{"id":53932,"date":"2024-12-01T18:55:03","date_gmt":"2024-12-01T10:55:03","guid":{"rendered":"https:\/\/swarma.org\/?p=53932"},"modified":"2024-12-01T18:55:03","modified_gmt":"2024-12-01T10:55:03","slug":"%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e6%a1%86%e6%9e%b6nis%ef%bc%9a%e9%80%9a%e8%bf%87%e6%9c%80%e5%a4%a7%e5%8c%96%e6%9c%89%e6%95%88%e4%bf%a1%e6%81%af%e8%af%86%e5%88%ab%e5%9b%a0%e6%9e%9c-2","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=53932","title":{"rendered":"\u673a\u5668\u5b66\u4e60\u6846\u67b6NIS+\uff1a\u901a\u8fc7\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\u8bc6\u522b\u201c\u56e0\u679c\u6d8c\u73b0\u201d\uff5c\u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
\n
\n
\n
\n

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

\n
\n
\n
\n
\n
\n

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

\u5bfc\u8bed<\/strong><\/p>\n<\/section>\n<\/section>\n

\n

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

NIS+\uff08Neural Information Squeezer Plus\uff09\u662f\u4e00\u4e2a\u673a\u5668\u5b66\u4e60\u6846\u67b6\uff0c\u53ef\u4ee5\u4ece\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u4e2d\u5b66\u4e60\u51fa\u7cfb\u7edf\u5728\u5fae\u89c2\u3001\u5b8f\u89c2\u4e0d\u540c\u5c3a\u5ea6\u7684\u52a8\u529b\u5b66\uff0c\u5e76\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u3002\u8be5\u6846\u67b6\u901a\u8fc7\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\uff0c\u5f97\u5230\u4e00\u4e2a\u5b8f\u89c2\u52a8\u6001\u6a21\u578b\uff0c\u5b83\u662f\u5bf9NIS\u6846\u67b6\u7684\u63a8\u5e7f\u3002\u6a21\u62df\u548c\u5b9e\u9645\u6570\u636e\u4e0a\u7684\u591a\u9879\u5b9e\u9a8c\u53ef\u4ee5\u8bc1\u660e\u8be5\u6846\u67b6\u7684\u6709\u6548\u6027\uff0c\u4ee5\u53ca\u5728\u4e0d\u540c\u6d4b\u8bd5\u73af\u5883\u91cc\u8868\u73b0\u51fa\u7684\u66f4\u5f3a\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/span><\/strong><\/span><\/strong><\/p>\n


<\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n

\u8fd1\u5e74\u6765\uff0c\u5f20\u6c5f\u8001\u5e08<\/span><\/strong>\u5e26\u9886\u7814\u7a76\u7ec4\u5f00\u59cb\u805a\u7126\u57fa\u4e8e\u65b0\u5174AI\u6280\u672f\u8fdb\u884c\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\u521b\u5efa\u4e00\u4e2a\u53eb\u505a\u201c\u590d\u6742AI\u6b21\u65b9\u201d\u7684\u5f00\u653e\u5b9e\u9a8c\u5ba4<\/a>\uff0c\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\u6b22\u8fce\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><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n

\n


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

\u5173\u952e\u8bcd\uff1a\u56e0\u679c\u6d8c\u73b0\uff0c\u6709\u6548\u4fe1\u606f\uff0c\u4fe1\u606f\u5206\u89e3\uff0c\u673a\u5668\u5b66\u4e60\uff0c\u5206\u5e03\u5916\u6cdb\u5316<\/strong><\/span><\/strong><\/strong><\/strong><\/section>\n
<\/strong><\/strong><\/section>\n
<\/strong><\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
<\/section>\n<\/section>\n
\n

\u6f58\u7433\u8389\u3001\u5f20\u6c5f<\/span> <\/span>| \u4f5c\u8005<\/span><\/p>\n

\u5f20\u6c5f\u3001\u6f58\u7433\u8389\u3001\u6768\u660e\u54f2<\/span> <\/span>| \u5ba1\u6821<\/span><\/span><\/p>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

\u76ee\u5f55<\/strong><\/p>\n

\n

1. \u95ee\u9898\u4e0e\u80cc\u666f<\/span><\/strong><\/p>\n

1.1 \u56e0\u679c\u6d8c\u73b0\u8bc6\u522b<\/span><\/section>\n

1.1.1 \u57fa\u4e8e\u4fe1\u606f\u5206\u89e3\u7684\u56e0\u679c\u6d8c\u73b0\u8bc6\u522b<\/span><\/p>\n

1.1.2 NIS\u7cfb\u5217<\/span><\/p>\n

1.2 \u673a\u5668\u5b66\u4e60\u9886\u57df\u7684\u5206\u5e03\u5916\u6cdb\u5316\u95ee\u9898<\/span><\/section>\n

2. \u95ee\u9898\u63cf\u8ff0<\/span><\/strong><\/p>\n

3. NIS\u6846\u67b6\u53ca\u5176\u7f3a\u9677<\/span><\/strong><\/p>\n

4. \u5f3a\u5316\u7248\u795e\u7ecf\u4fe1\u606f\u538b\u7f29\u673a\uff08NIS+\uff09<\/span><\/strong><\/p>\n

4.1 \u6a21\u578b\u6846\u67b6<\/span><\/section>\n
4.2 NIS+ \u6846\u67b6\u6709\u6548\u6027\u7684\u9a8c\u8bc1\uff08\u6570\u503c\u5b9e\u9a8c\uff09<\/span><\/section>\n
4.2.1 SIR\u6a21\u578b\u6570\u636e<\/span><\/section>\n

4.2.1.1 NIS+\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u7684\u80fd\u529b<\/span><\/p>\n

4.2.1.2 NIS+\u4e0e\u5176\u4ed6\u6a21\u578b\u6bd4\u8f83\u9884\u6d4b\u548c\u6cdb\u5316\u80fd\u529b<\/span><\/p>\n

4.2.1.3 NIS+\u80fd\u5426\u53d1\u73b0\u771f\u6b63\u7684\u5b8f\u89c2\u52a8\u6001<\/span><\/p>\n

4.2.2 Boids \u6a21\u578b\u6570\u636e<\/span><\/section>\n
4.2.2.1 NIS+\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u7684\u80fd\u529b<\/span><\/section>\n
4.2.2.2 NIS+\u7c97\u7c92\u5316\u7b56\u7565\u7684\u53ef\u89e3\u91ca\u6027<\/span><\/section>\n
4.2.2.3 NIS+\u7684\u6cdb\u5316\u80fd\u529b<\/span><\/section>\n
4.2.2.4 \u5185\u5728\u566a\u97f3\u548c\u5916\u90e8\u566a\u97f3\u5bf9NIS+\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u7684\u5f71\u54cd<\/span><\/section>\n
4.2.3 \u751f\u547d\u6e38\u620f\u6a21\u578b\u6570\u636e<\/span><\/section>\n
4.2.3.1 NIS+\u7684\u62d3\u5c55<\/span><\/section>\n
4.2.3.2 NIS+\u6355\u83b7\u6a21\u5f0f\u7684\u80fd\u529b<\/span><\/section>\n
4.2.3.3 NIS+\u7684\u6cdb\u5316\u80fd\u529b<\/span><\/section>\n
4.2.3.4 NIS+\u8bc6\u522bCE\u7684\u80fd\u529b<\/span><\/section>\n
4.2.4 \u5927\u8111fMRI \u771f\u5b9e\u6570\u636e<\/span><\/section>\n
4.2.4.1 \u5bf9\u5fae\u89c2\u72b6\u6001\u7684\u9884\u6d4b\u80fd\u529b<\/span><\/section>\n
4.2.4.2 \u5c1d\u8bd5\u7814\u7a76\u7c97\u7c92\u5316\u5982\u4f55\u5c06\u8f93\u5165\u6570\u636e\u8f6c\u5316\u4e3a\u4e00\u7ef4\u5b8f\u89c2\u72b6\u6001<\/span><\/section>\n
4.3 \u5173\u952e\u5b9a\u7406\u4e0e\u8bc1\u660e<\/span><\/section>\n
4.3.1 \u5b8f\u89c2EI\u7684\u53d8\u5206\u4e0b\u754c<\/span><\/section>\n
4.3.2 \u7f16\u7801\u5668\u7684\u901a\u7528\u903c\u8fd1\u5b9a\u7406<\/span><\/section>\n
4.4 \u673a\u5668\u5b66\u4e60\u7b97\u6cd5<\/span><\/section>\n
4.4.1 \u6837\u672c\u91cd\u52a0\u6743<\/span><\/section>\n
4.4.2 \u53cd\u5411\u52a8\u529b\u5b66<\/span><\/section>\n

5. \u603b\u7ed3\u4e0e\u5c55\u671b<\/span><\/strong><\/p>\n

5.1 \u603b\u7ed3<\/span><\/section>\n
5.2 \u5c55\u671b<\/span><\/section>\n
<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

