\u5e0c\u671b\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>L<\/span><\/mi>\u2192<\/span><\/mo>+<\/span><\/mo>\u221e<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u65f6\u5019\uff0cEI\u80fd\u591f\u6536\u655b\u5230\u4e00\u4e2a\u6709\u9650\u7684\u6570\u3002\u7136\u800c\uff0c\u5b9e\u9645\u7684EI\u662f\u4e00\u4e2a\u548cx\u5b9a\u4e49\u57df\u5927\u5c0f\u6709\u5173\u7684\u91cf\uff0c\u6240\u4ee5EI\u662f\u53c2\u6570L\u7684\u51fd\u6570\u3002\u8fd9\u4e00\u70b9\u53ef\u4ee5\u4eceEI\u7684\u5b9a\u4e49\u4e2d\u770b\u51fa\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
     \uff084\uff09<\/span><\/p>\n

    <\/span><\/section>\n
    \u8fd9\u91cc\uff0c<\/span><\/sub><\/mo><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u7ed9\u5b9ax\u7684\u6761\u4ef6\u4e0b\uff0cy\u7684\u6761\u4ef6\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u3002\u7531\u4e8e<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03b5<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u670d\u4ece\u5747\u503c\u4e3a0\uff0c\u65b9\u5dee\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-math>\u03c3<\/span><\/mi>2<\/span><\/sup><\/mn><\/msup><\/mjx-assistive-mml><\/mjx-container>\u7684\u6b63\u6001\u5206\u5e03\uff0c\u6240\u4ee5<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>y<\/span><\/mi>=<\/span><\/mo>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo>+<\/span><\/mo>\u03b5<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5c31\u670d\u4ece\u5747\u503c\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u65b9\u5dee\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-math>\u03c3<\/span><\/mi>2<\/span><\/mn><\/msup><\/mjx-assistive-mml><\/mjx-container>\u7684\u6b63\u6001\u5206\u5e03\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    y\u7684\u79ef\u5206\u533a\u95f4\u4e3a\uff1a<\/span><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5373\u5c06x\u7684\u5b9a\u4e49\u57df<\/span><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\u7ecf\u8fc7f\u7684\u6620\u5c04\uff0c\u5f62\u6210y\u4e0a\u7684\u533a\u95f4\u8303\u56f4\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/p>\n
    <\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u4e3ay\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff0c\u5b83\u4e5f\u53ef\u4ee5\u7531\u8054\u5408\u6982\u7387\u5bc6\u5ea6\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>p<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>,<\/span><\/mo>y<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>p<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo>p<\/span><\/mi>(<\/span><\/mo>y<\/span><\/mi>|<\/span><\/mo><\/mrow>x<\/span><\/mi>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u5bf9x\u8fdb\u884c\u79ef\u5206\u5f97\u5230\u3002\u4e3a\u4e86\u540e\u7eed\u53d9\u8ff0\u65b9\u4fbf\uff0c\u6211\u4eec\u5c06x\u91cd\u65b0\u547d\u540d\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-math>x<\/span><\/mi>0<\/span><\/sub><\/mn><\/msub><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4ece\u800c\u4ee5\u533a\u5206\u51fa\u73b0\u57284\u4e2d\u7684\u5176\u5b83x\u53d8\u91cf\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7531\u4e8eL\u5f88\u5927\uff0c\u6240\u4ee5\u533a\u95f4<\/span><\/sub><\/mjx-assistive-mml><\/mjx-container><\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u5f88\u5927\uff0c\u8fdb\u800c\u5047\u8bbe\u533a\u95f4\uff1a<\/span><\/sub><\/mjx-assistive-mml><\/mjx-container><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4e5f\u5f88\u5927\u3002\u8fd9\u5c31\u4f7f\u5f97\uff0c\u4e0a\u8ff0\u79ef\u5206\u7684\u79ef\u5206\u4e0a\u4e0b\u754c\u53ef\u4ee5\u8fd1\u4f3c\u53d6\u5230\u65e0\u7a77\u5927\uff0c\u4e5f\u5c31\u67094\u4e2d\u7684\u7b2c\u4e00\u9879\u4e3a\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-spacer><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-script><\/mjx-msubsup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-tstrut><\/mjx-mtd><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-spacer><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msubsup><\/mjx-c><\/mjx-mi><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-tstrut><\/mjx-mtd><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-spacer><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msubsup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-spacer><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msubsup><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-surd><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-box><\/mjx-sqrt><\/mjx-msqrt><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-surd><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-box><\/mjx-sqrt><\/mjx-msqrt><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-tstrut><\/mjx-mtd><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-surd><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-box><\/mjx-sqrt><\/mjx-msqrt><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-itable><\/mjx-table><\/mjx-mtable><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mo><\/msubsup><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/p>\n
    <\/mo><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u5176\u4e2d\uff0ce\u4e3a\u81ea\u7136\u5bf9\u6570\u7684\u5e95\uff0c\u6700\u540e\u4e00\u4e2a\u7b49\u5f0f\u662f\u6839\u636e\u9ad8\u65af\u5206\u5e03\u51fd\u6570\u7684Shannon\u71b5\u516c\u5f0f\u8ba1\u7b97\u5f97\u51fa\u7684\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7136\u800c\uff0c\u8981\u8ba1\u7b97\u7b2c\u4e8c\u9879\uff0c\u5373\u4f7f\u4f7f\u7528\u4e86\u79ef\u5206\u533a\u95f4\u4e3a\u65e0\u7a77\u5927\u8fd9\u4e2a\u6761\u4ef6\uff0c\u4ecd\u7136\u5f88\u96be\u8ba1\u7b97\u5f97\u51fa\u7ed3\u679c\uff0c\u4e3a\u6b64\uff0c\u6211\u4eec\u5bf9\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-math>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>0<\/span><\/sub><\/mn><\/msub>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u8fdb\u884c\u4e00\u9636\u6cf0\u52d2\u5c55\u5f00\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>0<\/span><\/sub><\/mn><\/msub>)<\/span><\/mo>\u2248<\/span><\/mo>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo>+<\/span><\/mo>f<\/span><\/mi>\u2032<\/span><\/mo><\/msup>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo>(<\/span><\/mo>x<\/span><\/mi>0<\/span><\/sub><\/mn><\/msub>\u2212<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u8fd9\u91cc\uff0c<\/span><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\u662fx\u5b9a\u4e49\u57df\u4e0a\u7684\u4efb\u610f\u4e00\u70b9\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u56e0\u6b64\uff0cp(y)\u53ef\u4ee5\u88ab\u8fd1\u4f3c\u8ba1\u7b97\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/p>\n
    <\/mo><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5728\u8fd9\u4e00\u6b65\u4e2d\uff0c\u6211\u4eec\u4e0d\u4ec5\u5c06<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-math>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>0<\/span><\/sub><\/mn><\/msub>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u8fd1\u4f3c\u4e3a\u4e00\u4e2a\u7ebf\u6027\u51fd\u6570\uff0c\u540c\u65f6\u8fd8\u5f15\u5165\u4e86\u4e00\u4e2a\u5047\u8bbe\uff0c\u5373p(y)\u7684\u7ed3\u679c\u4e0ey\u65e0\u5173\uff0c\u800c\u4e0e<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>x<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u6709\u5173\u3002\u6211\u4eec\u77e5\u9053\u5728\u5bf9EI\u8ba1\u7b97\u7684\u7b2c\u4e8c\u9879\u4e2d\u5305\u542b\u7740\u5bf9x\u7684\u79ef\u5206\uff0c\u56e0\u6b64\u8fd9\u4e00\u8fd1\u4f3c\u4e5f\u5c31\u610f\u5473\u7740\u4e0d\u540cx\u5904\u7684p(y)\u8fd1\u4f3c\u662f\u4e0d\u540c\u7684\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8fd9\u6837\uff0c4\u4e2d\u7684\u7b2c\u4e8c\u9879\u8fd1\u4f3c\u4e3a\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-spacer><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-script><\/mjx-msubsup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-itable><\/mjx-table><\/mjx-mtable><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mo><\/msubsup><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/p>\n
    <\/mi><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u6700\u7ec8\u7684EI\u53ef\u4ee5\u7531\u4e0b\u5f0f\u8fd1\u4f3c\u8ba1\u7b97\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mo><\/mjx-surd><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-box><\/mjx-sqrt><\/mjx-msqrt><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-spacer><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-script><\/mjx-msubsup><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/section>\n
    <\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u4e0e\u4e0a\u8ff0\u63a8\u5bfc\u7c7b\u4f3c\u7684\u63a8\u5bfc\u9996\u89c1\u4e8eHoel2013\u7684\u6587\u7ae0\u4e2d[2]\uff0c\u5e76\u5728\u795e\u7ecf\u4fe1\u606f\u538b\u7f29\u5668\u4e00\u6587\u4e2d[5]\u4e2d\u8fdb\u884c\u4e86\u8be6\u7ec6\u8ba8\u8bba\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    5.1.2 \u9ad8\u7ef4\u60c5\u51b5<\/span><\/strong><\/span><\/h3>\n

    <\/span><\/section>\n
    \u6211\u4eec\u53ef\u4ee5\u628a\u4e0a\u8ff0\u5bf9\u4e00\u7ef4\u53d8\u91cf\u7684EI\u8ba1\u7b97\u63a8\u5e7f\u5230\u66f4\u4e00\u822c\u7684n\u7ef4\u60c5\u666f\u3002\u5373\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/p>\n

    <\/section>\n

    <\/span><\/section>\n
    \u5176\u4e2d\uff0c<\/span><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a3<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u9ad8\u65af\u566a\u58f0<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03be<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u534f\u65b9\u5dee\u77e9\u9635\u3002\u9996\u5148\uff0c\u6211\u4eec\u5c06<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>x<\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u5e72\u9884\u6210<\/span><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mn>\uff0c<\/span><\/mjx-utext><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>[<\/span><\/mo>\u2212<\/span><\/mo>L<\/span><\/mi>\/<\/span><\/mo><\/mrow>2<\/span><\/mn>\uff0c<\/span><\/mi>L<\/span><\/mi>\/<\/span><\/mo><\/mrow>2<\/span><\/mn>]<\/span><\/mo>n<\/span><\/sup><\/mi><\/msup>\u2282<\/span><\/mo>R<\/span><\/mi><\/mrow>n<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e0a\u7684\u5747\u5300\u5206\u5e03<\/span>\uff0c<\/span><\/mjx-utext><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>[<\/span><\/mo>\u2212<\/span><\/mo>L<\/span><\/mi>\/<\/span><\/mo><\/mrow>2<\/span><\/mn>\uff0c<\/span><\/mi>L<\/span><\/mi>\/<\/span><\/mo><\/mrow>2<\/span><\/mn>]<\/span><\/mo>n<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793an\u7ef4\u7a7a\u95f4\u4e2d\u7684\u8d85\u7acb\u65b9\u4f53\uff0c\u6211\u4eec\u5047\u8bbe<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi><\/mrow>\u2208<\/span><\/mo>R<\/span><\/mi><\/mrow>m<\/span><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5176\u4e2d<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>n<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>m<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u6b63\u6574\u6570\u3002\u53ea\u5b58\u5728\u89c2\u6d4b\u566a\u58f0\u7684\u60c5\u51b5\u4e0b\uff0cEI\u53ef\u4ee5\u63a8\u5e7f\u4e3a\u4ee5\u4e0b\u5f62\u5f0f\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/p>\n

    <\/span><\/section>\n
    \u5176\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>|<\/span><\/mo>\u22c5<\/span><\/mo>|<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u7edd\u5bf9\u503c\u8fd0\u7b97\uff0c<\/span><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>det<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u884c\u5217\u5f0f\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    5.2 \u7ef4\u5ea6\u5e73\u5747\u7684 EI<\/span><\/strong><\/span><\/h2>\n