1. \u95ee\u9898\u4e0e\u80cc\u666f<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u5728\u81ea\u7136\u754c\u548c\u4eba\u7c7b\u793e\u4f1a\u4e2d\uff0c\u5b58\u5728\u7740\u8bb8\u591a\u7531\u65e0\u6570\u76f8\u4e92\u4f5c\u7528\u7684\u5143\u7d20\u6784\u6210\u7684\u590d\u6742\u7cfb\u7edf\uff0c\u5982\u6c14\u5019\u7cfb\u7edf\u3001\u751f\u6001\u7cfb\u7edf\u3001\u9e1f\u7fa4\u3001\u8681\u7fa4\u3001\u7ec6\u80de\u548c\u5927\u8111\u7b49\u3002\u8fd9\u4e9b\u7cfb\u7edf\u5c55\u73b0\u51fa\u4e30\u5bcc\u7684\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u884c\u4e3a\u3002\u5982\u679c\u6211\u4eec\u4ec5\u5173\u6ce8\u5fae\u89c2\u7684\u5c3a\u5ea6\uff0c\u4f1a\u53d1\u73b0\u5b83\u4eec\u7684\u884c\u4e3a\u975e\u5e38\u590d\u6742\u4e14\u96be\u4ee5\u9884\u6d4b\u3002\u5f53\u6211\u4eec\u4ece\u66f4\u5b8f\u89c2\u7684\u5c3a\u5ea6\u89c2\u5bdf\u8fd9\u4e9b\u7cfb\u7edf\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u66f4\u52a0\u7b80\u6d01\u7684\u8bed\u8a00\u548c\u89c4\u5f8b\u6765\u63cf\u8ff0\u548c\u9884\u6d4b\u8fd9\u4e9b\u7cfb\u7edf\u3002\u8fd9\u79cd\u5b8f\u89c2\u6240\u5c55\u73b0\u51fa\u7684\u65e0\u6cd5\u7b80\u5355\u5f52\u56e0\u4e8e\u5fae\u89c2\u7684\u5c5e\u6027\u6216\u89c4\u5f8b\u4fbf\u662f\u590d\u6742\u7cfb\u7edf\u72ec\u6709\u7684\u6d8c\u73b0\u73b0\u8c61\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u6d8c\u73b0\u73b0\u8c61\u4e0e\u56e0\u679c\u5173\u7cfb\u7d27\u5bc6\u76f8\u8fde\u3002\u4e00\u65b9\u9762\uff0c\u6d8c\u73b0\u662f\u7cfb\u7edf\u5185\u90e8\u5404\u5143\u7d20\u95f4\u590d\u6742\u975e\u7ebf\u6027\u56e0\u679c\u4f5c\u7528\u7684\u7ed3\u679c\uff1b\u53e6\u4e00\u65b9\u9762\uff0c\u8fd9\u4e9b\u6d8c\u73b0\u7684\u7279\u6027\u53c8\u4f1a\u5bf9\u7cfb\u7edf\u4e2d\u7684\u4e2a\u4f53\u4ea7\u751f\u4e00\u5b9a\u7684\u56e0\u679c\u529b\u3002\u540c\u65f6\uff0c\u590d\u6742\u7cfb\u7edf\u5f80\u5f80\u4f1a\u5728\u4e0d\u540c\u7684\u5c3a\u5ea6\u5c55\u73b0\u51fa\u4e0d\u540c\u7684\u56e0\u679c\u89c4\u5f8b\uff0c\u6709\u7684\u65f6\u5019\u6211\u4eec\u4ece\u5fae\u89c2\u53ef\u4ee5\u66f4\u597d\u5730\u628a\u63e1\u590d\u6742\u7cfb\u7edf\u7684\u89c4\u5f8b\uff0c\u6709\u7684\u65f6\u5019\u5219\u9700\u8981\u8fc7\u6e21\u5230\u5b8f\u89c2\u5c3a\u5ea6\u6765\u628a\u63e1\u590d\u6742\u7cfb\u7edf\u7684\u56e0\u679c\u89c4\u5f8b\u3002\u56e0\u679c\u6d8c\u73b0\u8fd9\u4e2a\u6982\u5ff5\u63cf\u8ff0\u4e86\u5b8f\u89c2\u5c42\u9762\u76f8\u5bf9\u4e8e\u5fae\u89c2\u5c42\u9762\u5728\u56e0\u679c\u6548\u5e94\u4e0a\u53ef\u80fd\u4f1a\u589e\u5f3a\u8fd9\u4e00\u73b0\u8c61\uff0c\u8fd9\u63ed\u793a\u4e86\u540c\u4e00\u4e2a\u7cfb\u7edf\u5728\u5b8f\u89c2\u4e0e\u5fae\u89c2\u4e24\u79cd\u5c3a\u5ea6\u4e4b\u95f4\u7684\u5dee\u5f02\u548c\u8054\u7cfb\u3002\u8be5\u6982\u5ff5\u6700\u65e9\u7531\u7f8e\u56fd\u7406\u8bba\u795e\u7ecf\u79d1\u5b66\u7814\u7a76\u8005Erik Hoel\u548c\u6574\u5408\u4fe1\u606f\u4e4b\u7236Tononi\u6240\u521b\u5efa\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u56e0\u679c\u6d8c\u73b0\u7684\u6982\u5ff5\u4e0d\u4ec5\u5c06\u56e0\u679c\u63a8\u65ad\u4e0e\u590d\u6742\u7cfb\u7edf\u7684\u6d8c\u73b0\u7279\u6027\u76f8\u7ed3\u5408\uff0c\u800c\u4e14\u4e3a\u89e3\u51b3\u4e00\u7cfb\u5217\u54f2\u5b66\u95ee\u9898\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5b9a\u91cf\u5316\u7684\u89c6\u89d2\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u76ee\u524d\uff0c\u5173\u4e8e\u5982\u4f55\u5b9a\u4e49\u56e0\u679c\u6d8c\u73b0\uff0c\u4eba\u4eec\u5206\u522b\u63d0\u51fa\u4e86\u56db\u4e2a\u6709\u4ee3\u8868\u6027\u7684\u7406\u8bba\uff0c\u5206\u522b\u662f\uff1a\u2460Hoel\u7b49\u57fa\u4e8e\u6709\u6548\u4fe1\u606f\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba<\/span>\uff08\u7b80\u79f0Hoel\u7b49\u4eba\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\uff09<\/span>[1][2]\u3001\u2461Rosas\u7b49\u57fa\u4e8e\u4fe1\u606f\u5206\u89e3\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba<\/span>\uff08\u7b80\u79f0Rosas\u7b49\u4eba\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\uff09<\/span>[3]\u3001\u2462\u5f20\u6c5f\u7b49\u4eba\u57fa\u4e8e\u53ef\u9006\u6027\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba[4]\u3001\u2463Barnett\u7b49\u7684\u57fa\u4e8e\u52a8\u529b\u5b66\u89e3\u8026\u7684\u6d8c\u73b0\u7406\u8bba[5]\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5177\u4f53\u5185\u5bb9\u53ef\u4ee5\u53c2\u8003\u8bcd\u6761\u56e0\u679c\u6d8c\u73b0\u3002<\/span><\/section>\n

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

1.1 \u56e0\u679c\u6d8c\u73b0\u8bc6\u522b<\/span><\/strong><\/span><\/h2>\n


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

\u4e0a\u8ff0\u7406\u8bba\u6846\u67b6\u5f88\u597d\u5730\u5b9a\u91cf\u523b\u753b\u4e86\u5404\u79cd\u6d8c\u73b0\u73b0\u8c61\u3002\u4f46\u662f\u5728\u73b0\u5b9e\u4e2d\uff0c\u6211\u4eec\u66f4\u9700\u8981\u89e3\u51b3\u7684\u662f\u4ece\u6570\u636e\u4e2d\u8fa8\u8bc6\u51fa\u56e0\u679c\u6d8c\u73b0\u662f\u5426\u53d1\u751f\u7684\u95ee\u9898\u3002\u4ece\u6570\u636e\u4e2d\u8bc6\u522b\u51fa\u590d\u6742\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0\uff0c\u4e00\u65b9\u9762\u53ef\u4ee5\u8282\u7ea6\u9884\u6d4b\u6210\u672c\uff0c\u589e\u5f3a\u9884\u6d4b\u6548\u679c\uff0c\u5c24\u5176\u662f\u6cdb\u5316\u6548\u679c\uff1b\u53e6\u4e00\u65b9\u9762\u4e5f\u53ef\u80fd\u8bf1\u5bfc\u6216\u8005\u9884\u9632\u6d8c\u73b0\u7684\u53d1\u751f\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u4e00\u4e9b\u5fae\u89c2\u6570\u636e\u96be\u4ee5\u6355\u6349\uff0c\u6211\u4eec\u5f80\u5f80\u53ea\u80fd\u6536\u96c6\u5230\u89c2\u6d4b\u6570\u636e\uff0c\u5e76\u63a8\u65ad\u7cfb\u7edf\u7684\u771f\u5b9e\u52a8\u529b\u5b66\u3002\u56e0\u6b64\uff0c\u4ece\u53ef\u89c2\u6d4b\u6570\u636e\u4e2d\u8bc6\u522b\u7cfb\u7edf\u4e2d\u56e0\u679c\u6d8c\u73b0\u7684\u53d1\u751f\u662f\u4e00\u4e2a\u5173\u952e\u7684\u95ee\u9898\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8fd1\u5e74\u6765\uff0c\u57fa\u4e8e\u795e\u7ecf\u7f51\u7edc\u7684\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u53d6\u5f97\u4e86\u7a81\u7834\u6027\u8fdb\u5c55[6][7][8][9][10]\uff0c\u501f\u52a9\u6b64\u65b9\u6cd5\uff0c\u4ee5\u6570\u636e\u9a71\u52a8\u7684\u65b9\u5f0f\u81ea\u4e3b\u53d1\u73b0\u590d\u6742\u7cfb\u7edf\u7684\u56e0\u679c\u5173\u7cfb\u3001\u56e0\u679c\u673a\u5236\uff0c\u4ee5\u81f3\u52a8\u529b\u5b66\u90fd\u6210\u4e3a\u53ef\u80fd\u3002\u6b64\u5916\uff0c\u673a\u5668\u5b66\u4e60\u548c\u795e\u7ecf\u7f51\u7edc\u8fd8\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u627e\u5230\u66f4\u597d\u7684\u7c97\u7c92\u5316\u7b56\u7565\u3001\u4ece\u6570\u636e\u4e2d\u53d1\u73b0\u5b8f\u89c2\u5c42\u9762\u7684\u56e0\u679c\u5173\u7cfb\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4e0b\u9762\u4ecb\u7ecd\u4e24\u79cd\u56e0\u679c\u6d8c\u73b0\u7684\u8bc6\u522b\u65b9\u6cd5\uff1a\u2460\u57fa\u4e8e\u4fe1\u606f\u5206\u89e3\u7684\u56e0\u679c\u6d8c\u73b0\u8bc6\u522b\u8fd1\u4f3c\u65b9\u6cd5\u3001\u2461\u795e\u7ecf\u4fe1\u606f\u538b\u7f29\u5668\u65b9\u6cd5\u7cfb\u5217<\/span>\uff08Neural Information Squeezer\uff0c\u7b80\u79f0NIS\uff09<\/span>\u3002<\/span><\/section>\n

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

1.1.1 \u57fa\u4e8e\u4fe1\u606f\u5206\u89e3\u7684\u56e0\u679c\u6d8c\u73b0\u8bc6\u522b<\/span><\/strong><\/h3>\n

<\/span><\/section>\n
Rosas\u7b49\u5b66\u8005[3][11]\u901a\u8fc7\u4fe1\u606f\u5206\u89e3\u6846\u67b6\u7ed9\u51fa\u4e86\u548cHoel\u7b49\u4eba\u4e0d\u540c\u7684\u5bf9\u56e0\u679c\u6d8c\u73b0\u7684\u65b0\u5b9a\u4e49\uff0c\u5e76\u57fa\u4e8e\u6b64\u8bc6\u522b\u91cf\u5316\u56e0\u679c\u6d8c\u73b0\u3002\u4f46\u662f\u4fe1\u606f\u5206\u89e3\u6846\u67b6\u4e2d\u5b9a\u4e49\u7684\u4fe1\u606f\u539f\u5b50\u96be\u4ee5\u8ba1\u7b97\uff0c\u6240\u4ee5\u4f5c\u8005\u63a8\u5bfc\u51fa\u53ea\u9700\u8981\u8ba1\u7b97\u4e92\u4fe1\u606f\u7684\u8fd1\u4f3c\u516c\u5f0f\uff0c\u63d0\u51fa\u4e86\u5224\u5b9a\u56e0\u679c\u6d8c\u73b0\u53d1\u751f\u7684\u5145\u5206\u6761\u4ef6\uff0c\u5373<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/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-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a8<\/span><\/mi>t<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub>(<\/span><\/mo>V<\/span><\/mi>)<\/span><\/mo>><\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u91cc<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03a8<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u7684\u5177\u4f53\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a<\/span><\/section>\n

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

<\/p>\n


<\/span><\/section>\n
\u5f0f\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>V<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u7ed9\u5b9a\u7684\u5b8f\u89c2\u72b6\u6001\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub>\u3001<\/span><\/mjx-utext><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>V<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>\u3001<\/span><\/mo><\/mrow>V<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4ee3\u8868\u4e24\u4e2a\u8fde\u7eed\u65f6\u95f4\u7684\u5b8f\u89c2\u72b6\u6001\u53d8\u91cf\uff0c<\/sub>\u8868\u793a\u7b2c j \u7ef4t\u65f6\u523b\u7684\u5fae\u89c2\u53d8\u91cf\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>I<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4ee3\u8868\u4e92\u4fe1\u606f\uff0c\u6bd4\u5982<\/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-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-mrow><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>I<\/span><\/mi>(<\/span><\/mo>V<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>;<\/span><\/mo>V<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub>)<\/span><\/mo><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>V<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>V<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e4b\u95f4\u7684\u4e92\u4fe1\u606f\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/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-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a8<\/span><\/mi>t<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub>(<\/span><\/mo>V<\/span><\/mi>)<\/span><\/mo>><\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u7cfb\u7edf\u53d1\u751f\u56e0\u679c\u6d8c\u73b0\u3002\u4f46\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a8<\/span><\/mi><\/mrow><<\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u6211\u4eec\u4e0d\u80fd\u786e\u5b9a\u7cfb\u7edf\u662f\u5426\u53d1\u751f\u56e0\u679c\u6d8c\u73b0\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u9700\u8981\u6307\u51fa\u7684\u662f\uff0cRosas\u7684\u56e0\u679c\u6d8c\u73b0\u8bc6\u522b\u65b9\u6cd5\u662f\u5bf9\u4e92\u4fe1\u606f\u8fdb\u884c\u8fdb\u4e00\u6b65\u5206\u89e3\uff0c\u6574\u4e2a\u8fc7\u7a0b\u6ca1\u6709\u5f15\u5165do\u5e72\u9884\uff0c\u56e0\u800c\u662f\u57fa\u4e8e\u76f8\u5173\u6027\u5ea6\u91cf\u7684\u3002\u800cHoel\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u5219\u662f\u57fa\u4e8eJudea Pearl\u7684\u56e0\u679c\u7406\u8bba\uff0c\u5e76\u5f15\u5165\u4e86do\u64cd\u4f5c\u7684\u3002<\/span><\/section>\n

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

Rosas\u65b9\u6cd5\u56e0\u4e3a\u662f\u57fa\u4e8e\u76f8\u5173\u6027\u7684\uff0c\u6240\u4ee5\u8ba1\u7b97\u6bd4\u8f83\u65b9\u4fbf\uff0c\u4e0d\u9700\u8981\u627e\u5230\u5e95\u5c42\u7684\u52a8\u529b\u5b66\u673a\u5236\u3002\u4e14\u5bf9\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u6ca1\u6709\u9a6c\u5c14\u53ef\u592b\u6027\u7684\u5047\u8bbe\u548c\u8981\u6c42\u3002\u4f46\u662f\u8be5\u65b9\u6cd5\u4e5f\u5b58\u5728\u4e00\u4e9b\u7f3a\u70b9\uff1a<\/span><\/p>\n

    \n
  • \n
    \u8be5\u65b9\u6cd5\u53ea\u662f\u57fa\u4e8e\u4e92\u4fe1\u606f\u8ba1\u7b97\uff0c\u56e0\u6b64\u5f97\u5230\u7684\u7ed3\u679c\u4ec5\u4ec5\u662f\u76f8\u5173\u6027\u523b\u753b\u800c\u4e0d\u662f\u56e0\u679c\u6027\u7684\u523b\u753b\uff1b<\/span><\/section>\n<\/li>\n
  • \n
    \u8be5\u5224\u522b\u65b9\u6cd5\u5f97\u5230\u7684\u4ec5\u4ec5\u662f\u53d1\u751f\u56e0\u679c\u6d8c\u73b0\u7684\u8fd1\u4f3c\u7684\u5145\u5206\u6761\u4ef6\uff1b<\/span><\/section>\n<\/li>\n
  • \n
    \u8be5\u65b9\u6cd5\u9700\u8981\u624b\u52a8\u7ed9\u5b9a\u7c97\u7c92\u5316\u7b56\u7565\uff0c\u4ee5\u53ca\u57fa\u4e8e\u6b64\u7c97\u7c92\u5316\u5f97\u5230\u5b8f\u89c2\u53d8\u91cfV\uff0c\u800c\u4e0d\u540c\u7684\u7c97\u7c92\u5316\u6d4b\u91cf\u4f1a\u5bf9\u7ed3\u679c\u9020\u6210\u4e0d\u540c\u7684\u663e\u8457\u5f71\u54cd\uff1b<\/span><\/section>\n<\/li>\n
  • \n

    \u5728\u9ad8\u7ef4\u7cfb\u7edf\u4e2d\uff0c\u03a8\u4f5c\u4e3a\u8fd1\u4f3c\u6761\u4ef6\uff0c\u8bef\u5dee\u975e\u5e38\u5927\uff0c\u5f88\u5bb9\u6613\u5f97\u5230\u8d1f\u503c\uff0c\u4ece\u800c\u65e0\u6cd5\u51c6\u786e\u5730\u5224\u65ad\u662f\u5426\u6709\u56e0\u679c\u6d8c\u73b0\u53d1\u751f\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n


    <\/section>\n
    \u4e3a\u4e86\u80fd\u591f\u81ea\u52a8\u627e\u5230\u6700\u4f73\u7684\u7c97\u7c92\u5316\u7b56\u7565\uff0c\u8fd9\u5957\u7406\u8bba\u6846\u67b6\u4e5f\u53d1\u5c55\u51fa\u4e86\u76f8\u5e94\u7684\u673a\u5668\u5b66\u4e60\u6c42\u89e3\u65b9\u6848[12]\u3002Kaplanis\u7b49\u4eba\u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u65b9\u6cd5\u5b66\u4e60\u5b8f\u89c2\u6001<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>V<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4ee5\u53ca\u6700\u5927\u5316<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a8<\/span><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff1a\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u6765\u5b66\u4e60\u5c06\u5fae\u89c2\u8f93\u5165\u7c97\u7c92\u5316\u6210\u5b8f\u89c2\u8f93\u51fa\uff0c\u540c\u65f6\u4f7f\u7528\u4e24\u4e2a\u795e\u7ecf\u7f51\u7edc\u6765\u5206\u522b\u5b66\u4e60\u4e92\u4fe1\u606f\u7684\u8ba1\u7b97\uff0c\u6700\u540e\u901a\u8fc7\u6700\u5927\u5316\u4e24\u8005\u4e4b\u95f4\u7684\u5dee<\/span> (\u5373<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a8<\/span><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>) <\/span>\u6765\u4f18\u5316\u5b66\u4e60\u3002\u8fd9\u79cd\u65b9\u6cd5\u867d\u7136\u80fd\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u7f13\u89e3\u4e0a\u8ff0\u56f0\u5883\uff0c\u4f46\u662f\u5b83\u4ecd\u65e7\u65e0\u6cd5\u89e3\u51b3\u5927\u89c4\u6a21\u8ba1\u7b97\u7684\u95ee\u9898\u3002\u8fd9\u662f\u56e0\u4e3a\uff0c\u6839\u636e\u8be5\u673a\u5668\u5b66\u4e60\u6846\u67b6\uff0c\u795e\u7ecf\u7f51\u7edc\u7684\u6570\u91cf\u4f1a\u968f\u7740\u53d8\u91cf\u6570\u7684\u589e\u52a0\u800c\u5448\u73b0\u5e73\u65b9\u901f\u5ea6\u7684\u589e\u957f\u3002<\/span><\/section>\n

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

    1.1.2 NIS\u7cfb\u5217<\/span><\/strong><\/h3>\n

    <\/span><\/section>\n
    \u5f20\u6c5f\u7b49[13]\u5b66\u8005\u57fa\u4e8e\u795e\u7ecf\u7f51\u7edc\u63d0\u51fa\u4e86\u4e00\u79cd\u6570\u636e\u9a71\u52a8\u7684\u56e0\u679c\u6d8c\u73b0\u8bc6\u522b\u65b9\u6cd5\uff0c\u5373\u795e\u7ecf\u4fe1\u606f\u538b\u7f29\u5668<\/span>\uff08Neural Information Squeezer\uff0c\u7b80\u79f0NIS\uff09<\/span>\u3002\u8be5\u6846\u67b6\u80fd\u4ece\u65f6\u95f4\u5e8f<\/span>\u5217\u6570\u636e\u4e2d\u8bc6\u522b\u7cfb\u7edf\u4e2d\u7684\u56e0\u679c\u6d8c\u73b0\uff0c\u5e76\u4e14\u81ea\u52a8\u63d0\u53d6\u6709\u6548\u7684\u7c97\u7c92\u5316\u7b56\u7565\u548c\u5b8f\u89c2\u52a8\u529b\u5b66\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8be5\u6a21\u578b\u7531\u7f16\u7801\u5668<\/span>\uff08encoder\uff09<\/span>\u3001\u52a8\u529b\u5b66\u5b66\u4e60\u5668\uff08<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff09\u4ee5\u53ca\u89e3\u7801\u5668<\/span>\uff08decoder\uff09<\/span>\u4e09\u4e2a\u90e8\u5206\u6784\u6210\uff0c\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\u4e3b\u8981\u7531\u53ef\u9006\u795e\u7ecf\u7f51\u7edc<\/span>\uff08Invertible Neural Network\uff0c\u7b80\u79f0INN\uff09<\/span>[14]\u6784\u5efa\uff0c\u52a8\u529b\u5b66\u5b66\u4e60\u5668\u7531\u591a\u5c42\u611f\u77e5\u673a<\/span>\uff08Multilayer Perceptron\uff0c\u7b80\u79f0MLP\uff09<\/span>\u6784\u5efa\u3002\u6b64\u6a21\u578b\u6846\u67b6\u53ef\u4ee5\u770b\u6210\u662f\u4e00\u4e2a\u795e\u7ecf\u4fe1\u606f\u538b\u7f29\u5668\uff0c\u5c06\u5305\u542b\u566a\u97f3\u7684\u5fae\u89c2\u6001\u538b\u7f29\u6210\u5b8f\u89c2\u6001\uff0c\u4e22\u5f03\u65e0\u7528\u7684\u4fe1\u606f\uff0c\u4ece\u800c\u4f7f\u5f97\u5b8f\u89c2\u52a8\u529b\u5b66\u7684\u56e0\u679c\u6027\u66f4\u5f3a\u3002NIS\u65b9\u6cd5\u7684\u6a21\u578b\u6846\u67b6\u5982\u4e0b\u56fe\u6240\u793a\u3002<\/span><\/section>\n