    <\/span><\/section>\n
    \u5728\u79bb\u6563\u72b6\u6001\u7684\u7cfb\u7edf\u4e2d\uff0c\u5f53\u6211\u4eec\u6bd4\u8f83\u4e0d\u540c\u5c3a\u5ea6\u7cfb\u7edf\u7684\u65f6\u5019\uff0c\u53ef\u4ee5\u76f4\u63a5\u8ba1\u7b97EI\u7684\u5dee\u5f02\u4e5f\u53ef\u4ee5\u8ba1\u7b97\u5f52\u4e00\u5316\u7684EI\u5dee\u5f02\u3002\u5f52\u4e00\u5316\u7684EI\u662f\u9664\u4ee5<\/span><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>log<\/span><\/mi>\u2061<\/span><\/mo>N<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u91cc<\/span><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u79bb\u6563\u72b6\u6001\u7a7a\u95f4<\/span><\/sub><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u4e2d\u7684\u5143\u7d20\u4e2a\u6570\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7136\u800c\uff0c\u5728\u9488\u5bf9\u8fde\u7eed\u53d8\u91cf\u8fdb\u884c\u6269\u5c55\u7684\u65f6\u5019\uff0c\u5982\u679c\u4f7f\u7528\u539f\u59cb\u7684EI\uff0c\u90a3\u4e48\u5c31\u4f1a\u51fa\u73b0\u4e0d\u5408\u7406\u7684\u60c5\u51b5\u3002\u9996\u5148\uff0c\u5982\u516c\u5f0f6\u6240\u793a\uff0cEI\u7684\u8ba1\u7b97\u516c\u5f0f\u4e2d\u5305\u542b\u7740<\/span><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-math>ln<\/span><\/mi>\u2061<\/span><\/mo>L<\/span><\/mi>n<\/span><\/mi><\/msup><\/mjx-assistive-mml><\/mjx-container>\u9879\u3002\u7531\u4e8eL\u4e3a\u4e00\u4e2a\u5f88\u5927\u7684\u6b63\u6570\uff0c\u56e0\u800cEI\u7684\u8ba1\u7b97\u7ed3\u679c\u5c06\u4f1a\u53d7\u5230L\u7684\u4e25\u91cd\u5f71\u54cd\u3002\u5176\u6b21\uff0c\u5982\u679c\u8ba1\u7b97\u5f52\u4e00\u5316\u7684EI\uff0c\u5373Eff\uff0c\u90a3\u4e48\u4f1a\u9047\u5230\u4e00\u4e2a\u95ee\u9898\u662f\uff0c\u5bf9\u4e8e\u8fde\u7eed\u53d8\u91cf\u6765\u8bf4\uff0c\u5176\u72b6\u6001\u7a7a\u95f4\u7684\u5143\u7d20\u4e2a\u6570\u4e3a\u65e0\u7a77\u591a\u4e2a\uff0c\u5982\u679c\u76f4\u63a5\u4f7f\u7528\uff0c\u52bf\u5fc5\u4f1a\u5f15\u5165\u65e0\u7a77\u5927\u91cf\u3002\u4e00\u79cd\u89e3\u51b3\u529e\u6cd5\u662f\u5c06\u7a7a\u95f4\u7684\u4f53\u79ef\u89c6\u4f5c\u4e2a\u6570N\uff0c\u56e0\u6b64\u5e94\u8be5\u9664\u4ee5\u5f52\u4e00\u5316\u53d8\u91cf\u4e3a\uff1a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>n<\/span><\/mi>ln<\/span><\/mi>\u2061<\/span><\/mo>L<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff0c\u7531\u6b64\u53ef\u89c1\u5b83\u662f\u6b63\u6bd4\u4e8en\u548clnL\u7684\uff0c\u5373\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-ext><\/mjx-mark><\/mjx-stretchy-v><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-ext><\/mjx-mark><\/mjx-stretchy-v><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/p>\n
    <\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u7136\u800c\uff0c\u5728\u8fd9\u4e2a\u5f0f\u5b50\u4e2d\uff0c\u4ecd\u7136\u5305\u542b\u7740L\u9879\uff0c\u56e0\u800c\u4e5f\u4f1a\u5bf9Eff\u9020\u6210\u5f88\u5927\u7684\u5f71\u54cd\u3002\u5e76\u4e14\uff0c\u5f53\u6211\u4eec\u6bd4\u8f83\u5fae\u89c2<\/span>\uff08n\u7ef4\uff09<\/span>\u548c\u5b8f\u89c2<\/span>\uff08m\u7ef4\uff0c\u4e14m<n\uff09<\/span>\u4e24\u4e2a\u7ef4\u5ea6\u7684Eff\u65f6\uff0c\u5373\u8ba1\u7b97\u5f52\u4e00\u5316\u7684\u56e0\u679c\u6d8c\u73b0\u7684\u65f6\u5019\uff0cL\u5e76\u4e0d\u80fd\u6d88\u6389\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u770b\u6765\uff0c\u8fde\u7eed\u53d8\u91cf\u7cfb\u7edf\u7684\u5f52\u4e00\u5316\u95ee\u9898\u5e76\u4e0d\u80fd\u7b80\u5355\u5e73\u79fb\u79bb\u6563\u53d8\u91cf\u7684\u7ed3\u679c\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728\u795e\u7ecf\u4fe1\u606f\u538b\u7f29\u5668<\/span>\uff08Neural information squeezer, NIS\uff09<\/span>\u7684\u6846\u67b6\u88ab\u63d0\u51fa\u65f6[5]\uff0c\u4f5c\u8005\u4eec\u53d1\u660e\u4e86\u53e6\u4e00\u79cd\u5bf9\u8fde\u7eed\u53d8\u91cf\u7684\u6709\u6548\u4fe1\u606f\u8fdb\u884c\u5f52\u4e00\u5316\u65b9\u5f0f\uff0c\u5373\u7528\u72b6\u6001\u7a7a\u95f4\u7ef4\u6570\u6765\u5f52\u4e00\u5316EI\uff0c\u4ece\u800c\u89e3\u51b3\u8fde\u7eed\u72b6\u6001\u53d8\u91cf\u4e0a\u7684EI\u6bd4\u8f83\u95ee\u9898\uff0c\u8fd9\u4e00\u6307\u6807\u88ab\u79f0\u4e3a\u7ef4\u5ea6\u5e73\u5747\u7684\u6709\u6548\u4fe1\u606f<\/span>\uff08Dimension Averaged Effective Information\uff0c\u7b80\u79f0dEI\uff09<\/span>\u3002\u5176\u63cf\u8ff0\u4e3a\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/section>\n
    <\/mi><\/mfrac><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u8fd9\u91cc\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>n<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u72b6\u6001\u7a7a\u95f4\u7684\u7ef4\u5ea6\u3002\u53ef\u4ee5\u8bc1\u660e\uff0c\u5728\u79bb\u6563\u7684\u72b6\u6001\u7a7a\u95f4\u4e2d\uff0c\u7ef4\u5ea6\u5e73\u5747\u7684EI\u548c\u6709\u6548\u6027\u6307\u6807<\/span>\uff08Eff\uff09<\/span>\u5b9e\u9645\u4e0a\u662f\u7b49\u4ef7\u7684\u3002\u5173\u4e8e\u8fde\u7eed\u53d8\u91cf\u4e0a\u7684EI\uff0c\u6211\u4eec\u5c06\u5728\u4e0b\u6587\u8fdb\u4e00\u6b65\u8be6\u8ff0\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5bf9\u4e8en\u7ef4\u8fed\u4ee3\u52a8\u529b\u7cfb\u7edf\u6765\u8bf4\uff0c\u9996\u5148\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>y<\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>x<\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u662f\u540c\u4e00\u7ef4\u5ea6\u7684\u53d8\u91cf\uff0c\u56e0\u6b64<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>m<\/span><\/mi>=<\/span><\/mo>n<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff0c\u56e0\u800c\uff1a\u5c06\u516c\u5f0f6\u4ee3\u5165\u7ef4\u5ea6\u5e73\u5747EI\uff0c\u5f97\u5230\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/p>\n
    <\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u867d\u7136L\u4ecd\u7136\u6ca1\u6709\u6d88\u5931\uff0c\u4f46\u662f\u5f53\u6211\u4eec\u8ba1\u7b97\u7ef4\u5ea6\u5e73\u5747\u7684\u56e0\u679c\u6d8c\u73b0\u7684\u65f6\u5019\uff0c\u5373\u5047\u8bbe\u6211\u4eec\u53ef\u4ee5\u5c06n\u7ef4\u7684\u72b6\u6001\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>x<\/span><\/mi><\/mrow>t<\/span><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u6295\u5f71\u5230\u4e00\u4e2aN\u7ef4\u7684\u5b8f\u89c2\u6001\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>X<\/span><\/mi><\/mrow>t<\/span><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4ee5\u53ca\u76f8\u5bf9\u5e94\u7684\u5b8f\u89c2\u52a8\u529b\u5b66(F)\uff0c\u548c\u566a\u58f0\u7684\u534f\u65b9\u5dee<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-math>\u03a3<\/span><\/mi>\u2032<\/span><\/mo><\/msup><\/mjx-assistive-mml><\/mjx-container>\u5219\u5b8f\u89c2\u52a8\u529b\u5b66\u7684\u7ef4\u5ea6\u5e73\u5747EI\u4e0e\u5fae\u89c2\u52a8\u529b\u5b66\u7684\u7ef4\u5ea6\u5e73\u5747EI\u4e4b\u5dee\u4e3a\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/section>\n
    <\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    \u6ce8\u610f\uff0c\u4e0a\u5f0f\u4e2d\u7684\u79ef\u5206\u53ef\u4ee5\u5199\u6210\u5747\u5300\u5206\u5e03\u4e0b\u7684\u671f\u671b\uff0c\u5373<\/sub>\uff0c\u7ee7\u800c<\/span>\u4e0a\u5f0f\u5316\u4e3a<\/span>\uff1a<\/span><\/section>\n

    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-ext><\/mjx-mark><\/mjx-stretchy-v><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mrow><\/mjx-script><\/mjx-msup><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-ext><\/mjx-mark><\/mjx-stretchy-v><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-ext><\/mjx-mark><\/mjx-stretchy-v><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-ext><\/mjx-mark><\/mjx-stretchy-v><\/mjx-mo><\/mjx-mrow><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/section>\n
    <\/mo><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/section>\n
    \u8fd9\u91cc<\/span><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u7acb\u65b9\u4f53<\/span><\/sub><\/mi><\/msup><\/mjx-assistive-mml><\/mjx-container>\u4e0a\u7684\u5747\u5300\u5206\u5e03\u3002\u7531\u6b64\u53ef\u89c1\uff0c\u5c3d\u7ba1\u5728\u671f\u671b\u4e2d\u4ecd\u7136\u9690\u542b\u5730\u5305\u542bL\uff0c\u4f46\u8be5\u5f0f\u4e2d\u6240\u6709\u663e\u542bL\u7684\u9879\u5c31\u90fd\u88ab\u6d88\u5931\u4e86\u3002\u5728\u5b9e\u9645\u6570\u503c\u8ba1\u7b97\u7684\u65f6\u5019\uff0c\u671f\u671b\u7684\u8ba1\u7b97\u53ef\u4ee5\u8868\u73b0\u4e3a\u5728<\/span><\/sub><\/mjx-assistive-mml><\/mjx-container><\/mi><\/msup><\/mjx-assistive-mml><\/mjx-container>\u4e0a\u591a\u4e2a\u91c7\u6837\u53d6\u5e73\u5747\uff0c\u56e0\u800c\u4e5f\u662f\u4e0eL\u7684\u5927\u5c0f\u65e0\u5173\u7684\u3002\u8fd9\u5c31\u5c55\u793a\u51fa\u6765\u5f15\u5165\u7ef4\u5ea6\u5e73\u5747EI\u7684\u4e00\u5b9a\u7684\u5408\u7406\u6027\u3002<\/span>
    <\/section>\n

    <\/span><\/section>\n
    5.3 \u968f\u673a\u8fed\u4ee3\u7cfb\u7edf<\/span><\/strong><\/h2>\n