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

    <\/span><\/section>\n
    \u56fe\u4e2d\uff0c\u6a21\u578b\u8f93\u5165\u662f\u5fae<\/span>\u89c2\u72b6\u6001<\/span><\/sub><\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u8f93\u5165\u6570\u636e\u7684\u7ef4\u6570\u3002<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u7c97\u7c92\u5316\u51fd\u6570<\/span>\uff08\u7f16\u7801\u5668\uff09<\/span>\uff0c\u5c06\u8f93\u5165\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u6570\u636e\u6620\u5c04\u5230<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u6570\u636e\u4e0a\uff0c\u5f97\u5230\u5b8f\u89c2\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u6b64\u6b65\u8fd8\u5305\u62ec\u4e86\u901a\u8fc7\u6295\u5f71\u7b97\u5b50\u629b\u5f03<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi>\u2212<\/span><\/mo>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u4fe1\u606f\u7684\u64cd\u4f5c\u3002<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u52a8\u529b\u5b66\u5b66\u4e60\u5668\uff0c\u5728\u5b8f\u89c2\u5c42\u9762\u4e0a\u5b66\u4e60\u6709\u6548\u7684\u9a6c\u5c14\u53ef\u592b\u52a8\u529b\u5b66\u3002<\/span><\/sub><\/span><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u901a\u8fc7<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>f<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u9884\u6d4b\u7684t+1\u65f6\u523b\u7684\u5b8f\u89c2\u72b6\u6001\u3002\u7531\u4e8e\u6b64\u65f6\u6570\u636e\u662f<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u7684\uff0c\u4e3a\u4e86\u4f7f\u7528\u53cd\u7c97\u7c92\u5316\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>\u2020<\/span><\/sup><\/mo><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff08\u89e3\u7801\u5668\uff09<\/span>\uff0c\u6a21\u578b\u9700\u8981\u7528<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi>\u2212<\/span><\/mo>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u9ad8\u65af\u968f\u673a\u5411\u91cf<\/span><\/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-texatom><\/mjx-mstyle><\/mjx-math>N<\/span><\/mi>(<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo>I<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u586b\u5145\u7ef4\u5ea6\u4e0d\u8db3\u7684\u6570\u636e\u3002\u5b8f\u89c2\u53d8\u91cf\u7ecf\u8fc7\u53cd\u7c97\u7c92\u5316\u51fd\u6570\u4e4b\u540e\u53ef\u4ee5\u5f97\u5230\u9884\u6d4b\u7684\u5fae\u89c2\u53d8\u91cf<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u800c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/sub>\u4e4b\u95f4\u7684\u5dee\u503c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>L<\/span><\/mi>1<\/span><\/sub><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5373\u4e3a\u9884\u6d4b\u635f\u5931\u8bc4\u4f30\u503c\uff0c\u53ef\u4ee5\u7528\u6765\u8bad\u7ec3\u6574\u4e2a\u7f51\u7edc\u67b6\u6784\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u8be5\u65b9\u6cd5\u7684\u76ee\u6807\u51fd\u6570\u662f\u5e0c\u671b\u5728\u4fdd\u8bc1\u5fae\u89c2\u72b6\u6001\u9884\u6d4b\u8bef\u5dee\u5f88\u5c0f\u7684\u6761\u4ef6\u4e0b\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\uff0c\u4fdd\u8bc1\u9884\u6d4b\u8bef\u5dee\u7ea6\u675f\u8db3\u591f\u5c0f\u662f\u4e3a\u4e86\u907f\u514d\u5e73\u51e1\u89e3<\/span>\uff08\u7c97\u7c92\u5316\u4e22\u5931\u592a\u591a\u4fe1\u606f\uff0c\u4ee5\u81f4\u5b8f\u89c2\u52a8\u529b\u5b66\u65e0\u6548\uff09<\/span>\u7684\u51fa\u73b0\u3002NIS\u6700\u7ec8\u5e0c\u671b\u5f97\u5230\u80fd\u591f\u8ba9\u6709\u6548\u4fe1\u606f\u6700\u5927\u7684\u6709\u6548\u7c97\u7c92\u5316\u7ef4\u5ea6<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3001\u7c97\u7c92\u5316\u7b56\u7565<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi><\/mrow>q<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c\u5b8f\u89c2\u52a8\u529b\u5b66<\/span><\/sub><\/mi><\/msub><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7136\u800c\uff0cNIS\u6846\u67b6\u5e76\u6ca1\u6709\u5b9e\u73b0\u771f\u6b63\u610f\u4e49\u4e0a\u7684\u5168\u53c2\u6570\u7a7a\u95f4\u7684\u6709\u6548\u4fe1\u606f\u6700\u5927\u5316\uff0c\u5b83\u53ea\u662f\u901a\u8fc7\u7ebf\u6027\u641c\u7d22\u53c2\u6570q\u7684\u65b9\u5f0f\u5b8c\u6210\u7684\u3002\u5177\u4f53\u5185\u5bb9\u8bf7\u53c2\u8003NIS\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e3a\u4e86\u89e3\u51b3\u4e0a\u8ff0NIS\u6846\u67b6\u7684\u82e5\u5e72\u95ee\u9898\uff0cNIS\u7684\u4f5c\u8005\u6240\u5728\u7684\u7814\u7a76\u7ec4\u8fdb\u4e00\u6b65\u5f00\u53d1\u4e86\u5168\u65b0\u7684\u795e\u7ecf\u7f51\u7edc\u6846\u67b6\uff0c\u5373NIS+\u3002<\/span><\/section>\n

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

    1.2 \u673a\u5668\u5b66\u4e60\u9886\u57df\u7684\u5206\u5e03\u5916\u6cdb\u5316\u95ee\u9898<\/span><\/strong><\/span><\/h2>\n

    <\/span><\/section>\n
    \u76ee\u524d\uff0c\u673a\u5668\u5b66\u4e60\u4efb\u52a1\u9700\u8981\u5efa\u7acb\u5728\u8bad\u7ec3\u6570\u636e\u548c\u6d4b\u8bd5\u6570\u636e\u662f\u72ec\u7acb\u540c\u5206\u5e03<\/span>\uff08Independent and Identically Distributed\uff0c\u7b80\u79f0IID\uff09<\/span>\u7684\u57fa\u7840\u4e4b\u4e0a\uff0c\u8fd9\u662f\u4e00\u79cd\u7406\u60f3\u5316\u7684\u5047\u8bbe\u3002\u73b0\u5b9e\u5e94\u7528\u4e2d\uff0c\u51e0\u4e4e\u4e0d\u80fd\u6ee1\u8db3IID\u5047\u8bbe\uff0c\u6240\u4ee5\u6a21\u578b\u7684\u6027\u80fd\u90fd\u4f1a\u6709\u4e0d\u540c\u7a0b\u5ea6\u7684\u4e0b\u964d[15]\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4ee5\u4e00\u4e2a\u72d7\u8bc6\u522b\u7684\u56fe\u50cf\u5224\u522b\u4efb\u52a1\u4e3a\u4f8b\u3002\u8bad\u7ec3\u56fe\u50cf\u7684\u80cc\u666f\u4e00\u822c\u662f\u5728\u8349\u5730\u4e0a\uff0c\u5305\u542b\u4e86\u5b8c\u6574\u7684\u72d7\u3002\u7ecf\u8fc7\u5927\u91cf\u6570\u636e\u8bad\u7ec3\u540e\uff0c\u82e5\u7814\u7a76\u4eba\u5458\u7ed9\u6a21\u578b\u4e00\u4e2a\u5728\u8349\u5730\u4e0a\u7684\u72d7\u7684\u56fe\u50cf\uff0c\u90a3\u6a21\u578b\u7684\u6b63\u786e\u7387\u53ef\u4ee5\u572895%\u4ee5\u4e0a\uff1b\u82e5\u7ed9\u4e00\u5f20\u5728\u6c34\u6ce5\u5730\u4e0a\uff0c\u4e14\u906e\u6321\u4e86\u72d7\u90e8\u5206\u8eab\u4f53\u7684\u56fe\u50cf\uff0c\u90a3\u4e48\u6a21\u578b\u7684\u6b63\u786e\u7387\u53ef\u80fd\u5c31\u53ea\u6709\u4e00\u534a\u4e86\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u673a\u5668\u5b66\u4e60\u7ecf\u8fc7\u8bad\u7ec3\u5b66\u4e60\u5f97\u5230\u7684\u5f88\u5927\u7a0b\u5ea6\u4e0a\u662f\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u5173\u7cfb\uff0c\u8fd9\u79cd\u76f8\u5173\u5173\u7cfb\u6709\u53ef\u80fd\u6765\u81ea\u6837\u672c\u9009\u62e9\u504f\u5dee<\/span>\uff08Sample Selection Bias\uff09<\/span>\u3002\u5f53\u8003\u8651\u4e86\u5176\u4ed6\u53d8\u91cf\u540e\uff0c\u539f\u672c\u770b\u4f3c\u6709\u76f8\u5173\u6027\u7684\u53d8\u91cf\u53ef\u80fd\u5b9e\u9645\u4e0a\u5e76\u65e0\u5173\u8054\uff0c\u8fd9\u662f\u4e00\u79cd\u865a\u5047\u7684\u76f8\u5173\u5173\u7cfb\u3002\u5728\u4e0a\u9762\u7684\u72d7\u8bc6\u522b\u7684\u4f8b\u5b50\u4e2d\uff0c\u673a\u5668\u5b66\u4e60\u5b66\u5230\u7684\u53ef\u80fd\u662f\u6839\u636e\u8349\u5730\u548c\u72d7\u9f3b\u5b50\u8fd9\u4e24\u4e2a\u56e0\u7d20\u6765\u5224\u65ad\u56fe\u7247\u4e2d\u7684\u5bf9\u8c61\u662f\u4e0d\u662f\u72d7\u7684\uff0c\u4f46\u662f\u8fd9\u4e2a\u573a\u666f\u4e2d\u771f\u6b63\u6709\u56e0\u679c\u5173\u7cfb\u7684\u56e0\u7d20\u662f\u72d7\u9f3b\u5b50\uff0c\u800c\u4e0d\u662f\u8349\u5730\u3002\u4e4b\u6240\u4ee5\u6a21\u578b\u5b66\u4e60\u5230\u4ee5\u8349\u5730\u4e3a\u7279\u5f81\uff0c\u53ef\u80fd\u662f\u56e0\u4e3a\u6837\u672c\u7684\u5206\u5e03\u4e0d\u5747\u5300<\/span>\uff08\u7edd\u5927\u90e8\u5206\u56fe\u7247\u6837\u672c\u90fd\u5305\u542b\u4e86\u8349\u5730\uff09<\/span>\u3002\u8fd9\u5c31\u5bfc\u81f4\u4e86\u6a21\u578b\u4e0d\u80fd\u6709\u6548\u8bc6\u522b\u51fa\u5728\u6c34\u91cc\u3001\u6c99\u6f20\u91cc\u7684\u72d7\u3002\u7b80\u5355\u6765\u8bf4\uff0c\u8349\u5730\u548c\u72d7\u6807\u7b7e\u4e4b\u95f4\u662f\u4e00\u79cd\u5f3a\u76f8\u5173\u3001\u5f31\u56e0\u679c\u7684\u5173\u7cfb\uff0c\u800c\u72d7\u9f3b\u5b50\u548c\u72d7\u6807\u7b7e\u4e4b\u95f4\u5219\u662f\u4e00\u79cd\u5f3a\u76f8\u5173\u3001\u5f3a\u56e0\u679c\u7684\u8054\u7cfb\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u800c\u5728\u52a8\u529b\u5b66\u7cfb\u7edf\u4e2d\uff0c\u6a21\u578b\u53ef\u80fd\u5bf9\u521d\u59cb\u6761\u4ef6\u975e\u5e38\u654f\u611f\uff0c\u5373\u4f7f\u662f\u5fae\u5c0f\u7684\u521d\u59cb\u6761\u4ef6\u53d8\u5316\u4e5f\u53ef\u80fd\u5bfc\u81f4\u7cfb\u7edf\u884c\u4e3a\u7684\u663e\u8457\u5dee\u5f02[16]\u3002\u5982\u679c\u8bad\u7ec3\u6570\u636e\u7684\u521d\u59cb\u6761\u4ef6\u5206\u5e03\u4e0e\u6d4b\u8bd5\u6570\u636e\u4e0d\u540c\uff0c\u6a21\u578b\u53ef\u80fd\u65e0\u6cd5\u51c6\u786e\u9884\u6d4b\u6d4b\u8bd5\u6570\u636e\u4e0b\u7684\u7cfb\u7edf\u884c\u4e3a\u3002\u6211\u4eec\u5e0c\u671b\u7684\u662f\uff0c\u6a21\u578b\u53ef\u4ee5\u900f\u8fc7\u521d\u59cb\u6761\u4ef6\u7684\u5dee\u5f02\uff0c\u6293\u4f4f\u7cfb\u7edf\u52a8\u529b\u5b66\u7684\u672c\u8d28\u3002\u751a\u81f3\u6709\u65f6\u5019\uff0c\u6211\u4eec\u671f\u5f85\u6a21\u578b\u53ef\u4ee5\u6cdb\u5316\u5230\u67d0\u4e9b\u52a8\u529b\u5b66\u53c2\u6570\u4e0d\u540c\u7684\u7cfb\u7edf\u6d4b\u8bd5\u6570\u636e\u4e0a\uff0c\u8ba9\u6a21\u578b\u4f9d\u65e7\u6709\u4e0d\u9519\u7684\u8868\u73b0\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u5e0c\u671b\u5b66\u4e60\u5230\u7684\u662f\u56e0\u679c\u5173\u7cfb<\/span>\uff08Causation\uff09<\/span>[17]\u800c\u4e0d\u662f\u865a\u5047\u7684\u76f8\u5173\uff0c\u53ea\u6709\u8fd9\u6837\u624d\u80fd\u4f7f\u5f97\u7ed3\u679c\u66f4\u52a0\u7a33\u5b9a\u4e14\u5177\u6709\u53ef\u89e3\u91ca\u6027\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5206\u5e03\u5916\u6cdb\u5316<\/span>\uff08Out-of-Distribution Generalization\uff0c\u7b80\u79f0OOD Generalization\uff09<\/span>\u662f\u6307\u6a21\u578b\u5728\u9762\u5bf9\u4e0e\u8bad\u7ec3\u6570\u636e\u5206\u5e03\u4e0d\u540c\u7684\u65b0\u6570\u636e\u65f6\uff0c\u4ecd\u7136\u80fd\u591f\u4fdd\u6301\u8f83\u597d\u7684\u6027\u80fd\u3002\u8fd9\u5c31\u6d89\u53ca\u5230\u6a21\u578b\u5bf9\u672a\u77e5\u6216\u672a\u89c1\u60c5\u51b5\u7684\u9002\u5e94\u80fd\u529b\uff0c\u4ee5\u53ca\u662f\u5426\u80fd\u524a\u5f31\u6837\u672c\u9009\u62e9\u504f\u5dee\u7684\u95ee\u9898\u3002\u6b64\u95ee\u9898\u901a\u5e38\u8868\u73b0\u4e3a\u6a21\u578b\u5728\u8bad\u7ec3\u96c6\u4e0a\u8fd0\u884c\u826f\u597d\uff0c\u4f46\u5728\u9762\u5bf9\u5206\u5e03\u5916\u7684\u5404\u79cd\u6570\u636e\u65f6\uff0c\u6a21\u578b\u6027\u80fd\u6709\u6240\u4e0b\u964d\u3002\u9020\u6210\u8fd9\u4e2a\u95ee\u9898\u7684\u539f\u56e0\u53ef\u80fd\u662f\u6a21\u578b\u8fc7\u5ea6\u62df\u5408\u4e86\u8bad\u7ec3\u6570\u636e\uff0c\u5bfc\u81f4\u6a21\u578b\u6cdb\u5316\u80fd\u529b\u5dee\uff1b\u4e5f\u53ef\u80fd\u662f\u7531\u4e8e\u8bad\u7ec3\u6570\u636e\u65e0\u6cd5\u8986\u76d6\u6240\u6709\u53ef\u80fd\u7684\u8f93\u5165\u60c5\u51b5\uff0c\u7279\u522b\u662f\u7f55\u89c1\u6216\u6781\u7aef\u7684\u60c5\u51b5\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e3a\u4e86\u589e\u5f3a\u5206\u5e03\u5916\u6cdb\u5316\u80fd\u529b\uff0c\u5b66\u8005\u4eec\u9664\u4e86\u53ef\u4ee5\u751f\u6210\u591a\u6837\u5316\u7684\u6570\u636e\uff0c\u6a21\u62df\u4e0d\u540c\u7684\u6d4b\u8bd5\u73af\u5883\uff0c\u8fd8\u53ef\u4ee5\u901a\u8fc7\u57df\u9002\u5e94\u6280\u672f<\/span>\uff08Domain Adaptation\uff09<\/span>[18]\uff0c\u4f7f\u6a21\u578b\u53ef\u4ee5\u9002\u5e94\u4e0d\u540c\u7684\u6d4b\u8bd5\u6570\u636e\u5206\u5e03\u3002\u53e6\u5916\uff0c\u5b66\u8005\u4eec\u4e5f\u63d0\u51fa\u4e86\u4e0d\u53d8\u6027\u5b66\u4e60<\/span>\uff08Invariant Learning\uff09<\/span>[19]\u3001\u5143\u5b66\u4e60<\/span>\uff08Meta Learning\uff09<\/span>[20]\u7b49\u65b9\u6cd5\u89e3\u51b3\u8be5\u95ee\u9898\u3002<\/span><\/section>\n

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

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

    \n
    \n
    \n
    \n
    \n

    <\/section>\n

    <\/section>\n
    \n
    <\/svg><\/section>\n<\/section>\n<\/section>\n
    \n

    2. \u95ee\u9898\u63cf\u8ff0<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

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


    <\/p>\n

    \u63a5\u4e0b\u6765\uff0c\u672c\u8bcd\u6761\u5c06\u7ed9\u51fa\u7528\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u95ee\u9898\u7684\u5f62\u5f0f\u5316\u5b9a\u4e49\uff0c\u5176\u6b21\uff0c\u4ecb\u7ecdNIS\u6846\u67b6\u7684\u89e3\u51b3\u601d\u8def\uff0c\u6700\u540e\u4ecb\u7ecdNIS+\u7684\u6846\u67b6\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5047\u8bbe\u590d\u6742\u52a8\u6001\u7cfb\u7edf\u7684\u884c\u4e3a\u6570\u636e\u662f\u65f6\u95f4\u5e8f\u5217 <\/span><\/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>{<\/span><\/mo>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>}<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u65f6\u95f4\u6b65\u957f<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn>\uff0c<\/span><\/mjx-utext><\/mjx-mi><\/mjx-c><\/mjx-mo>\uff0c<\/span><\/mjx-utext><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>t<\/span><\/mi>=<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>2<\/span><\/mn>\uff0c<\/span><\/mi>\u2026<\/span><\/mo>\uff0c<\/span><\/mi>T<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u7ef4\u6570\u662fp\uff0c\u5b83\u4eec\u6784\u6210\u4e86\u53ef\u89c2\u6d4b\u7684\u5fae\u89c2\u72b6\u6001\u3002\u6240\u8c13\u7684\u56e0\u679c\u6d8c\u73b0\u8bc6\u522b\u95ee\u9898\uff0c\u662f\u6307\u5982\u4e0b\u4f18\u5316\u95ee\u9898\uff1a<\/span><\/section>\n

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

    <\/span><\/section>\n
    \u5176\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>t<\/span><\/mi>+<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\u523b\u7684\u5fae\u89c2\u72b6\u6001\u503c\uff0c<\/span><\/sub><\/span><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ecf\u8fc7\u7c97\u7c92\u5316\u3001\u5b8f\u89c2\u52a8\u529b\u5b66\u5b66\u4e60\u5668\u3001\u53cd\u7c97\u7c92\u5316\u540e\u5f97\u5230\u7684\u9884\u6d4b\u5fae\u89c2\u6001\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03f5<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u7ed9\u5b9a\u7684\u5e38\u6570\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-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>:<\/span><\/mo>R<\/span><\/mi>p<\/span><\/sub><\/mi><\/msub>\u2192<\/span><\/mo>R<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u4e00\u4e2a\u7c97\u7c92\u5316\u7b56\u7565\uff0c\u5176\u4e2d <\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>q<\/span><\/mi>\u2264<\/span><\/mo>p<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c <\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u5b8f\u89c2\u72b6\u6001\u7684\u7ef4\u5ea6\uff0c\u4f5c\u4e3a\u8d85\u53c2\u6570\u7ed9\u5b9a\uff1b<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/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-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>\u2020<\/span><\/sup><\/mo><\/msup>:<\/span><\/mo>R<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub>\u2192<\/span><\/mo>R<\/span><\/mi>p<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u4e00\u4e2a\u4e0e<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03d5<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u76f8\u5e94\u7684\u53cd\u7c97\u7c92\u5316\u7b56\u7565\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u4e00\u4e2a\u5b8f\u89c2\u52a8\u529b\u5b66\u5b66\u4e60\u5668\u3002<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>J<\/span><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u7ef4\u5ea6\u5e73\u5747\u7684\u6709\u6548\u4fe1\u606f[13]\u3002\u56e0\u6b64\uff0c\u8be5\u95ee\u9898\u5c31\u662f\u4e00\u4e2a\u5e26\u7ea6\u675f\u7684\u6cdb\u51fd\u4f18\u5316\u95ee\u9898\uff0c\u5176\u4e2d\u88ab\u4f18\u5316\u7684\u81ea\u53d8\u91cf\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3001<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>\u2020<\/span><\/sup><\/mo><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/section>\n

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


    <\/h1>\n

    \n
    \n
    \n
    \n
    \n

    <\/section>\n

    <\/section>\n
    \n
    <\/svg><\/section>\n<\/section>\n<\/section>\n
    \n

    3. NIS\u6846\u67b6\u53ca\u5176\u7f3a\u9677<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

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


    <\/p>\n

    \u5bf9\u4e8e\u5f0f1\u7684\u6c42\u89e3\uff0cNIS\u7387\u5148\u7ed9\u51fa\u4e86\u795e\u7ecf\u7f51\u7edc\u6c42\u89e3\u7684\u65b9\u6848\uff0c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/span><\/section>\n