    <\/span><\/section>\n
    \u6211\u4eec\u53ef\u4ee5\u628a\u4e0a\u8ff0\u7ed3\u8bba\uff0c\u63a8\u5e7f\u5230\u7ebf\u6027\u8fed\u4ee3\u52a8\u529b\u7cfb\u7edf\u4e2d\uff0c\u4e5f\u5c31\u662f\u5bf9\u4e8e\u5f62\u5982<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub>=<\/span><\/mo>A<\/span><\/mi>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>+<\/span><\/mo>\u03b5<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>,<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u7684\u8fed\u4ee3\u7cfb\u7edf\uff0c\u5176\u4e2d\uff0c<\/span><\/sub><\/mi><\/mrow><\/msup><\/mjx-assistive-mml><\/mjx-container>\u662f\u5c3a\u5ea6\u4e3an*n\u7684\u6ee1\u79e9\u7684\u65b9\u9635\uff0c\u4ee3\u8868\u7ebf\u6027\u8fed\u4ee3\u7cfb\u7edf\u4e2d\u7684\u52a8\u529b\u5b66\u7cfb\u6570, <\/span><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4e3an\u7ef4\u7684\u9ad8\u65af\u566a\u58f0\uff0c\u6ee1\u8db30\u5747\u503c\uff0c\u534f\u65b9\u5dee\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03a3<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u6b63\u6001\u5206\u5e03\uff0c\u5176\u4e2d\uff0c\u534f\u65b9\u5dee\u77e9\u9635<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03a3<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e5f\u662f\u6ee1\u79e9\u7684\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u53ef\u4ee5\u770b\u51fa\u8fd9\u4e00\u8fed\u4ee3\u7cfb\u7edf\u53ef\u4ee5\u770b\u505a\u662f\u516c\u5f0f5\u7684\u7279\u4f8b\uff0c\u5176\u4e2d<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>y<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u5bf9\u5e94\u8fd9\u91cc\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-math>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u5373\u662f<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>A<\/span><\/mi>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e3a\u5b9a\u4e49EI\uff0c\u8bbe\u5e72\u9884\u7a7a\u95f4\u5927\u5c0f\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>L<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5bf9\u4e8e\u5355\u6b65\u7684\u6620\u5c04\u6211\u4eec\u53ef\u4ee5\u5f97<\/span>\u5230\u7ef4\u5ea6\u5e73\u5747\u6709\u6548<\/span>\u4fe1\u606f<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-nstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-script><\/mjx-msup><\/mjx-mstyle><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-nstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-script><\/mjx-msup><\/mjx-mstyle><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-mstyle><\/mjx-mstyle><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/p>\n
    <\/mo><\/mstyle><\/mstyle><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u6709\u6548\u4fe1\u606f\u53ef\u4ee5\u5206\u89e3\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027\u4e3a\u4e24\u9879\uff0c<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/section>\n
    <\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u5176\u4e2d\u786e\u5b9a\u6027<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/section>\n
    <\/mo><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u63cf\u8ff0\u7cfb\u7edf\u524d\u4e00\u65f6\u523b\u72b6\u6001\u5df2\u77e5\u7684\u60c5\u51b5\u4e0b\uff0c\u540e\u4e00\u65f6\u523b\u7684\u968f\u673a\u6027\uff0c\u786e\u5b9a\u6027\u8d8a\u5f3a\uff0c\u968f\u673a\u6027\u8d8a\u5c0f\uff0c\u8d8a\u5bb9\u6613\u5bf9\u7cfb\u7edf\u672a\u6765\u8d8b\u52bf\u8fdb\u884c\u9884\u6d4b\uff1b<\/span><\/section>\n

    <\/span><\/section>\n
    \u7b80\u5e76\u6027:<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-over><\/mjx-c><\/mjx-mi><\/mjx-base><\/mjx-mover><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/p>\n
    <\/mo><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u63cf\u8ff0\u540e\u4e00\u65f6\u523b\u5df2\u77e5\u7684\u60c5\u51b5\u4e0b\uff0c\u5bf9\u524d\u4e00\u65f6\u523b\u7684\u53ef\u8ffd\u6eaf\u6027\uff0c\u7b80\u5e76\u6027\u8d8a\u5f31\uff0c\u8d8a\u5bb9\u6613\u63a8\u65ad\u7cfb\u7edf\u4ee5\u5f80\u7684\u6f14\u5316\u8def\u5f84\u3002\u5176\u4e2d\uff0c<\/span><\/sub><\/mn><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u662f\u4fdd\u6301\u56e0\u679c\u673a\u5236\u4e0d\u53d8\uff0c\u7ecf\u8fc7\u5e72\u9884\u4ee5\u540e\u5f97\u5230\u7684\u65b0\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u53d8\u91cf\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u786e\u5b9a\u6027\u8d8a\u5f3a\uff0c\u7b80\u5e76\u6027\u8d8a\u5f31\uff0c\u6709\u6548\u4fe1\u606f\u5219\u4f1a\u8d8a\u5927\uff0c\u56e0\u679c\u6548\u5e94\u8d8a\u5f3a\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5b8f\u89c2\u6709\u6548\u4fe1\u606f\u4e0e\u5fae\u89c2\u6709\u6548\u4fe1\u606f\u505a\u5dee\u4e4b\u540e\u5c31\u53ef\u4ee5\u5f97\u5230\u968f\u5373\u8fed\u4ee3\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0\u4e3a\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mi><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/p>\n

    <\/span><\/section>\n
    \u5176\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>W<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u7c97\u7c92\u5316\u77e9\u9635\uff0c\u5b83\u7684\u9636\u6570\u4e3an*m\uff0cm\u4e3a\u5b8f\u89c2\u72b6\u6001\u7a7a\u95f4\u7684\u7ef4\u5ea6\uff0c\u5b83\u7684\u4f5c\u7528\u662f\u628a\u4efb\u610f\u7684\u5fae\u89c2\u6001<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u6620\u5c04\u4e3a\u5b8f\u89c2\u6001<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math>W<\/span><\/mi>\u2020<\/span><\/mo><\/mrow><\/msup><\/mjx-assistive-mml><\/mjx-container>\u4e3aW\u7684\u4f2a\u9006\u8fd0\u7b97\u3002\u5f0f\u4e2d\u7b2c\u4e00\u9879\u662f\u7531\u786e\u5b9a\u6027\u5f15\u53d1\u7684\u6d8c\u73b0\uff0c\u7b80\u79f0\u786e\u5b9a\u6027\u6d8c\u73b0 <\/span>(Determinism Emergence)<\/span>\uff0c\u7b2c\u4e8c\u9879\u4e3a\u7b80\u5e76\u6027\u5f15\u53d1\u7684\u6d8c\u73b0\uff0c\u7b80\u79f0\u7b80\u5e76\u6027\u6d8c\u73b0\u3002\u66f4\u8be6\u7ec6\u7684\u5185\u5bb9\u53c2\u770b\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    5.4 \u524d\u9988\u795e\u7ecf\u7f51\u7edc<\/span><\/strong><\/span><\/h2>\n

    <\/span><\/section>\n
    \u9488\u5bf9\u590d\u6742\u7cfb\u7edf\u81ea\u52a8\u5efa\u6a21\u4efb\u52a1\uff0c\u6211\u4eec\u5f80\u5f80\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u6765\u5efa\u6a21\u7cfb\u7edf\u52a8\u529b\u5b66\u3002\u5177\u4f53\u7684\uff0c\u5bf9\u4e8e\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u6765\u8bf4\uff0c\u5f20\u6c5f\u7b49\u4eba\u63a8\u5bfc\u51fa\u4e86\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u6709\u6548\u4fe1\u606f\u7684\u8ba1\u7b97\u516c\u5f0f[5]\uff0c\u5176\u4e2d\u795e\u7ecf\u7f51\u7edc\u7684\u8f93\u5165\u662f<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>1<\/span><\/sub><\/mn><\/msub>,<\/span><\/sub><\/mo>.<\/span><\/mo>.<\/span><\/mo>.<\/span><\/mo>,<\/span><\/mo>x<\/span><\/mi>n<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8f93\u51fa\u662f<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>(<\/span><\/mo>y<\/span><\/mi>1<\/span><\/sub><\/mn><\/msub>,<\/span><\/mo>.<\/span><\/mo>.<\/span><\/mo>.<\/span><\/mo>,<\/span><\/mo>y<\/span><\/mi>n<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5e76\u4e14\u6ee1\u8db3<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>=<\/span><\/mo>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u7531\u795e\u7ecf\u7f51\u7edc\u5b9e\u73b0\u7684\u786e\u5b9a\u6027\u6620\u5c04\u3002\u7136\u800c\uff0c\u6839\u636e\u516c\u5f0f5\uff0c\u6620\u5c04\u4e2d\u5fc5\u987b\u5305\u542b\u566a\u58f0\u624d\u80fd\u591f\u4f53\u73b0\u4e0d\u786e\u5b9a\u6027\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u56e0\u800c\uff0c\u5728\u795e\u7ecf\u7f51\u7edc\u4e2d\uff0c\u6211\u4eec\u5047\u8bbe\u795e\u7ecf\u7f51\u7edc\u4ece\u8f93\u5165\u5230\u8f93\u51fa\u7684\u8ba1\u7b97\u4e5f\u662f\u4e0d\u786e\u5b9a\u6027\u7684\uff0c\u5373\u4e5f\u7b26\u5408\u516c\u5f0f5\uff1a<\/span><\/section>\n

    <\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>=<\/span><\/mo>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo>+<\/span><\/mo>\u03be<\/span><\/mi>,<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u8fd9\u91cc\uff0c<\/span><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u4e00\u9ad8\u65af\u566a\u58f0\uff0c\u4e14<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-math>\u03a3<\/span><\/mi>=<\/span><\/mo>diag<\/span><\/mi><\/mrow>(<\/span><\/mo>\u03c3<\/span><\/mi>1<\/span><\/sub><\/mn><\/msub>,<\/span><\/mo>\u03c3<\/span><\/mi>2<\/span><\/sub><\/mn><\/msub>,<\/span><\/mo>\u22ef<\/span><\/mo>,<\/span><\/mo>\u03c3<\/span><\/mi>n<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u91cc<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>\u03c3<\/span><\/mi>i<\/span><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u7b2ci\u4e2a\u7ef4\u5ea6\u7684\u6700\u5c0f\u5e73\u65b9\u8bef\u5dee<\/span>\uff08Mean Square Error\uff0c\u7b80\u79f0MSE\u8bef\u5dee\uff09<\/span>\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u5047\u8bbe\u4ecex\u5230y\u7684\u795e\u7ecf\u7f51\u7edc\u6620\u5c04\u5b9e\u9645\u4e0a\u6ee1\u8db3\u4e00\u4e2a\u5747\u503c\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u534f\u65b9\u5dee\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03a3<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u6761\u4ef6\u9ad8\u65af\u5206\u5e03\uff0c\u5373\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/section>\n
    <\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u7531\u6b64\uff0c\u5957\u7528\u9ad8\u7ef4\u6620\u5c04\u4e00\u822c\u60c5\u51b5\u4e0b\u7684\u7ed3\u8bba\uff0c\u6211\u4eec\u53ef\u4ee5\u7ed9\u51fa\u795e\u7ecf\u7f51\u7edc\u6709\u6548\u4fe1\u606f\u7684\u4e00\u822c\u8ba1\u7b97\u516c\u5f0f\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-itable><\/mjx-table><\/mjx-mtable><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/p>\n
    <\/mo><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u5176\u4e2d<\/span><\/sub><\/mo><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u8303\u56f4\u5728<\/span><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>[<\/span><\/mo>\u2212<\/span><\/mo>L<\/span><\/mi>\/<\/span><\/mo><\/mrow>2<\/span><\/mn>,<\/span><\/mo>L<\/span><\/mi>\/<\/span><\/mo><\/mrow>2<\/span><\/mn>]<\/span><\/mo><\/mrow>n<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e0a\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>n<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u5747\u5300\u5206\u5e03\uff0c<\/span><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>det<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u884c\u5217\u5f0f\u3002\u7ef4\u5ea6\u5e73\u5747EI\u4e3a\uff1a<\/span><\/section>\n

    <\/span><\/section>\n
    <\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-itable><\/mjx-table><\/mjx-mtable><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
    <\/p>\n
    <\/mo><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

    <\/span><\/section>\n
    \u5982\u679c\u8bbe\u5fae\u89c2\u7684\u52a8\u529b\u5b66\u53ef\u4ee5\u7528\u795e\u7ecf\u7f51\u7edcf\u6765\u62df\u5408\uff0c\u5b8f\u89c2\u52a8\u529b\u5b66\u5219\u53ef\u4ee5\u7528F\u6765\u62df\u5408\uff0c\u5219\u56e0\u679c\u6d8c\u73b0\u53ef\u4ee5\u7531\u4e0b\u5f0f\u8ba1\u7b97\uff1a<\/span><\/section>\n