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

    <\/span><\/section>\n
    \u56fe\u4e2d\uff0c\u6a21\u578b\u8f93\u5165\u662f\u5fae\u89c2\u72b6\u6001<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u7c97\u7c92\u5316\u51fd\u6570<\/span>\uff08\u7f16\u7801\u5668\uff09<\/span>\uff0c\u5f97\u5230\u5b8f\u89c2\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u52a8\u529b\u5b66\u5b66\u4e60\u5668\uff0c\u5728\u5b8f\u89c2\u5c42\u9762\u4e0a\u5b66\u4e60\u6709\u6548\u7684\u9a6c\u5c14\u53ef\u592b\u52a8\u529b\u5b66\u3002<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u901a\u8fc7<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>f<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u9884\u6d4b\u7684t+1\u65f6\u523b\u7684\u5b8f\u89c2\u72b6\u6001\u3002\u7531\u4e8e\u6b64\u65f6\u6570\u636e\u7ecf\u8fc7\u964d\u7ef4\u64cd\u4f5c\uff0c\u4e3a\u4e86\u4f7f\u7528\u53cd\u7c97\u7c92\u5316\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>\u2020<\/span><\/sup><\/mo><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff08\u89e3\u7801\u5668\uff09<\/span>\uff0c\u6a21\u578b\u9700\u8981\u7528\u9ad8\u65af\u968f\u673a\u5411\u91cf<\/span><\/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-texatom><\/mjx-mstyle><\/mjx-math>N<\/span><\/mi>(<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo>I<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u586b\u5145\u7ef4\u5ea6\u4e0d\u8db3\u7684\u6570\u636e\u3002\u5b8f\u89c2\u53d8\u91cf\u7ecf\u8fc7\u53cd\u7c97\u7c92\u5316\u51fd\u6570\u4e4b\u540e\u53ef\u4ee5\u5f97\u5230\u9884\u6d4b\u7684\u5fae\u89c2\u53d8\u91cf<\/span><\/sub><\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/msub><\/mrow><\/mstyle><\/mjx-container><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u800c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/sub><\/span><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e4b\u95f4\u7684\u5dee\u503c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>L<\/span><\/mi>o<\/span><\/mi>s<\/span><\/mi>s<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5373\u4e3a\u9884\u6d4b\u635f\u5931\u8bc4\u4f30\u503c\uff0c\u53ef\u4ee5\u7528\u6765\u8bad\u7ec3\u6574\u4e2a\u7f51\u7edc\u67b6\u6784\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u4e3a\u4e86\u6570\u5b66\u6027\u8d28\u548c\u53ef\u89e3\u91ca\u6027\uff0c\u4ee5\u53ca\u964d\u4f4e\u6a21\u578b\u53c2\u6570\u91cf\uff0cNIS\u91c7\u7528\u4e86\u53ef\u9006\u795e\u7ecf\u7f51\u7edc<\/span>\uff08INN\uff09<\/span>\u3002\u5176\u4e2d\u7f16\u7801\u5668\u5bf9\u5e94\u4e86\u5f0f1\u4e2d\u7684\u7c97\u7c92\u5316\u7b56\u7565<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03d5<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff08<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u5fae\u89c2\u6570\u636e\u503c\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u5b8f\u89c2\u6570\u636e\u503c\uff09<\/span>\u5b83\u662f\u7531\u4e24\u6b65\u64cd\u4f5c\u590d\u5408\u800c\u6210\u7684\uff0c\u5373\uff1a<\/span><\/section>\n

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

    <\/p>\n


    <\/span><\/section>\n
    \u8fd9\u91cc\uff0c<\/span><\/section>\n

    <\/span><\/section>\n
    \u2460\u53cc\u5c04\u6620\u5c04\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-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c8<\/span><\/mi>:<\/span><\/mo>R<\/span><\/mi>p<\/span><\/sub><\/mi><\/msub>\u2192<\/span><\/mo>R<\/span><\/mi>p<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>R<\/span><\/mi>p<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u7684\u6570\u636e\u7a7a\u95f4\uff0c\u6b64\u6b65\u65e0\u4fe1\u606f\u4e22\u5931\uff0c\u7531\u53ef\u9006\u795e\u7ecf\u7f51\u7edc\u5b9e\u73b0\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u2461\u6295\u5f71\u8fd0\u7b97\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c7<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u6b64\u6b65\u5c06\u8f93\u5165\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u6570\u636e\u6620\u5c04\u5230<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u6570\u636e\u4e0a\uff0c\u5f97\u5230\u5b8f\u89c2\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u6b64\u6b65\u4e22\u5931<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi>\u2212<\/span><\/mo>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u4fe1\u606f\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u540c\u6837\u5730\uff0c\u89e3\u7801\u5668\uff0c\u4e5f\u5c31\u662f\u53cd\u7c97\u7c92\u5316\u51fd\u6570\u4e5f\u5206\u4e3a\u4e24\u4e2a\u6b65\u9aa4\uff1a<\/span><\/section>\n

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

    <\/span><\/section>\n
    \u8fd9\u91cc\uff0c<\/span><\/section>\n

    <\/span><\/section>\n
    \u2460\u7528<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi>\u2212<\/span><\/mo>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u9ad8\u65af\u968f\u673a\u5411\u91cf\u586b\u5145\u6570\u636e\u5f97\u5230<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\u6570\u636e\u3002\u5f0f\u4e2d\uff0c\u03be\u4e3ap\u2212q\u7ef4\u7684\u6807\u51c6\u9ad8\u65af\u968f\u673a\u5411\u91cf\uff0c\u2295\u8868\u793a\u5411\u91cf\u62fc\u63a5\u64cd\u4f5c\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u2461\u4f7f\u7528\u53cd\u7c97\u7c92\u5316\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>\u2020<\/span><\/sup><\/mo><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5f97\u5230\u9884\u6d4b\u7684\u5fae\u89c2\u53d8\u91cf<\/sub><\/mn><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/msub><\/mrow><\/mstyle><\/mjx-container>\u3002\u7531\u4e8e\u4f7f\u7528\u53ef\u9006\u795e\u7ecf\u7f51\u7edc\uff0c\u6b64\u6b65\u548c\u7f16\u7801\u5668\u4e2d\u7684\u53cc\u5c04\u6620\u5c04\u5171\u4eab\u53c2\u6570\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u5728\u7f16\u7801\u5668\u8fd9\u4e00\u6b65\uff0c\u867d\u7136\u6709\u4e22\u5931\u4fe1\u606f\uff0c\u4f46\u662f\u901a\u8fc7\u6570\u5b66\u8bc1\u660e\u53ef\u4ee5\u5f97\u77e5\uff0c\u5f53\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u6536\u655b\u65f6\uff0c\u6570\u636e\u4e2d\u76f8\u90bb\u5b8f\u89c2\u72b6\u6001\u4e4b\u95f4\u7684\u4e92\u4fe1\u606f\u503e\u5411\u4e8e\u63a5\u8fd1\u4e24\u4e2a\u76f8\u90bb\u65f6\u95f4\u6b65\u7684\u5fae\u89c2\u6001\u4e92\u4fe1\u606f\uff0c\u4e22\u5931\u7684\u4fe1\u606f\u4e0e\u9884\u6d4b\u51e0\u4e4e\u65e0\u5173\uff0c\u6240\u6709\u6709\u6548\u7684\u4fe1\u606f\u90fd\u6c47\u805a\u5230\u52a8\u529b\u5b66\u5b66\u4e60\u5668\u7684\u4fe1\u606f\u74f6\u9888\u4e4b\u4e2d\u3002\u4e14\u5728\u6b64\u6846\u67b6\u4e0b\uff0c\u4fe1\u606f\u74f6\u9888\u7684\u5e94\u7528\u66f4\u52a0\u660e\u663e\u3001\u66f4\u5177\u53ef\u89e3\u91ca\u6027\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7136\u800c\u7531\u4e8e\u8be5\u76ee\u6807\u51fd\u6570\u662f\u4e00\u4e2a\u6cdb\u51fd\u4f18\u5316\u95ee\u9898\uff0c\u5f80\u5f80\u5f88\u96be\u4f18\u5316\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u4f5c\u8005\u5c06\u4f18\u5316\u8fc7\u7a0b\u5206\u4e3a\u4e24\u4e2a\u9636\u6bb5\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7b2c\u4e00\u4e2a\u9636\u6bb5\uff1a\u5728\u7ed9\u5b9a\u5b8f\u89c2\u5c3a\u5ea6<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u60c5\u51b5\u4e0b\uff0c\u6700\u5c0f\u5316\u9884\u6d4b\u8bef\u5dee<\/span><\/sub><\/mo><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u53ef\u4ee5\u91c7\u7528\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u6280\u672f\uff0c\u901a\u8fc7\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u89e3\u51b3\u3002\u5728\u6b64\u6b65\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u4f9d\u8d56\u4e8e<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u6709\u6548\u7c97\u7c92\u5316\u7b56\u7565\u548c\u5b8f\u89c2\u52a8\u529b\u5b66\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7b2c\u4e8c\u4e2a\u9636\u6bb5\uff1a\u7531\u4e8e\u53c2\u6570 <\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container> \u662f\u4e00\u7ef4\u7684\uff0c\u4e14 <\/span><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>0<\/span><\/mn><<\/span><\/mo>q<\/span><\/mi><<\/span><\/mo>p<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u7b80\u5355\u8fed\u4ee3\u627e\u5230\u6709\u6548\u4fe1\u606f\u6700\u5927\u7684\u5b8f\u89c2\u5c3a\u5ea6\u3002\u6b64\u6b65\u5c06\u590d\u6742\u7684\u6cdb\u51fd\u95ee\u9898\u8f6c\u5316\u6210\u4e00\u7ef4\u7a7a\u95f4\u4e2d\u7ebf\u6027\u641c\u7d22\u95ee\u9898\u3002<\/span><\/section>\n

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

    \u867d\u7136\u6b64\u6a21\u578b\u5728\u5f39\u7c27\u632f\u5b50\u3001\u9a6c\u5c14\u79d1\u592b\u94fe\u3001\u5e03\u5c14\u7f51\u7edc\u7b49\u7b80\u5355\u6a21\u578b\u4e0a\u5f97\u5230\u4e86\u5b9e\u9a8c\u9a8c\u8bc1\uff0c\u4f46\u662f\u6b64\u6a21\u578b\u8fd8\u6709\u4e00\u4e9b\u7f3a\u70b9\u548c\u5c1a\u672a\u6539\u8fdb\u7684\u5730\u65b9\uff1a<\/span><\/p>\n

      \n
    • \n
      \u6b64\u6846\u67b6\u76ee\u524d\u53ea\u80fd\u5728\u5c0f\u6570\u636e\u96c6\u4e0a\u4f7f\u7528\uff0c\u96be\u4ee5\u62d3\u5c55\u5230\u66f4\u5927\u89c4\u6a21\u7684\u590d\u6742\u7cfb\u7edf\u4e0a\u3002<\/span><\/section>\n<\/li>\n
    • \n

      \u6b64\u65b9\u6cd5\u7684\u6570\u5b66\u5f62\u5f0f\u662f\u4e00\u4e2a\u6cdb\u51fd\u95ee\u9898\uff0c\u65e0\u6cd5\u76f4\u63a5\u8fdb\u884c\u4f18\u5316\uff0c\u867d\u7136\u53ef\u4ee5\u901a\u8fc7\u4e24\u4e2a\u9636\u6bb5\u5f97\u5230\u7ed3\u679c\uff0c\u4f46\u662fNIS\u6ca1\u6709\u771f\u6b63\u5730\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n


      <\/span><\/section>\n
      \u5177\u4f53\u8bf7\u9605\u8bfb\u8bcd\u6761NIS\u3002<\/span><\/section>\n


      <\/span><\/h1>\n


      <\/h1>\n

      \n
      \n
      \n
      \n
      \n

      <\/section>\n

      <\/section>\n
      \n
      <\/svg><\/section>\n<\/section>\n<\/section>\n
      \n

      4. \u5f3a\u5316\u7248\u795e\u7ecf\u4fe1\u606f\u538b\u7f29\u673a\uff08NIS+\uff09<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

      \n

      <\/section>\n

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


      <\/p>\n

      \u4e3a\u4e86\u89e3\u51b3NIS\u7684\u9057\u7559\u95ee\u9898\uff0c\u7279\u522b\u662f\u5728\u6cdb\u51fd\u7a7a\u95f4\u4e0a\u4e0d\u80fd\u591f\u771f\u6b63\u4f18\u5316\u6709\u6548\u4fe1\u606f\u7684\u95ee\u9898\uff0cNIS+\u5e94\u8fd0\u800c\u751f[21]\u3002<\/span><\/section>\n

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

      4.1 \u6a21\u578b\u6846\u67b6<\/span><\/strong><\/span><\/h2>\n


      <\/span><\/strong><\/span><\/p>\n

      <\/section>\n

      \u56fe\u6ce8\uff1a\u5728\u6b64\u6846\u67b6\u4e2d\uff0c\u8f93\u5165\u53ef\u89c2\u6d4b\u7684\u6570\u636e\uff08\u5982\u56fe(a)\uff0c\u53ef\u4ee5\u662f\u8f68\u8ff9\u3001\u56fe\u50cf\u5e8f\u5217\u3001\u65f6\u95f4\u5e8f\u5217\uff09\uff0c\u8f93\u51fa\u662f\u56e0\u679c\u6d8c\u73b0\u7684\u7a0b\u5ea6\u3001\u5b8f\u89c2\u52a8\u529b\u5b66\u3001\u6d8c\u73b0\u6591\u56fe\u4ee5\u53ca\u7c97\u7c92\u5316\u7b56\u7565\uff08\u5982\u56fe(c)\uff09\u3002\u5728NIS+\u4e2d\uff08\u5982\u56fe(b)\uff09\uff0c\u4f5c\u8005\u9996\u5148\u4f7f\u7528\u4e92\u4fe1\u606f\u548c\u53d8\u5206\u4e0d\u7b49\u5f0f\u7684\u516c\u5f0f\u5c06\u4e92\u4fe1\u606f\u7684\u6700\u5927\u5316\u95ee\u9898\u8f6c\u5316\u4e3a\u673a\u5668\u5b66\u4e60\u95ee\u9898\uff0c\u5176\u4e2d\uff0c\u901a\u8fc7\u5b66\u4e60\u4e00\u4e2a\u53cd\u5411\u5b8f\u89c2\u52a8\u529b\u5b66<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>g<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4e5f\u5c31\u662f\u901a\u8fc7<\/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-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-mstyle><\/mjx-math>y<\/span><\/mi>t<\/sub><\/span><\/mi>+<\/sub><\/span><\/mo>1<\/sub><\/span><\/mn><\/mrow><\/msub>=<\/span><\/mo>\u03d5<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>t<\/sub><\/span><\/mi>+<\/sub><\/span><\/mo>1<\/sub><\/span><\/mn><\/mrow><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u6765\u9884\u6d4b<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5f97\u5230<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8be5\u6846\u67b6\u4fdd\u8bc1\u4e86\u4e92\u4fe1\u606f\u7684\u6700\u5927\u5316\u3002\u6700\u540e\uff0c\u8be5\u6846\u67b6\u63d0\u51fa\u5229\u7528\u6837\u672c\u91cd\u52a0\u6743\u6280\u672f\u6765\u89e3\u51b3\u5747\u5300\u5206\u5e03\u5e72\u9884\u7684\u6311\u6218\uff0c\u4ece\u800c\u4fdd\u8bc1\u4e86\u4f18\u5316\u7684\u76ee\u6807\u51fd\u6570\u662f\u6709\u6548\u4fe1\u606f\u3002\u6240\u6709\u8fd9\u4e9b\u6280\u672f\u7ec4\u6210\u4e86\u589e\u5f3a\u7248\u795e\u7ecf\u4fe1\u606f\u538b\u7f29\u673a(NIS+)[21]\u3002<\/span><\/p>\n


      <\/span><\/section>\n
      \u5176\u4e2d\uff0c\u6a21\u578b\u8f93\u5165\u662f\u5fae\u89c2\u72b6\u6001<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u7c97\u7c92\u5316\u51fd\u6570<\/span>\uff08\u7f16\u7801\u5668\uff09<\/span>\uff0c\u5f97\u5230\u5b8f\u89c2\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u52a8\u529b\u5b66\u5b66\u4e60\u5668\uff0c\u5728\u5b8f\u89c2\u5c42\u9762\u4e0a\u5b66\u4e60\u6709\u6548\u7684\u9a6c\u5c14\u53ef\u592b\u52a8\u529b\u5b66\u3002<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u901a\u8fc7<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>f<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u9884\u6d4b\u7684t+1\u65f6\u523b\u7684\u5b8f\u89c2\u72b6\u6001\u3002\u7531\u4e8e\u6b64\u65f6\u6570\u636e\u7ecf\u8fc7\u964d\u7ef4\u64cd\u4f5c\uff0c\u4e3a\u4e86\u4f7f\u7528\u53cd\u7c97\u7c92\u5316\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>\u2020<\/span><\/mo><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff08\u89e3\u7801\u5668\uff09<\/span>\uff0c\u6570\u636e\u9700\u8981\u62fc\u63a5\u9ad8\u65af\u968f\u673a\u5411\u91cf<\/span><\/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-texatom><\/mjx-mstyle><\/mjx-math>N<\/span><\/mi>(<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo>I<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u5b8f\u89c2\u53d8\u91cf\u7ecf\u8fc7\u53cd\u7c97\u7c92\u5316\u51fd\u6570\u4e4b\u540e\u53ef\u4ee5\u5f97\u5230\u9884\u6d4b\u7684\u5fae\u89c2\u53d8<\/span>\u91cf<\/span><\/sub><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/msub><\/mrow><\/mjx-container><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u800c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/sub><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/msub><\/mrow><\/mjx-container><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e4b\u95f4\u7684\u5dee\u503c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>L<\/span><\/mi>1<\/span><\/sub><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5373\u4e3a\u9884\u6d4b\u635f\u5931\u8bc4\u4f30\u503c\u3002\u540c\u6837\uff0c\u5c06\u5fae\u89c2\u72b6\u6001<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8f93\u5165\uff0c\u7ecf\u8fc7\u7c97\u7c92\u5316\u51fd\u6570<\/span>\uff08\u7f16\u7801\u5668\uff09<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5f97\u5230\u5b8f\u89c2\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-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>g<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u53cd\u5411\u52a8\u529b\u5b66\u5b66\u4e60\u5668\u3002<\/span><\/sub><\/span><\/mi><\/mjx-container><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u901a\u8fc7<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>g<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u9884\u6d4b\u7684t\u65f6\u523b\u7684\u5b8f\u89c2\u72b6\u6001\u3002\u800c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/sub><\/span><\/mjx-container><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e4b\u95f4\u7684\u5dee\u503c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>L<\/span><\/mi>2<\/span><\/sub><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5373\u4e3a\u53cd\u5411\u9884\u6d4b\u635f\u5931\u8bc4\u4f30\u503c\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u4e0e\u524d\u4e00\u4e2a\u7248\u672c\u76f8\u6bd4\uff0cNIS\u7531\u7f16\u7801\u5668\u3001\u5b8f\u89c2\u52a8\u529b\u5b66\u5b66\u4e60\u5668\u3001\u89e3\u7801\u5668\u7ec4\u6210\uff0c\u5176\u4e2d\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\u4f7f\u7528\u7684\u795e\u7ecf\u7f51\u7edc\u662f\u5171\u4eab\u53c2\u6570\u7684\u53ef\u9006\u795e\u7ecf\u7f51\u7edc\uff1b\u800cNIS+\u5219\u5728\u6b64\u57fa\u7840\u4e0a\u591a\u4e86\u4e00\u4e2a\u53cd\u5411\u5b8f\u89c2\u52a8\u529b\u5b66\u5b66\u4e60\u5668\u3002\u5728\u5b8f\u89c2\u5c3a\u5ea6\u7684\u9009\u62e9\u4e0a\uff0c\u4e8c\u8005\u90fd\u9700\u8981\u4e8b\u5148\u7ed9\u5b9a\u8d85\u53c2\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>q<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u5728\u635f\u5931\u51fd\u6570\u4e0a\uff0cNIS\u53ea\u662f\u4f18\u5316\u6b63\u5411\u7684\u5fae\u89c2\u9884\u6d4b\u635f\u5931\uff0c\u800cNIS+\u9996\u5148\u7ed3\u5408\u6837\u672c\u91cd\u52a0\u6743\u7684\u6280\u672f\uff0c\u8ba1\u7b97\u5e26\u6709\u6743\u91cd\u7684\u6b63\u5411\u5fae\u89c2\u9884\u6d4b\u635f\u5931\uff0c\u53e6\u5916\u6839\u636e\u53cd\u5411\u52a8\u529b\u5b66\u5b66\u4e60\u5668\uff0c\u8ba1\u7b97\u5e26\u6709\u6743\u91cd\u7684\u53cd\u5411\u5b8f\u89c2\u9884\u6d4b\u635f\u5931\u3002\u4e24\u79cd\u9884\u6d4b\u635f\u5931\u4f1a\u4ee5\u4e00\u5b9a\u7684\u6bd4\u4f8b\u7ed3\u5408\u5728\u4e00\u8d77\u4f18\u5316\u3002\u5728\u8f93\u5165\u8f93\u51fa\u4e0a\uff0c\u4e8c\u8005\u8f93\u5165\u7684\u90fd\u662f\u591a\u7ef4\u7684\u5fae\u89c2\u65f6\u95f4\u5e8f\u5217\uff0c\u8f93\u51fa\u7684\u662f\u5b8f\u89c2\u52a8\u529b\u5b66\uff0c\u7c97\u7c92\u5316\u7b56\u7565\uff0cEI\u548cCE\u7684\u5927\u5c0f\u3002\u5176\u4e2dNIS+\u5f97\u5230\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u548c\u7c97\u7c92\u5316\u7b56\u7565\u662f\u4f7f\u5f97\u5b8f\u89c2\u52a8\u529b\u5b66\u6709\u6548\u4fe1\u606f\u6700\u5927\u7684\u51fd\u6570\u3002<\/span><\/section>\n