    <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-itable><\/mjx-table><\/mjx-mtable><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
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    <\/span><\/section>\n
    \u5176\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>m<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u5b8f\u89c2\u6001\u7ef4\u5ea6\uff0c<\/span><\/sub><\/mo><\/msubsup><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u7b2ci\u4e2a\u5b8f\u89c2\u7ef4\u5ea6\u7684\u5e73\u5747\u5e73\u65b9\u8bef\u5dee<\/span>\uff08MSE\uff09<\/span>\uff0c\u8fd9\u4e00\u8bef\u5dee\u53ef\u4ee5\u901a\u8fc7\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u8ba1\u7b97\u7684\u5b8f\u89c2\u6001<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>X<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u7684\u68af\u5ea6\u8ba1\u7b97\u5f97\u51fa\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u6ce8\u610f\uff0c\u4e0a\u8ff0\u7ed3\u8bba\u90fd\u8981\u6c42\uff1a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u2202<\/span><\/mi>x<\/span><\/sub><\/mi><\/mrow><\/msub>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e0d\u4e3a0\uff0c\u800c\u5bf9\u4e8e\u6240\u6709\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u2202<\/span><\/mi>x<\/span><\/sub><\/mi><\/mrow><\/msub>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5904\u5904\u4e3a0\u65f6\uff0c\u6211\u4eec\u5f97\u5230\uff1a <\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-tstrut><\/mjx-mtd><\/mjx-mtr><\/mjx-itable><\/mjx-table><\/mjx-mtable><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>E<\/span><\/mi>I<\/span><\/mi>(<\/span><\/mo>f<\/span><\/mi>)<\/span><\/mo>\u2248<\/span><\/mo><\/mtd><\/mtr><\/mtable>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u5bf9\u4e8e\u66f4\u4e00\u822c\u7684\u60c5\u5f62\uff0c\u5219\u9700\u8981\u8003\u8651\u77e9\u9635\u4e0d\u6ee1\u79e9\u7684\u60c5\u51b5\uff0c\u8bf7\u53c2\u8003\u795e\u7ecf\u7f51\u7edc\u7684\u6709\u6548\u4fe1\u606f\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    5.5 \u8fde\u7eed\u7cfb\u7edfEI\u7684\u6e90\u4ee3\u7801<\/span><\/strong><\/span><\/h2>\n

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    \u53ef\u9006\u795e\u7ecf\u7f51\u7edc\u4e0b\u7684\u6570\u503c\u89e3\u4ee5\u53ca\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u89e3\u6790\u89e3\u90fd\u53ef\u4ee5\u7ed9\u51fa\u8ba1\u7b97\u65b9\u6cd5\u3002<\/span><\/section>\n

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    \u5bf9\u4e8e\u4e00\u822c\u7684\u795e\u7ecf\u7f51\u7edc\uff0c\u5b83\u53ef\u770b\u505a\u662f\u4ece\u8f93\u5165X\u5230\u8f93\u51faY\u7684\u4e00\u79cd\u4e0d\u786e\u5b9a\u7684\u51fd\u6570\u6620\u5c04\uff1a <\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>=<\/span><\/mo>f<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo>+<\/span><\/mo>\u03be<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

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    \u5176\u4e2dx\u7684\u7ef4\u5ea6\u4e3ainput_size\uff0cy\u7684\u7ef4\u5ea6\u4e3aoutput_size\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03be<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u4e00\u9ad8\u65af\u5206\u5e03\uff0c\u5176\u534f\u65b9\u5dee\u77e9\u9635\u4e3a\uff1a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-math>\u03a3<\/span><\/mi>=<\/span><\/mo>diag<\/span><\/mi><\/mrow>(<\/span><\/mo>\u03c3<\/span><\/mi>1<\/span><\/sub><\/mn><\/msub>,<\/span><\/mo>\u03c3<\/span><\/mi>2<\/span><\/sub><\/mn><\/msub>,<\/span><\/mo>\u22ef<\/span><\/mo>,<\/span><\/mo>\u03c3<\/span><\/mi>n<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u91cc\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>\u03c3<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u8be5\u795e\u7ecf\u7f51\u7edc\u7b2ci\u4e2a\u7ef4\u5ea6\u7684\u5747\u65b9\u8bef\u5dee<\/span>\uff08MSE\uff09<\/span>\u3002\u8be5\u77e9\u9635\u7684\u9006\u8bb0\u4e3asigmas_matrix\u3002\u6620\u5c04\u51fd\u6570f\u8bb0\u4e3afunc\uff0c\u5219\u53ef\u4ee5\u7528\u4e0b\u9762\u7684\u4ee3\u7801\u8ba1\u7b97\u8be5\u795e\u7ecf\u7f51\u7edc\u7684EI\u3002\u8be5\u7b97\u6cd5\u7684\u57fa\u672c\u601d\u60f3\u662f\u5229\u7528\u8499\u7279\u5361\u6d1b\u65b9\u6cd5\u8ba1\u7b97\u516c\u5f0f6\u7684\u79ef\u5206\u3002<\/span><\/section>\n

    <\/span><\/section>\n
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      \u8f93\u5165\u53d8\u91cf\uff1a<\/span><\/section>\n<\/li>\n<\/ul>\n

      <\/span><\/section>\n
      \u795e\u7ecf\u7f51\u7edc\u7684\u8f93\u5165\u7ef4\u5ea6<\/span>\uff08input_size\uff09<\/span>\u8f93\u51fa\u7ef4\u6570<\/span>\uff08output_size\uff09<\/span>\u3001\u8f93\u51fa\u53d8\u91cf\u89c6\u4e3a\u9ad8\u65af\u5206\u5e03\u540e\u7684\u534f\u65b9\u5dee\u77e9\u9635\u7684\u9006<\/span>\uff08sigmas_matrix\uff09<\/span>\u3001\u6620\u5c04\u51fd\u6570<\/span>\uff08func\uff09<\/span>\u3001\u5e72\u9884\u533a\u95f4\u5927\u5c0f<\/span>\uff08L\u7684\u53d6\u503c\uff09<\/span>\u3001\u4ee5\u53ca\u8499\u7279\u5361\u7f57\u79ef\u5206\u7684\u6837\u672c\u6570<\/span>\uff08num_samples\uff09<\/span>\u3002<\/span><\/section>\n

      <\/span><\/section>\n
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        \u8f93\u51fa\u53d8\u91cf\uff1a<\/span><\/section>\n<\/li>\n<\/ul>\n

        <\/span><\/section>\n
        \u7ef4\u5ea6\u5e73\u5747EI\uff08d_EI\uff09\u3001EI\u7cfb\u6570\uff08eff\uff09\u3001EI\u503c\uff08EI\uff09\u3001\u786e\u5b9a\u6027\uff08term1\uff09\u3001\u7b80\u5e76\u6027\uff08term2\uff09\u548c<\/span><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>ln<\/span><\/mi>\u2061<\/span><\/mo>L<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff08-np.log(rho)\uff09\u3002<\/span><\/section>\n

        <\/span><\/section>\n
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          def<\/span> approx_ei(input_size, output_size, sigmas_matrix, func, num_samples, L, easy=True, device=None):<\/span><\/span><\/code>
          <\/span><\/code>    rho<\/span>=1\/(2*L)**input_size #the density of X even distribution<\/span><\/span><\/code>    <\/span><\/span><\/code>    #the first term of EI, the entropy of a gaussian distribution<\/span><\/span><\/code>    #sigmas_matrix_np=sigmas_matrix.cpu() if use_cuda else sigmas_matrix<\/span><\/span><\/code>    dett<\/span>=1.0<\/span><\/span><\/code>    if<\/span> easy:<\/span><\/span><\/code>        dd<\/span> = torch.diag(sigmas_matrix)<\/span><\/span><\/code>        dett<\/span> = torch.log(dd).sum()<\/span><\/span><\/code>    else<\/span>:<\/span><\/span><\/code>        #dett = np.log(np.linalg.det(sigmas_matrix_np))<\/span><\/span><\/code>        dett<\/span> = torch.log(torch.linalg.det(sigmas_matrix))<\/span><\/span><\/code>    term1<\/span> = - (output_size + output_size * np.log(2*np.pi) + dett)\/2 <\/span><\/span><\/code>    <\/span><\/span><\/code>    #sampling x on the space [-L,L]^n, n is the number of samples<\/span><\/span><\/code>    xx<\/span>=L*2*(torch.rand(num_samples, input_size, device=sigmas_matrix.device)-1\/2)<\/span><\/span><\/code>    <\/span><\/code>    dets<\/span> = 0<\/span><\/span><\/code>    logdets<\/span> = 0<\/span><\/span><\/code>    <\/span><\/span><\/code>    #iterate all samples of x<\/span><\/span><\/code>    for<\/span> i in range(xx.size()[0]):<\/span><\/span><\/code>        jac<\/span>=jacobian(func, xx[i,:]) #use pytorch's jacobian function to obtain jacobian matrix<\/span><\/span><\/code>        det<\/span>=torch.abs(torch.det(jac)) #calculate the determinate of the jacobian matrix<\/span><\/span><\/code>        dets<\/span> += det.item()<\/span><\/span><\/code>        if<\/span> det!=0:<\/span><\/span><\/code>            logdets+<\/span>=torch.log(det).item() #log jacobian<\/span><\/span><\/code>        else<\/span>:<\/span><\/span><\/code>            #if det==0 then, it becomes a gaussian integration<\/span><\/span><\/code>            logdet<\/span> = -(output_size+output_size*np.log(2*np.pi)+dett)<\/span><\/span><\/code>            logdets+<\/span>=logdet.item()<\/span><\/span><\/code>    <\/span><\/code>    int_jacobian<\/span> = logdets \/ xx.size()[0] #take average of log jacobian<\/span><\/span><\/code>    <\/span><\/code>    term2<\/span> = -np.log(rho) + int_jacobian # derive the 2nd term<\/span><\/span><\/code>    <\/span><\/code>    if<\/span> dets==0:<\/span><\/span><\/code>        term2<\/span> = - term1<\/span><\/span><\/code>    EI<\/span> = max(term1 + term2, 0)<\/span><\/span><\/code>    if<\/span> torch.is_tensor(EI):<\/span><\/span><\/code>        EI<\/span> = EI.item()<\/span><\/span><\/code>    eff<\/span> = -EI \/ np.log(rho)<\/span><\/span><\/code>    d_EI<\/span> = EI\/output_size<\/span><\/span><\/code>    <\/span><\/code>    return<\/span> d_EI, eff, EI, term1, term2, -np.log(rho)<\/span><\/span><\/code><\/pre>\n<\/section>\n

          <\/section>\n
          \u5bf9\u4e8e\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\uff0c\u7531\u4e8e\u662f\u89e3\u6790\u89e3\uff0c\u76f8\u5bf9\u4f1a\u7b80\u5355\u8bb8\u591a\u3002\u65e2\u53ef\u4ee5\u76f4\u63a5\u8ba1\u7b97\uff0c\u4e5f\u53ef\u4ee5\u4f5c\u4e3a\u4e0a\u8ff0\u795e\u7ecf\u7f51\u7edc\u8ba1\u7b97\u7ed3\u679c\u7684\u5bf9\u7167\u3002\u8f93\u5165\u7684\u53d8\u91cf\u5206\u522b\u4e3a\u53c2\u6570\u77e9\u9635\u548c\u534f\u65b9\u5dee\u77e9\u9635\u3002<\/span><\/section>\n

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            def<\/span> EI_calculate_SIS<\/span>(A,Sigma)<\/span>:<\/span><\/span><\/code>    n=A.shape[0<\/span>]<\/span><\/code>    return<\/span> math.log(abs(sl.det(A))\/(np.sqrt(sl.det(Sigma))*math.pow(2<\/span>*np.pi*np.e,n\/2<\/span>)))<\/span><\/code><\/pre>\n<\/section>\n

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            6. EI\u4e0e\u5176\u5b83\u76f8\u5173\u4e3b\u9898<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n
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            <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

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            6.1 EI\u4e0e\u6574\u5408\u4fe1\u606f\u8bba<\/span><\/strong><\/span><\/h2>\n

            <\/span><\/section>\n
            \u6709\u6548\u4fe1\u606f\u8fd9\u4e00\u6307\u6807\u6700\u65e9\u51fa\u73b0\u5728\u6587\u732eTononi\u7b49\u4eba<\/span>(2003)<\/span>\u7684\u6587\u7ae0\u4e2d[1]\uff0c\u5728\u8fd9\u7bc7\u6587\u7ae0\u4e2d\uff0c\u4f5c\u8005\u4eec\u5b9a\u4e49\u4e86\u6574\u5408\u4fe1\u606f\u80fd\u529b\u8fd9\u4e00\u6307\u6807\uff0c\u5e76\u5efa\u7acb\u4e86\u6574\u5408\u4fe1\u606f\u7406\u8bba\uff0c\u8fd9\u4e00\u7406\u8bba\u540e\u6765\u6f14\u5316\u6210\u610f\u8bc6\u7406\u8bba\u7684\u4e00\u4e2a\u91cd\u8981\u5206\u652f\u3002\u800c\u6574\u5408\u4fe1\u606f\u80fd\u529b\u8fd9\u4e00\u6307\u6807\u7684\u5b9a\u4e49\u662f\u4ee5\u6709\u6548\u4fe1\u606f\u4e3a\u57fa\u7840\u7684\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            6.1.1 EI\u4e0e\u03a6<\/span><\/strong><\/span><\/h3>\n

            <\/span><\/section>\n
            \u6574\u5408\u4fe1\u606f\u80fd\u529b<\/span>\uff08\u6216\u8005\u53eb\u6574\u5408\u7a0b\u5ea6\uff09<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a6<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u53ef\u4ee5\u88ab\u5b9a\u4e49\u4e3a\u7cfb\u7edf\u7684\u4efb\u610f\u4e00\u4e2a\u4e8c\u5212\u5206\u4e24\u90e8\u5206\u4e4b\u95f4\u76f8\u4e92\u5f71\u54cd\u7684\u6709\u6548\u4fe1\u606f\u6700\u5c0f\u503c\u3002\u5047\u5982\u7cfb\u7edf\u662fX\uff0cS\u662fX\u7684\u4e00\u4e2a\u5b50\u96c6\uff0c\u5b83\u88ab\u5212\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\uff0c\u5206\u522b\u662fA\u548cB\u3002\u90a3\u4e48\uff0cA\u3001B\u4e4b\u95f4\u4ee5\u53ca\u5b83\u4eec\u8ddfX\u4e2d\u5176\u4f59\u7684\u90e8\u5206\u90fd\u5b58\u5728\u7740\u76f8\u4e92\u4f5c\u7528\u548c\u56e0\u679c\u5173\u7cfb\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            <\/section>\n
            \u6574\u5408\u4fe1\u606f\u8bba\u4e2d\u7684\u5212\u5206<\/span><\/section>\n

            <\/span><\/section>\n
            \u8fd9\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5ea6\u91cf\u8fd9\u4e9b\u56e0\u679c\u5173\u7cfb\u7684\u5f3a\u5f31\u3002\u9996\u5148\uff0c\u6211\u4eec\u6765\u8ba1\u7b97\u4eceA\u5230B\u7684\u6709\u6548\u4fe1\u606f\u3002\u5373\u5e72\u9884A\uff0c\u4f7f\u5176\u670d\u4ece\u6700\u5927\u71b5\u5206\u5e03\uff0c\u7136\u540e\u5ea6\u91cfA\u548cB\u4e4b\u95f4\u7684\u4e92\u4fe1\u606f\uff1a<\/span><\/section>\n

            <\/span><\/section>\n
            <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
            <\/p>\n

            <\/p>\n
            <\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

            <\/span><\/section>\n
            \u8fd9\u91cc<\/span><\/sub><\/mi><\/mrow><\/msup><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793aA\u4e0a\u7684\u6700\u5927\u71b5\u5206\u5e03\uff0c\u4e5f\u5c31\u662f\u524d\u6587\u4e2d\u7684\u5747\u5300\u5206\u5e03\u3002\u8be5\u5f0f\u5b50\u4e2d\u6ca1\u6709\u660e\u786e\u8868\u793a\uff0c\u4f46\u5b9e\u9645\u4e0a\u6697\u542b\u4e86\u4e00\u79cd\u4eceA\u5230B\u7684\u56e0\u679c\u673a\u5236\uff0c\u5373<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>P<\/span><\/mi>r<\/span><\/mi>(<\/span><\/mo>B<\/span><\/mi>|<\/span><\/mo><\/mrow>A<\/span><\/mi>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u3002\u5b83\u5728\u5e72\u9884\u4e2d\u59cb\u7ec8\u4fdd\u6301\u4e0d\u53d8\u3002\u8fd9\u6837\uff0c\u5982\u679cA\u7684\u4e0d\u540c\u72b6\u6001\u4f1a\u5bfc\u81f4B\u6709\u5f88\u4e0d\u4e00\u6837\u7684\u53d8\u5316\uff0c\u8fd9\u4e2aEI\u503c\u4f1a\u5f88\u9ad8\uff1b\u53cd\u4e4b\uff0c\u5982\u679c\u65e0\u8bbaA\u600e\u4e48\u53d8\uff0cB\u90fd\u53d7\u5230\u5f88\u5c11\u7684\u5f71\u54cd\uff0c\u90a3\u4e48EI\u5c31\u4f1a\u5f88\u4f4e\u3002\u663e\u7136\uff0c\u8fd9\u79cd\u5ea6\u91cf\u662f\u6709\u65b9\u5411\u7684\uff0cA\u5bf9B\u7684EI\u548cB\u5bf9A\u7684EI\u53ef\u4ee5\u5f88\u4e0d\u540c\u3002\u6211\u4eec\u53ef\u4ee5\u628a\u8fd9\u4e24\u4e2a\u65b9\u5411\u7684EI\u52a0\u5728\u4e00\u8d77\uff0c\u5f97\u5230S\u5728\u67d0\u4e00\u4e2a\u5212\u5206\u4e0b\u7684EI\u5927\u5c0f\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>E<\/span><\/mi>I<\/span><\/mi>(<\/span><\/mo>A<\/span><\/mi>\u2194<\/span><\/mo>B<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>E<\/span><\/mi>I<\/span><\/mi>(<\/span><\/mo>A<\/span><\/mi>\u2192<\/span><\/mo>B<\/span><\/mi>)<\/span><\/mo>+<\/span><\/mo>E<\/span><\/mi>I<\/span><\/mi>(<\/span><\/mo>B<\/span><\/mi>\u2192<\/span><\/mo>A<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

            <\/span><\/section>\n
            \u904d\u5386\u5404\u79cd\u5212\u5206\uff0c\u5982\u679c\u5b58\u5728\u67d0\u4e00\u4e2a\u5212\u5206S\uff0c\u4f7f\u5f97EI\u4e3a0\uff0c\u8bf4\u660e\u8fd9\u4e2aS\u53ef\u4ee5\u88ab\u770b\u505a\u662f\u4e24\u4e2a\u56e0\u679c\u72ec\u7acb\u7684\u90e8\u5206\uff0c\u6240\u4ee5\u6574\u5408\u7a0b\u5ea6\u4e5f\u5e94\u8be5\u662f0\u3002\u4ece\u8fd9\u79cd\u7279\u6b8a\u4f8b\u5b50\u4e2d\u6211\u4eec\u53ef\u4ee5\u770b\u51fa\uff0c\u6211\u4eec\u5e94\u8be5\u5173\u6ce8\u6240\u6709\u5212\u5206\u4e2d\u6709\u6548\u4fe1\u606f\u6700\u5c0f\u7684\u90a3\u4e2a\u3002\u5f53\u7136\uff0c\u4e0d\u540c\u5212\u5206\u4f1a\u5bfc\u81f4A\u548cB\u7684\u72b6\u6001\u7a7a\u95f4\u5c31\u4e0d\u4e00\u6837\uff0c\u6240\u4ee5\u5e94\u8be5\u505a\u4e00\u4e2a\u5f52\u4e00\u5316\u5904\u7406\uff0c\u5373\u9664\u4ee5A\u548cB\u6700\u5927\u71b5\u503c\u4e2d\u8f83\u5c0f\u7684\u90a3\u4e00\u4e2a\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u6709\u4e00\u4e2a\u6700\u5c0f\u4fe1\u606f\u5212\u5206<\/span>\uff08minimum information bipartition\uff0cMIB\uff09<\/span>\u3002\u6574\u5408\u7a0b\u5ea6<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a6<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5b9a\u4e49\u5982\u4e0b\uff1a<\/span><\/section>\n

            <\/span><\/section>\n
            <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a6<\/span><\/mi>(<\/span><\/mo>S<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>E<\/span><\/mi>I<\/span><\/mi>(<\/span><\/mo>M<\/span><\/mi>I<\/span><\/mi>B<\/span><\/mi>(<\/span><\/mo>S<\/span><\/mi>)<\/span><\/mo>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

            <\/span><\/section>\n
            \u8fd9\u5c31\u662f\u6574\u5408\u4fe1\u606f\u80fd\u529b\u4e0e\u6709\u6548\u4fe1\u606f\u7684\u5173\u7cfb\u3002<\/span><\/section>\n

            <\/span><\/h3>\n
            6.1.2 <\/span><\/strong><\/span>\u533a\u522b<\/span><\/strong><\/h3>\n

            <\/span><\/section>\n
            \u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u4e0e\u9a6c\u5c14\u79d1\u592b\u94fe\u7684EI\u8ba1\u7b97\u4e0d\u540c\uff0c\u8fd9\u91cc\u7684EI\u66f4\u591a\u8861\u91cf\u7684\u662f\u7cfb\u7edf\u4e2d\u4e24\u4e2a\u90e8\u5206\u5f7c\u6b64\u4e4b\u95f4\u7684\u56e0\u679c\u8054\u7cfb\u3002\u800c\u9a6c\u5c14\u79d1\u592b\u94fe\u7684EI\u8861\u91cf\u7684\u662f\u540c\u4e00\u4e2a\u7cfb\u7edf\u5728\u4e0d\u540c\u4e24\u4e2a\u65f6\u523b\u4e4b\u95f4\u7684\u56e0\u679c\u5173\u8054\u5f3a\u5ea6\u3002<\/span><\/section>\n

            <\/span><\/h2>\n
            6.2 EI\u4e0e\u5176\u5b83\u56e0\u679c\u5ea6\u91cf\u6307\u6807<\/span><\/strong><\/span><\/h2>\n

            <\/span><\/section>\n
            EI\u662f\u4e00\u79cd\u5ea6\u91cf\u56e0\u679c\u673a\u5236\u4e2d\u56e0\u679c\u53d8\u91cf\u7684\u56e0\u679c\u8054\u7cfb\u5f3a\u5f31\u7684\u4e00\u79cd\u6307\u6807\u3002\u800c\u5728EI\u63d0\u51fa\u4e4b\u524d\uff0c\u5df2\u6709\u591a\u4e2a\u56e0\u679c\u5ea6\u91cf\u6307\u6807\u88ab\u63d0\u51fa\u4e86\u3002\u90a3\u4e48\uff0cEI\u548c\u8fd9\u4e9b\u56e0\u679c\u5ea6\u91cf\u6307\u6807\u4e4b\u95f4\u5b58\u5728\u7740\u4ec0\u4e48\u6837\u7684\u8054\u7cfb\u5462\uff1f\u4e8b\u5b9e\u4e0a\uff0c\u6b63\u5982Comolatti\u4e0eHoel\u57282022\u5e74\u7684\u6587\u7ae0\u4e2d\u6240\u6307\u51fa\u7684\uff0c\u5305\u62ecEI\u5728\u5185\u7684\u8fd9\u4e9b\u56e0\u679c\u5ea6\u91cf\u6307\u6807\u90fd\u53ef\u4ee5\u7edf\u4e00\u8868\u8fbe\u4e3a\u4e24\u4e2a\u57fa\u672c\u8981\u7d20\u7684\u7ec4\u5408[11]\u3002\u8fd9\u4e24\u4e2a\u57fa\u672c\u8981\u7d20\u88ab\u79f0\u4e3a\u201c\u56e0\u679c\u5143\u8bed\u201d<\/span>\uff08Causal Primatives\uff09<\/span>\uff0c\u5206\u522b\u4ee3\u8868\u4e86\u56e0\u679c\u5173\u7cfb\u4e2d\u7684\u5145\u5206\u6027\u548c\u5fc5\u8981\u6027\u3002<\/span><\/section>\n

            <\/span><\/h3>\n
            6.2.1 \u56e0\u679c\u5143\u8bed\u7684\u5b9a\u4e49<\/span><\/strong><\/h3>\n

            <\/span><\/mjx-utext><\/mjx-mtext><\/mjx-mtd><\/mjx-mtr><\/mjx-itable><\/mjx-table><\/mjx-mtable><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mjx-container><\/section>\n
            \u5145\u5206\u6027\uff1a<\/span><\/mtext> <\/span><\/mtext> <\/span><\/mtext> <\/span><\/mtext><\/mtd>s<\/span><\/mi>u<\/span><\/mi>f<\/span><\/mi>f<\/span><\/mi>(<\/span><\/mo>e<\/span><\/mi>,<\/span><\/mo>c<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>P<\/span><\/mi>(<\/span><\/mo>e<\/span><\/mi>|<\/span><\/mo><\/mrow>c<\/span><\/mi>)<\/span><\/mo><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
            \u5fc5\u8981\u6027\uff1a<\/span><\/mtext> <\/span><\/mtext> <\/span><\/mtext> <\/span><\/mtext><\/mtd>n<\/span><\/mi>e<\/span><\/mi>c<\/span><\/mi>(<\/span><\/mo>e<\/span><\/mi>,<\/span><\/mo>c<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>1<\/span><\/mn>\u2212<\/span><\/mo>P<\/span><\/mi>(<\/span><\/mo>e<\/span><\/mi>|<\/span><\/mo><\/mrow>C<\/span><\/mi>\u2216<\/span><\/mi>c<\/span><\/mi>)<\/span><\/mo><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

            \u5176\u4e2d<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>c<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>e<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5206\u522b\u8868\u793a\u56e0\u4e8b\u4ef6<\/span>\uff08cause\uff09<\/span>\u548c\u679c\u4e8b\u4ef6<\/span>\uff08effect\uff09<\/span>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>C<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u56e0\u4e8b\u4ef6\u7684\u5168\u90e8\u96c6\u5408\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>C<\/span><\/mi>\u2216<\/span><\/mi>c<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5219\u4e3a\u56e0\u4e8b\u4ef6<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>c<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u8865\u96c6\uff0c\u5373<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>c<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e4b\u5916\u7684\u4e8b\u4ef6\uff0c\u4e5f\u53ef\u8bb0\u4f5c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u00ac<\/span><\/mi>c<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u5145\u5206\u6027\u8868\u660e\u5f53\u56e0\u53d1\u751f\u65f6\uff0c\u679c\u53d1\u751f\u7684\u6982\u7387\uff0c\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>s<\/span><\/mi>u<\/span><\/mi>f<\/span><\/mi>f<\/span><\/mi>=<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\uff0c\u56e0\u53d1\u751f\u786e\u5b9a\u5bfc\u81f4\u679c\u53d1\u751f\uff1b\u800c\u5fc5\u8981\u6027\u5219\u8861\u91cf\u5f53\u56e0\u4e0d\u53d1\u751f\u65f6\uff0c\u679c\u4e5f\u4e0d\u53d1\u751f\u7684\u6982\u7387\uff1b\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>n<\/span><\/mi>e<\/span><\/mi>c<\/span><\/mi>=<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\uff0c\u56e0\u4e0d\u53d1\u751f\u5219\u679c\u4e00\u5b9a\u4e0d\u53d1\u751f\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u6709\u4e9b\u56e0\u679c\u6307\u6807\u4e2d\u7684\u5fc5\u8981\u6027\u8868\u73b0\u4e3a\u4ee5\u4e0b\u7684\u53d8\u578b\u5f62\u5f0f\uff0c\u5728\u6b64\u4e5f\u7ed9\u51fa\u5b9a\u4e49\uff1a<\/span><\/section>\n

            <\/mtext><\/msup><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
            \u5fc5\u8981\u6027<\/span><\/mtext>\u2032<\/span><\/mo><\/msup>\uff1a<\/span><\/mtext> <\/span><\/mtext> <\/span><\/mtext> <\/span><\/mtext>n<\/span><\/mi>e<\/span><\/mi>c<\/span><\/mi>\u2032<\/span><\/mo><\/msup>(<\/span><\/mo>e<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>1<\/span><\/mn>\u2212<\/span><\/mo>P<\/span><\/mi>(<\/span><\/mo>e<\/span><\/mi>|<\/span><\/mo><\/mrow>C<\/span><\/mi>)<\/span><\/mo><\/mtd><\/mtr><\/mtable><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

            <\/span><\/section>\n
            \u6839\u636e\u5b9a\u4e49\uff0c\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>c<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u6781\u5c0f\u6982\u7387\u4e8b\u4ef6\u65f6\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>n<\/span><\/mi>e<\/span><\/mi>c<\/span><\/mi>(<\/span><\/mo>e<\/span><\/mi>,<\/span><\/mo>c<\/span><\/mi>)<\/span><\/mo>\u2248<\/span><\/mo>n<\/span><\/mi>e<\/span><\/mi>c<\/span><\/mi>\u2032<\/span><\/mo><\/msup>(<\/span><\/mo>e<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>C<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u8fde\u7eed\u72b6\u6001\u7a7a\u95f4\u65f6\uff0c\u53ef\u8ba4\u4e3a\u4e24\u8005\u7b49\u4ef7\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u6ce8\u610f\uff1a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>n<\/span><\/mi>e<\/span><\/mi>c<\/span><\/mi>\u2032<\/span><\/mo><\/msup>(<\/span><\/mo>e<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u5b9a\u4e49\u4e0e\u6587\u732e[11]\u4e2d\u5b9a\u4e49\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>n<\/span><\/mi>e<\/span><\/mi>c<\/span><\/mi>\u2020<\/span><\/mo><\/msup>(<\/span><\/mo>e<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>P<\/span><\/mi>(<\/span><\/mo>e<\/span><\/mi>|<\/span><\/mo><\/mrow>C<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e0d\u540c\uff0c\u4e24\u8005\u5173\u7cfb\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>n<\/span><\/mi>e<\/span><\/mi>t<\/span><\/mi>\u2032<\/span><\/mo><\/msup>(<\/span><\/mo>e<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>1<\/span><\/mn>\u2212<\/span><\/mo>n<\/span><\/mi>e<\/span><\/mi>c<\/span><\/mi>\u2020<\/span><\/mo><\/msup>(<\/span><\/mo>e<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/section>\n

            <\/span><\/h3>\n
            6.2.2 \u56e0\u679c\u5143\u8bed\u4e0e\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027<\/span><\/strong><\/h3>\n

            <\/span><\/section>\n
            \u5982\u524d\u6240\u8ff0\uff0cEI\u53ef\u88ab\u5206\u89e3\u4e3a\u786e\u5b9a\u6027\u4e0e\u7b80\u5e76\u6027\u4e24\u9879\uff0c\u8fd9\u4e24\u9879\u5206\u522b\u5bf9\u5e94\u5145\u5206\u6027\u548c\u5fc5\u8981\u6027\u7684\u56e0\u679c\u5143\u8bed\u8868\u8fbe\uff1a<\/span><\/section>\n

            <\/span><\/section>\n
            <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-mspace><\/mjx-mstyle><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-base><\/mjx-row><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-under><\/mjx-row><\/mjx-munder><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-mrow><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mrow><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-c><\/mjx-mo><\/mjx-mrow><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
            <\/p>\n
            <\/mo><\/mrow><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

            <\/span><\/section>\n
            \u53ef\u4ee5\u770b\u5230\uff0c\u5145\u5206\u6027\u548c\u786e\u5b9a\u6027\u4e4b\u95f4\uff0c\u4ee5\u53ca\u5fc5\u8981\u6027\u548c\u7b80\u5e76\u6027\u4e4b\u95f4\u5b58\u5728\u5355\u8c03\u6620\u5c04\u5173\u7cfb\u3002\u5145\u5206\u6027\u8d8a\u9ad8\uff0c\u786e\u5b9a\u6027\u4e5f\u8d8a\u9ad8\uff1b\u5fc5\u8981\u6027\u8d8a\u9ad8\uff0c\u7b80\u5e76\u6027\u5219\u8d8a\u5c0f\u3002<\/span><\/section>\n

            <\/span><\/h3>\n
            6.2.3 <\/span>\u56e0\u679c\u5ea6\u91cf\u6307\u6807\u7684\u56e0\u679c\u5143\u8bed\u8868\u793a<\/span><\/strong><\/h3>\n

            <\/span><\/section>\n
             \u56e0\u679c\u5ea6\u91cf\u6307\u6807\u7684\u56e0\u679c\u5143\u8bed\u8868\u73b0\u5f62\u5f0f<\/span><\/strong><\/section>\n
            <\/p>\n

            <\/section>\n

            <\/span><\/h2>\n
            6.3 EI\u4e0e\u52a8\u529b\u5b66\u53ef\u9006\u6027<\/span><\/strong><\/span><\/h2>\n

            <\/span><\/section>\n
            \u6b63\u5982\u793a\u4f8bexample\u4e2d\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u6240\u793a\uff0c\u5f53\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u5448\u73b0\u4e3a\u4e00\u79cd\u6392\u5217\u7f6e\u6362\u77e9\u9635<\/span>\uff08Permutation matrix\uff09<\/span>\u7684\u65f6\u5019\uff0cEI\u4f1a\u66f4\u5927\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u53ef\u4ee5\u8bc1\u660e\uff0c\u6392\u5217\u7f6e\u6362\u77e9\u9635\u662f\u552f\u4e00\u4e00\u79cd\u80fd\u540c\u65f6\u6ee1\u8db3\u5982\u4e0b\u4e24\u4e2a\u6761\u4ef6\u7684\u77e9\u9635\uff1a<\/span><\/section>\n

            <\/span><\/section>\n
            1\u3001\u77e9\u9635\u662f\u53ef\u9006\u7684\uff1b2\u3001\u77e9\u9635\u6ee1\u8db3\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u5f52\u4e00\u5316\u6761\u4ef6\uff0c\u4e5f\u5c31\u662f\u5bf9\u4e8e\u4efb\u610f\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>i<\/span><\/mi>\u2208<\/span><\/mo>[<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>N<\/span><\/mi>]<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u6765\u8bf4\uff0c<\/span><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math>|<\/span><\/mo>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub>|<\/span><\/mo><\/mrow>1<\/span><\/mn><\/msub>=<\/span><\/mo>1<\/span><\/mn><\/mjx-assistive-mml><\/mjx-container><\/section>\n

            <\/span><\/section>\n
            \u6211\u4eec\u5c06\u8fd9\u4e00\u6027\u8d28\u79f0\u4e3a\u52a8\u529b\u5b66\u53ef\u9006\u6027\u3002\u56e0\u6b64\uff0c\u4ece\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u8bf4\uff0cEI\u8861\u91cf\u7684\u662f\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u4e00\u79cd\u52a8\u529b\u5b66\u53ef\u9006\u6027\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u91cc\u6240\u8bf4\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u52a8\u529b\u5b66\u53ef\u9006\u6027\u4e0e\u901a\u5e38\u610f\u4e49\u4e0b\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u53ef\u9006\u6027\u662f\u4e0d\u7b49\u540c\u7684\u3002\u524d\u8005\u7684\u53ef\u9006\u6027\u4f53\u73b0\u4e3a\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u7684\u53ef\u9006\u6027\uff0c\u4e5f\u5c31\u662f\u5b83\u9488\u5bf9\u72b6\u6001\u7a7a\u95f4\u4e2d\u7684\u6bcf\u4e00\u4e2a\u786e\u5b9a\u6027\u72b6\u6001\u7684\u8fd0\u7b97\u90fd\u662f\u53ef\u9006\u7684\uff0c\u6240\u4ee5\u4e5f\u79f0\u5176\u4e3a\u52a8\u529b\u5b66\u53ef\u9006\u7684\u3002\u4f46\u662f\uff0c\u6587\u732e\u4e2d\u901a\u5e38\u610f\u4e49\u4e0b\u7684\u53ef\u9006\u7684\u9a6c\u5c14\u79d1\u592b\u94fe\u5e76\u4e0d\u8981\u6c42\u8f6c\u79fb\u77e9\u9635\u662f\u53ef\u9006\u7684\uff0c\u800c\u662f\u8981\u4ee5\u7a33\u6001\u5206\u5e03\u4e3a\u65f6\u95f4\u53cd\u6f14\u5bf9\u79f0\u8f74\uff0c\u4f7f\u5f97\u5728\u52a8\u529b\u5b66P\u4f5c\u7528\u6784\u6210\u7684\u6f14\u5316\u4e0b\u7684\u6b63\u5411\u65f6\u95f4\u5f62\u6210\u7684\u72b6\u6001\u5206\u5e03\u5e8f\u5217\u548c\u9006\u5411\u72b6\u6001\u5206\u5e03\u5e8f\u5217\u5b8c\u5168\u76f8\u540c\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u7531\u4e8e\u6392\u5217\u7f6e\u6362\u77e9\u9635\u8fc7\u4e8e\u7279\u6b8a\uff0c\u6211\u4eec\u9700\u8981\u80fd\u591f\u8861\u91cf\u4e00\u822c\u7684\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u4e0e\u6392\u5217\u7f6e\u6362\u77e9\u9635\u7684\u9760\u8fd1\u7a0b\u5ea6\uff0c\u4ee5\u5ea6\u91cf\u5176\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\u3002\u5728\u6587\u732e[9]\u4e2d\uff0c\u4f5c\u8005\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u7528\u77e9\u9635\u7684\u7c7bSchatten\u8303\u6570\u6765\u5ea6\u91cf\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u6982\u7387\u8f6c\u79fb\u77e9\u9635\u7684\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\u7684\u65b9\u6cd5\uff0c\u5b9a\u4e49\u4e3a\uff1a<\/span><\/section>\n

            <\/span><\/section>\n
            <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-over><\/mjx-c><\/mjx-mo><\/mjx-base><\/mjx-row><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-under><\/mjx-row><\/mjx-munder><\/mjx-box><\/mjx-munderover><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-spacer><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msubsup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-spacer><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msubsup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
            <\/p>\n
            <\/mi><\/mrow><\/msubsup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

            <\/span><\/section>\n
            \u8fd9\u91cc\uff0c<\/span><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>|<\/span><\/mo>P<\/span><\/mi>|<\/span><\/mo>\u03b1<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u77e9\u9635P\u7684Schatten\u8303\u6570\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>\u0393<\/span><\/mi>\u03b1<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\u6307\u6807\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>\u03c3<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u6982\u7387\u8f6c\u79fb\u77e9\u9635P\u7684\u5947\u5f02\u503c\uff0c\u5e76\u4e14\u6309\u7167\u4ece\u5927\u5230\u5c0f\u7684\u987a\u5e8f\u6392\u5217\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-math>\u03b1<\/span><\/mi>\u2208<\/span><\/mo>(<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo>2<\/span><\/mn>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u4e00\u4e2a\u6307\u5b9a\u7684\u53c2\u6570\uff0c\u5b83\u8d77\u5230\u8ba9<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>\u0393<\/span><\/mi>\u03b1<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u80fd\u591f\u66f4\u591a\u5730\u53cd\u6620\u786e\u5b9a\u6027\u8fd8\u662f\u7b80\u5e76\u6027\u8fd9\u6837\u4e00\u79cd\u6743\u91cd\u6216\u503e\u5411\u6027\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4e0d\u96be\u770b\u51fa\uff0c\u5982\u679c\u8ba9<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math>\u03b1<\/span><\/mi>\u2192<\/span><\/mo>0<\/span><\/mn><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5219<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>\u0393<\/span><\/mi>\u03b1<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u5c31\u9000\u5316\u6210\u4e86\u77e9\u9635P\u7684\u79e9\uff0c\u5373\uff1a<\/span><\/section>\n

            <\/span><\/section>\n
            <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-over><\/mjx-c><\/mjx-mo><\/mjx-base><\/mjx-row><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-under><\/mjx-row><\/mjx-munder><\/mjx-box><\/mjx-munderover><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-spacer><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msubsup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n
            <\/p>\n
            <\/mn><\/mrow><\/msubsup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

            <\/span><\/section>\n
            \u800c\u77e9\u9635\u7684\u79e9\u8861\u91cf\u7684\u662f\u77e9\u9635P\u975e\u9000\u5316<\/span>\uff08\u4e5f\u5c31\u662f\u53ef\u9006\uff09<\/span>\u7684\u7a0b\u5ea6\uff0c\u4e0eDegeneracy\u6709\u7740\u7c7b\u4f3c\u7684\u6548\u679c\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u800c\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math>\u03b1<\/span><\/mi>\u2192<\/span><\/mo>2<\/span><\/mn><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5219<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>\u0393<\/span><\/mi>\u03b1<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u5c31\u9000\u5316\u6210\u4e86\u77e9\u9635P\u7684Frobinius\u8303\u6570\u7684\u5e73\u65b9\uff0c\u5373\uff1a<\/span><\/section>\n

            <\/span><\/section>\n
            <\/sub>\u8fd9\u4e00\u6307\u6807\u8861\u91cf\u7684\u662f\u77e9\u9635P\u7684\u786e\u5b9a\u6027\u7684\u7a0b\u5ea6\uff0c\u8fd9\u662f\u56e0\u4e3a\u53ea\u6709\u5f53\u77e9\u9635<\/span>P\u4e2d\u7684\u6240\u6709\u884c\u5411\u91cf\u90fd\u662f\u72ec\u70ed\u5411\u91cf<\/span>\uff08one-hot\uff09<\/span>\u7684\u65f6\u5019\uff0c<\/span><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-math>|<\/span><\/mo>|<\/span><\/mo><\/mrow>P<\/span><\/mi>|<\/span><\/mo><\/mrow>|<\/span><\/mo>F<\/span><\/mi><\/msub><\/mjx-assistive-mml><\/mjx-container>\u624d\u4f1a\u6700\u5927\uff0c\u56e0\u6b64\u5b83\u4e0eDeterminism\u6709\u7740\u7c7b\u4f3c\u7684\u8861\u91cf\u6548\u679c\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u6240\u4ee5\uff0c\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-math>\u03b1<\/span><\/mi>\u2208<\/span><\/mo>(<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo>2<\/span><\/mn>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u8fde\u7eed\u53d8\u5316\u7684\u65f6\u5019\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>\u0393<\/span><\/mi>\u03b1<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u5c31\u53ef\u4ee5\u5728\u7b80\u5e76\u6027\u4e0e\u786e\u5b9a\u6027\u4e8c\u8005\u4e4b\u95f4\u5207\u6362\u4e86\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u53d6<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math>\u03b1<\/span><\/mi>=<\/span><\/mo>1<\/span><\/mn><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u53ef\u4ee5\u8ba9<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>\u0393<\/span><\/mi>\u03b1<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u80fd\u591f\u5728\u786e\u5b9a\u6027\u4e0e\u7b80\u5e76\u6027\u4e4b\u95f4\u8fbe\u5230\u4e00\u79cd\u5e73\u8861\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u5728\u6587\u732e[9]\u4e2d\uff0c\u4f5c\u8005\u4eec\u8bc1\u660e\u4e86EI\u4e0e\u52a8\u529b\u5b66\u53ef\u9006\u6027<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>\u0393<\/span><\/mi>\u03b1<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u4e4b\u95f4\u5b58\u5728\u7740\u4e00\u79cd\u8fd1\u4f3c\u7684\u5173\u7cfb\uff1a<\/span><\/section>\n

            <\/span><\/section>\n
            <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>E<\/span><\/mi>I<\/span><\/mi>\u223c<\/span><\/mo>log<\/span><\/mi>\u2061<\/span><\/mo>\u0393<\/span><\/mi>\u03b1<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

            <\/span><\/section>\n
            \u5173\u4e8e\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\u7684\u8fdb\u4e00\u6b65\u8ba8\u8bba\u548c\u8bf4\u660e\uff0c\u8bf7\u53c2\u8003\u8bcd\u6761\uff1a\u8fd1\u4f3c\u52a8\u529b\u5b66\u53ef\u9006\u6027\uff0c\u4ee5\u53ca\u8bba\u6587\uff1a[9]<\/span><\/section>\n

            <\/span><\/section>\n
            6.4 EI\u4e0eJS\u6563\u5ea6<\/span><\/strong><\/span><\/h2>\n

            <\/span><\/section>\n
            \u6839\u636e2\u7684\u8868\u8fbe\u5f0f\uff0c\u6211\u4eec\u77e5\u9053\uff0cEI\u5b9e\u9645\u4e0a\u662f\u4e00\u79cd\u5e7f\u4e49\u7684JS\u6563\u5ea6\uff0c\u5373Jensen-Shannon divergence\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u6240\u8c13\u7684JS\u6563\u5ea6\u662f\u4e00\u79cd\u5ea6\u91cf\u4e24\u4e2a\u5b9a\u4e49\u5728\u540c\u4e00\u4e2a\u652f\u6491\u96c6\u4e0a\u7684\u6982\u7387\u5206\u5e03\u4e4b\u95f4\u5dee\u5f02\u7684\u6307\u6807\u3002\u8bbe\u4e24\u4e2a\u5b9a\u4e49\u5728\u652f\u6491\u96c6<\/span><\/sub><\/span><\/mrow><\/mjx-assistive-mml><\/mjx-container><\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\u4e0a\u7684\u6982\u7387\u5206\u5e03<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>P<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>Q<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5b83\u4eec\u4e4b\u95f4\u7684JS\u6563\u5ea6\u5b9a\u4e49\u4e3a\uff1a<\/span><\/section>\n

            <\/span><\/section>\n
            <\/p>\n

            <\/span><\/section>\n
            \u5176\u4e2d\uff0c<\/sub>\u4e3aP\u548cQ\u7684\u5e73\u5747\u5206\u5e03\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>D<\/span><\/mi>K<\/span><\/sub><\/mi>L<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u4e3aKL\u6563\u5ea6\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u4e0eKL\u6563\u5ea6\u76f8\u6bd4\uff0cJS\u6563\u5ea6\u662f\u4e00\u79cd\u5bf9\u79f0\u7684\u5ea6\u91cf\uff0c\u5373<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>J<\/span><\/mi>S<\/span><\/mi>D<\/span><\/mi>(<\/span><\/mo>P<\/span><\/mi>|<\/span><\/mo><\/mrow>|<\/span><\/mo><\/mrow>Q<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>J<\/span><\/mi>S<\/span><\/mi>D<\/span><\/mi>(<\/span><\/mo>Q<\/span><\/mi>|<\/span><\/mo><\/mrow>|<\/span><\/mo><\/mrow>P<\/span><\/mi>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u800cKL\u6563\u5ea6\u662f\u975e\u5bf9\u79f0\u7684\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u53ef\u4ee5\u770b\u51fa\uff0c\u8be5\u5f0f\u4e0e2\u5f0f\u7684\u76f8\u4f3c\u4e4b\u5904\u3002\u4e0d\u96be\u9a8c\u8bc1\uff0c\u5f53P\u548cQ\u90fd\u662f2\u7ef4\u5411\u91cf\uff0c\u4e14\u6784\u6210\u4e86\u4e00\u4e2a\u9a6c\u5c14\u79d1\u592b\u8f6c\u79fb\u77e9\u9635K\u7684\u65f6\u5019\uff0cK\u7684EI\u5c31\u662fP\u3001Q\u7684JS\u6563\u5ea6\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u8fdb\u4e00\u6b65\uff0c\u5728\u6587\u732e[17]\u4e2d\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86\u5e7f\u4e49\u7684JS\u6563\u5ea6\u4e3a\uff1a<\/span><\/section>\n

            <\/span><\/section>\n
              \uff08GJSD\uff09<\/span><\/p>\n

            <\/span><\/section>\n
            \u5176\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub>,<\/span><\/mo>i<\/span><\/mi>\u2208<\/span><\/mo>[<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>m<\/span><\/mi>]<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4e3a<\/span>\u4e00\u7ec4\u6982\u7387\u5206\u5e03\u5411\u91cf\uff0cm\u4e3a\u5b83\u4eec\u7684\u7ef4\u5ea6\uff0c\u800c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-math>\u03c0<\/span><\/mi>=<\/span><\/mo>(<\/span><\/mo>\u03c0<\/span><\/mi>1<\/span><\/sub><\/mn><\/msub>,<\/span><\/mo>\u03c0<\/span><\/mi>2<\/span><\/sub><\/mn><\/msub>,<\/span><\/mo>\u22ef<\/span><\/mo>,<\/span><\/mo>\u03c0<\/span><\/mi>n<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u4e00\u7ec4\u6743\u91cd\uff0c\u5e76\u6ee1\u8db3\uff1a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-math>\u03c0<\/span><\/mi>i<\/span><\/mi><\/msub>\u2208<\/span><\/mo>[<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo>1<\/span><\/mn>]<\/span><\/mo>,<\/span><\/mo>\u2200<\/span><\/mi>i<\/span><\/sub><\/mi>\u2208<\/span><\/mo>[<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>n<\/span><\/mi>]<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/sub><\/mn><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u901a\u8fc7\u4e0e\u516c\u5f0ftow_terms\u6bd4\u8f83\uff0c\u4e0d\u96be\u53d1\u73b0\uff0c\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-nstrut><\/mjx-c><\/mjx-mn><\/mjx-num><\/mjx-line><\/mjx-dstrut><\/mjx-c><\/mjx-mi><\/mjx-den><\/mjx-row><\/mjx-dtable><\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-math>\u03c0<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub>=<\/span><\/mo>1\/<\/span><\/mn>n<\/span><\/mi><\/mfrac><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5219<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>J<\/span><\/mi>S<\/span><\/mi>D<\/span><\/mi>\u03c0<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u5c31\u9000\u5316\u4e3aEI\u4e86\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u5728\u6587\u732e[18]\u4e2d\uff0c\u4f5c\u8005\u4eec\u8ba8\u8bba\u4e86\u5e7f\u4e49JS\u6563\u5ea6\u5728\u5206\u7c7b\u591a\u6837\u6027\u5ea6\u91cf\u65b9\u9762\u7684\u5e94\u7528\u3002\u56e0\u6b64\uff0cEI\u4e5f\u53ef\u4ee5\u7406\u89e3\u4e3a\u662f\u5bf9\u884c\u5411\u91cf\u591a\u6837\u5316\u7a0b\u5ea6\u7684\u4e00\u79cd\u5ea6\u91cf\u3002<\/span><\/section>\n

            <\/span><\/section>\n
            \u8fdb\u4e00\u6b65\uff0c\u5982\u679c\u6211\u4eec\u5c06Shannon\u71b5<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-math>H<\/span><\/mi>(<\/span><\/mo>P<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u770b\u505a\u4e00\u4e2a\u51fd\u6570\uff0c\u5219\u4e0d\u96be\u9a8c\u8bc1\uff0cH\u662f\u4e00\u4e2a\u51f9\u51fd\u6570\uff0c\u90a3\u4e48\u516c\u5f0fGJSD\u5b9e\u9645\u4e0a\u662fH\u51fd\u6570\u7684Jensen\u5dee\u8ddd\uff0c\u5373Jensen Gap\u3002\u5173\u4e8e\u8fd9\u4e00\u5dee\u8ddd\u7684\u6570\u5b66\u6027\u8d28\uff0c\u5305\u62ec\u5b83\u7684\u4e0a\u4e0b\u754c\u4f30\u8ba1\uff0c\u6709\u5927\u91cf\u7684\u8bba\u6587\u8fdb\u884c\u8ba8\u8bba[19]\u3002<\/span><\/section>\n

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            \u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n
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            1\uff1a1.0 1.1 Tononi, G.; Sporns, O. (2003). “Measuring information integration”. BMC Neuroscience. 4 (31).<\/span><\/section>\n
            2\uff1a2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Hoel, Erik P.; Albantakis, L.; Tononi, G. (2013). “Quantifying causal emergence shows that macro can beat micro”. Proceedings of the National Academy of Sciences. 110 (49): 19790\u201319795.<\/span><\/section>\n
            3\uff1a3.0 3.1 3.2 3.3 3.4 Judea Pearl; \u5218\u793c; \u6768\u77eb\u4e91; \u5ed6\u519b; \u674e\u5ec9 (4 2022). \u56e0\u679c\u8bba\u2014\u2014\u6a21\u578b\u3001\u63a8\u7406\u548c\u63a8\u65ad. \u673a\u68b0\u5de5\u4e1a\u51fa\u7248\u793e.<\/span><\/section>\n
            4\uff1a4.0 4.1 Chvykov P; Hoel E. (2021). “Causal Geometry”. Entropy. 23 (1): 24.<\/span><\/section>\n
            5\uff1a5.0 5.1 5.2 5.3 5.4 Zhang, Jiang; Liu, Kaiwei (2022). “Neural Information Squeezer for Causal Emergence”. Entropy. 25 (1): 26.<\/span><\/section>\n
            6\uff1a6.0 6.1 Mingzhe Yang; Zhipeng Wang; Kaiwei Liu; Yingqi Rong; Bing Yuan; Jiang Zhang (2024). “Finding emergence in data by maximizing effective information”. arXiv: 2308.09952.<\/span><\/section>\n
            7\uff1a7.0 7.1 Kaiwei Liu; Bing Yuan; Jiang Zhang (2024). “An Exact Theory of Causal Emergence for Stochastic Iterative Systems”. arXiv: 2405.09207.<\/span><\/section>\n
            8: Yuan, Bing; Zhang, Jiang; Lyu, Aobo; Wu, Jiaying; Wang, Zhipeng; Yang, Mingzhe; Liu, Kaiwei; Mou, Muyun; Cui, Peng (2024). “Emergence and Causality in Complex Systems: A Survey of Causal Emergence and Related Quantitative Studies”. Entropy. 26 (2): 108.<\/span><\/section>\n
            9: 9.0 9.1 9.2 9.3 Jiang Zhang; Ruyi Tao; Keng Hou Leong; Mingzhe Yang; Bing Yuan (2024). “Dynamical reversibility and a new theory of causal emergence”. arXiv.<\/span><\/section>\n
            10:Hoel, E.P. (2017). “When the Map Is Better Than the Territory”. Entropy. 19: 188.<\/span><\/section>\n
            11\uff1a11.0 11.1 Comolatti, R., & Hoel, E. (2022). Causal emergence is widespread across measures of causation. arXiv preprint arXiv:2202.01854.<\/span><\/section>\n
            12: Fitelson, B., & Hitchcock, C. (2011). Probabilistic measures of causal strength (pp. 600-627). na.<\/span><\/section>\n
            13:Suppes, P. (1973). A probabilistic theory of causality. British Journal for the Philosophy of Science, 24(4).<\/span><\/section>\n
            14:Eells, E. (1991). Probabilistic causality (Vol. 1). Cambridge University Press.<\/span><\/section>\n
            15:Cheng, P. W., & Novick, L. R. (1991). Causes versus enabling conditions. Cognition, 40(1-2), 83-120.<\/span><\/section>\n
            16:Lewis, D. (1973). Causation. The journal of philosophy, 70(17), 556-567.<\/span><\/section>\n
            17:Jianhua Lin (1991). “Divergence Measures Based on the Shannon Entropy”. IEEE TRANSACTIONS ON INFORMATION THEORY. 37 (1): 145-151.<\/span><\/section>\n
            18:Erik Englesson; Hossein Azizpour (2021). Generalized Jensen-Shannon Divergence Loss for Learning with Noisy Labels. 35th Conference on Neural Information Processing Systems (NeurIPS 2021).<\/span><\/section>\n
            19:Gao, Xiang; Sitharam, Meera; Roitberg, Adrian (2019). “Bounds on the Jensen Gap, and Implications for Mean-Concentrated Distributions” (PDF). The Australian Journal of Mathematical Analysis and Applications. 16 (2). arXiv:1712.05267.<\/span><\/section>\n

            <\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
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            \u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b<\/p>\n<\/section>\n<\/section>\n

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            \u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u4e94\u5b63<\/strong>
            <\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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            \u8de8\u5c3a\u5ea6\u3001\u8de8\u5c42\u6b21\u7684\u6d8c\u73b0\u662f\u590d\u6742\u7cfb\u7edf\u7814\u7a76\u7684\u5173\u952e\u95ee\u9898\uff0c\u751f\u547d\u8d77\u6e90\u548c\u610f\u8bc6\u8d77\u6e90\u8fd9\u4e24\u5ea7\u4ef0\u4e4b\u5f25\u9ad8\u7684\u5927\u5c71\u662f\u5176\u4ee3\u8868\u3002\u96c6\u667a\u4ff1\u4e50\u90e8\u300c\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u4e94\u5b63<\/a>\u300d\u7531\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u6559\u6388\u3001\u96c6\u667a\u4ff1\u4e50\u90e8\u521b\u59cb\u4eba\u5f20\u6c5f\u8001\u5e08\u9886\u8854\u53d1\u8d77\uff0c\u5c06\u8ffd\u8e2a\u56e0\u679c\u6d8c\u73b0\u9886\u57df\u7684\u524d\u6cbf\u8fdb\u5c55\uff0c\u5c55\u793a\u96c6\u667a\u793e\u533a\u6210\u5458\u7684\u539f\u521b\u6027\u5de5\u4f5c\uff0c\u5e0c\u671b\u63a2\u8ba8\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u3001\u590d\u6742\u7cfb\u7edf\u7684\u4f4e\u79e9\u8868\u793a\u7406\u8bba\u3001\u672c\u5f81\u5fae\u89c2\u6001\u7406\u8bba\u4e4b\u95f4\u7684\u76f8\u901a\u4e4b\u5904\uff0c\u5bf9\u590d\u6742\u7cfb\u7edf\u7684\u6d8c\u73b0\u73b0\u8c61\u6709\u66f4\u6df1\u523b\u7684\u7406\u89e3\u3002\u8bfb\u4e66\u4f1a\u4ece2024\u5e744\u670819\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u4e94\u665a20:00-22:00\u8fdb\u884c\uff0c\u6301\u7eed\u65f6\u95f4\u9884\u8ba18-10\u5468\u3002\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\u53c2\u4e0e\uff01<\/span><\/p>\n

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            \u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/section>\n
            \u835f\u8403\u590d\u6742\u7cfb\u7edf\u524d\u6cbf\u8fdb\u5c55\uff0c\u96c6\u7ed3\u56e0\u679c\u6d8c\u73b0\u5b66\u672f\u793e\u533a\uff1a\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u4e94\u5b63\u542f\u52a8<\/span><\/a>
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            \u201c\u590d\u6742 AI \u6b21\u65b9\u201d\u5f00\u653e\u5b9e\u9a8c\u5ba4\u62db\u52df<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

            <\/section>\n
            \u4f5c\u4e3a\u5317\u5e08\u5927\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u6559\u6388\u3001\u96c6\u667a\u4ff1\u4e50\u90e8\u4e0e\u96c6\u667a\u5b66\u56ed\u521b\u59cb\u4eba\u3001\u96c6\u667a\u79d1\u5b66\u7814\u7a76\u4e2d\u5fc3\u9662\u957f\uff0c\u5f20\u6c5f\u4ece2003\u5e74\u5f00\u59cb\u957f\u671f\u4ece\u4e8b\u6709\u5173\u590d\u6742\u7cfb\u7edf\u5efa\u6a21\u7684\u5de5\u4f5c\u3002\u8fd1\u5e74\u6765\uff0c\u5f20\u6c5f\u5e26\u9886\u7740\u5317\u5e08\u5927\u7684\u7814\u7a76\u7ec4\u5f00\u59cb\u805a\u7126\u5728\u57fa\u4e8e\u65b0\u5174AI\u6280\u672f\u8fdb\u884c\u57fa\u4e8e\u6570\u636e\u9a71\u52a8\u7684\u81ea\u52a8\u5efa\u6a21\u7814\u7a76\uff0c\u5e76\u7acb\u5fd7\u7834\u89e3\u590d\u6742\u7cfb\u7edf\u7684\u6d8c\u73b0\u4e4b\u8c1c\u3002\u6211\u4eec\u5e0c\u671b\u53ef\u4ee5\u6709\u5bf9\u590d\u6742\u7cfb\u7edf\u81ea\u52a8\u5efa\u6a21\u9886\u57df\u6709\u70ed\u60c5\uff0c\u4e14\u8ba4\u53ef\u8fd9\u4e2a\u9886\u57df\u53d1\u5c55\u524d\u666f\u7684\u670b\u53cb\u4e00\u8d77\u6765\u5408\u4f5c\uff0c\u4fc3\u8fdb\u8fd9\u4e00\u9886\u57df\u7684\u5feb\u901f\u53d1\u5c55\u3002<\/span>\u6211\u4eec\u5e0c\u671b\u8fd9\u4e2a\u53eb\u505a\u201c Complexity <\/span>AI<\/sup> \u201d\uff0c\u4e2d\u6587\u53eb\u505a\u201c\u590d\u6742AI\u6b21\u65b9\u201d\u7684\u5f00\u653e\u5b9e\u9a8c\u5ba4\uff0c\u80fd\u591f\u771f\u6b63\u5b9e\u73b0\u601d\u60f3\u5171\u4eab\u3001\u8d44\u6e90\u5171\u4eab\u3001\u8de8\u5b66\u79d1\u4ea4\u53c9\uff0c\u5171\u540c\u4e3a\u590d\u6742\u7cfb\u7edf\u81ea\u52a8\u5efa\u6a21\u800c\u594b\u8fdb\u3002<\/span><\/p>\n

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            \u8be6\u60c5\u8bf7\u89c1\uff1a<\/span>\u201c\u590d\u6742 AI \u6b21\u65b9\u201d\u5f00\u653e\u5b9e\u9a8c\u5ba4\u62db\u52df\uff0c\u6311\u6218\u201c\u6d8c\u73b0\u201d\u96be\u9898<\/a><\/span><\/p>\n

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            \u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/strong><\/section>\n
            1. <\/strong>\u96c6\u667a\u79d1\u5b66\u7814\u7a76\u4e2d\u5fc3\u91cd\u78c5\u7efc\u8ff0\uff1a\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u56e0\u679c\u548c\u6d8c\u73b0<\/a><\/strong><\/span><\/section>\n
            2. <\/strong>\u4ec0\u4e48\u662f\u6d8c\u73b0\uff1f\u4eba\u5de5\u667a\u80fd\u7ed9\u4f60\u7b54\u6848<\/a><\/strong><\/span><\/section>\n
            3.<\/strong> \u56e0\u679c\u6d8c\u73b0\uff1a\u6982\u5ff5\u3001\u7406\u8bba\u5230\u5e94\u7528\uff5c\u96c6\u667a\u767e\u79d1<\/a><\/strong><\/span><\/section>\n
            4. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
            5.<\/strong> \u9f99\u5e74\u5927\u8fd0\u8d77\uff0c\u5b66\u4e60\u6b63\u5f53\u65f6\uff01\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/strong><\/strong><\/section>\n
            6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n

            <\/p>\n

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            \u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/strong><\/span><\/strong><\/span><\/strong><\/p>\n
            <\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
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