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

      <\/p>\n


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

      4.2 NIS+ \u6846\u67b6\u6709\u6548\u6027\u7684\u9a8c\u8bc1\uff08\u6570\u503c\u5b9e\u9a8c\uff09<\/span><\/strong><\/span><\/h2>\n

      <\/span><\/section>\n
      \u5728\u6b64\u90e8\u5206\u4e2d\uff0c\u4f5c\u8005\u901a\u8fc7\u56db\u7ec4\u6570\u636e\u9a8c\u8bc1NIS+\u6846\u67b6\u6709\u6548\u6027\uff1aSIR\u6a21\u578b\u6570\u636e\u3001Boids\u6a21\u578b\u6570\u636e\u3001\u751f\u547d\u6e38\u620f\u6a21\u578b\u6570\u636e\u3001\u5927\u8111fMRI\u771f\u5b9e\u6570\u636e\u3002\u5b9e\u9a8c\u6570\u636e\u5305\u62ec\u4eba\u8111\u7684\u6838\u78c1\u5171\u632f\u771f\u5b9e\u7684\u6210\u50cf\u6570\u636e\u548c\u4e0d\u540c\u7684\u4eba\u5de5\u6a21\u578b<\/span> (\u52a8\u6001\u7cfb\u7edf\u3001\u591a\u4e3b\u4f53\u7cfb\u7edf\u548c\u5143\u80de\u81ea\u52a8\u673a)<\/span> \u751f\u6210\u7684\u6570\u636e\u3002\u6bcf\u4e2a\u5b9e\u9a8c\u4e2d\uff0c\u4f5c\u8005\u8bc4\u4f30\u4e86NIS+\u7684\u56e0\u679c\u6d8c\u73b0\u8bc6\u522b\u80fd\u529b\u548c\u6cdb\u5316\u80fd\u529b\u3002<\/span><\/section>\n

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

      4.2.1 SIR\u6a21\u578b\u6570\u636e<\/span><\/strong><\/h3>\n

      <\/span><\/section>\n
      SIR<\/span>\uff08Susceptible<\/span><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u2192<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>Infected<\/span><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u2192<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>Recovered Model\uff09<\/span>\u6a21\u578b\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u5b8f\u89c2\u52a8\u6001\u7cfb\u7edf\uff0c\u800c\u5fae\u89c2\u53d8\u91cf\u662f\u901a\u8fc7\u5728\u5b8f\u89c2\u53d8\u91cf\u4e2d\u5f15\u5165\u566a\u58f0\u6765\u4ea7\u751f\u7684\u3002\u8fd9\u662f\u4e00\u4e2a\u5df2\u77e5\u5b8f\u89c2\u673a\u5236\u7684\u73a9\u5177\u6a21\u578b\uff0c\u53ef\u4ee5\u9a8c\u8bc1NIS+\u662f\u5426\u771f\u7684\u505a\u5230\u4e86\u5b8f\u89c2\u6709\u6548\u4fe1\u606f\u6700\u5927\u5316\u3002<\/span><\/section>\n
      SIR\u5b8f\u89c2\u52a8\u529b\u5b66\u53ef\u4ee5\u63cf\u8ff0\u4e3a\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/span><\/section>\n
      \u5176\u4e2d<\/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-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>S<\/span><\/mi>,<\/span><\/mo>I<\/span><\/mi>,<\/span><\/mo>R<\/span><\/mi>\u2208<\/span><\/mo>[<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo>1<\/span><\/mn>]<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u79cd\u7fa4\u4e2d\u5065\u5eb7\uff0c\u611f\u67d3\u548c\u5eb7\u590d\u6216\u6b7b\u4ea1\u4e2a\u4f53\u7684\u6bd4\u4f8b\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b2<\/span><\/mi>=<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u611f\u67d3\u7387\uff0c\u5373\u5065\u5eb7\u4eba\u611f\u67d3\u6210\u611f\u67d3\u8005\u7684\u6982\u7387\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b3<\/span><\/mi>=<\/span><\/mo>0.5<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u6062\u590d\u7387\uff0c\u5373\u611f\u67d3\u8005\u5eb7\u590d\u6216\u8005\u6b7b\u4ea1\u7684\u6982\u7387\u3002\u56fe(a)\u663e\u793a\u4e86SIR\u52a8\u529b\u5b66\u7684\u76f8\u7a7a\u95f4(S, I, R)\u3002\u7531\u4e8eSIR\u6a21\u578b\u53ea\u6709\u4e24\u4e2a\u81ea\u7531\u5ea6\uff08<\/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-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>S<\/span><\/mi>+<\/span><\/mo>I<\/span><\/mi>+<\/span><\/mo>R<\/span><\/mi>=<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff09\uff0c\u6240\u4ee5\u6240\u6709\u7684\u5b8f\u89c2\u72b6\u6001\u90fd\u5206\u5e03\u5728\u4e09\u7ef4\u7684\u4e09\u89d2\u5f62\u5e73\u9762\u4e0a\uff0c\u6545\u4f5c\u8005\u4ec5\u7528S\u548cI\u6784\u6210\u5b8f\u89c2\u72b6\u6001\u53d8\u91cf<\/span><\/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-mstyle><\/mjx-math>y<\/span><\/mi>=<\/span><\/mo>(<\/span><\/mo>S<\/span><\/mi>,<\/span><\/mo>I<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u540c\u65f6\uff0c\u4f5c\u8005\u901a\u8fc7\u5f15\u5165\u9ad8\u65af\u566a\u58f0\u5c06<\/span><\/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-mstyle><\/mjx-math>y<\/span><\/mi>=<\/span><\/mo>(<\/span><\/mo>S<\/span><\/mi>,<\/span><\/mo>I<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5c55\u5f00\u4e3a\u4e00\u4e2a\u56db\u7ef4\u53d8\u91cf\uff0c\u5e76\u5c06\u5176\u770b\u505a\u5fae\u89c2\u72b6\u6001\u3002<\/span><\/section>\n

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

      <\/p>\n


      <\/span><\/section>\n
      \u5176\u4e2d\uff0c<\/span><\/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-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-mstyle><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03be<\/span><\/mi><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>1<\/span><\/sub><\/span><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/msub>,<\/span><\/mo>\u03be<\/span><\/mi><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>2<\/span><\/sub><\/span><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/msub>\u223c<\/span><\/mo>N<\/span><\/mi><\/mrow>(<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo>\u03a3<\/span><\/mi>)<\/span><\/mo><\/mstyle><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u76f8\u4e92\u72ec\u7acb\u7684\u4e8c\u7ef4\u9ad8\u65af\u566a\u58f0\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a3<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u76f8\u5173\u77e9\u9635\u3002\u5fae\u89c2\u72b6\u6001\u5e8f\u5217 <\/span> <\/sub><\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4f5c\u4e3a\u8bad\u7ec3\u6837\u672c\u3002\u4f5c\u8005\u5728\u56fe(a)\u7684\u4e09\u89d2\u5f62\u533a\u57df\u5185\u91c7\u6837\uff0c\u4ee5\u6b64\u6765\u968f\u673a\u9009\u62e9\u521d\u59cb\u6761\u4ef6\uff0c\u5e76\u4f7f\u7528\u4e0a\u8ff0\u8fc7\u7a0b\u751f\u6210\u65f6\u95f4\u5e8f\u5217\u6570\u636e\uff0c\u7528\u4ee5\u8bad\u7ec3\u6a21\u578b\u3002<\/span><\/section>\n

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


      <\/span><\/h4>\n

      4.2.1.1 NIS+\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u7684\u80fd\u529b<\/span><\/h4>\n


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

      \u9996\u5148\uff0c\u4e3a\u4e86\u786e\u4fddEI\u88abNIS+\u6700\u5927\u5316\uff0c\u4f5c\u8005\u7ed8\u5236\u76f8\u5e94\u56fe\u5f62\uff0c\u89c2\u5bdf\u7ef4\u5ea6\u5e73\u5747\u7684\u6709\u6548\u4fe1\u606f(J)\u5728\u8bad\u7ec3\u65f6\u671f\u7684\u6f14\u53d8\u3002<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u7ed3\u679c\u8868\u660e<\/span>\uff08\u56fe(b)\uff09<\/span>\uff0cNIS+(\u7ea2\u8272\u5b9e\u7ebf)\u3001NIS(\u9ed1\u8272\u865a\u7ebf)\u548cVAE+(\u7eff\u8272\u5b9e\u7ebf)\u7684\u66f2\u7ebf\u5448\u4e0a\u5347\u8d8b\u52bf\uff0c\u4f46NIS+\u7684\u589e\u957f\u901f\u5ea6\u66f4\u5feb\u3002\u8fd9\u8868\u660eNIS+\u6bd4\u5176\u4ed6\u6a21\u578b\u66f4\u80fd\u6709\u6548\u5730\u6700\u5927\u5316J\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0cNIS\u4e5f\u8868\u73b0\u51faEI\u7684\u81ea\u7136\u589e\u957f\uff0c\u56e0\u4e3a\u5b83\u9010\u6e10\u4f7f\u9884\u6d4b\u8bef\u5dee\u6700\u5c0f\u5316\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5176\u6b21\uff0c\u4e3a\u4e86\u68c0\u9a8cNIS+\u68c0\u6d4b\u548c\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u7684\u80fd\u529b\uff0c\u56fe(e)\u5c55\u793a\u4e86\u968f\u7740\u566a\u97f3\u7684\u589e\u5927\uff0c\u56e0\u679c\u6d8c\u73b0\u5f3a\u5ea6<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u0394<\/span><\/mi>J<\/span><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u53d8\u5316\u8d8b\u52bf\uff0c\u5e76\u5c06\u5176\u4e0eRosas\u7684\u56e0\u679c\u6d8c\u73b0\u5ea6\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a8<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u6307\u6807\u8fdb\u884c\u4e86\u6bd4\u8f83<\/span>\uff08\u4e3a\u4e86\u8ba9<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a8<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u53ef\u8ba1\u7b97\uff0c\u4f5c\u8005\u5229\u7528\u4eceNIS+\u4e2d\u5b66\u4e60\u5230\u7684\u5b8f\u89c2\u72b6\u6001\u6765\u4f5c\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03a8<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u8ba1\u7b97\u4e2d\u7684\u5b8f\u89c2\u53d8\u91cf\uff09<\/span>\u3002\u7ed3\u679c\u7528\u56fe(e)\u4e2d\u7684\u9ed1\u8272\u548c\u9ec4\u8272\u5b9e\u7ebf\u8868\u793a\u3002<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u7ed3\u679c\u8868\u660e\uff08\u56fe(e)\uff09\uff0c\u5f53\u566a\u97f3\u6c34\u5e73<\/span><\/mjx-c><\/mjx-mi>\uff1c<\/span><\/mjx-utext><\/mjx-mi><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c3<\/span><\/mi>\uff1c<\/span><\/mi>0.01<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u0394<\/span><\/mi>J<\/span><\/mi><\/mrow>><\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u59cb\u7ec8\u4fdd\u6301\u4e0d\u53d8\uff0c\u8fd9\u8868\u660e\uff0cNIS+\u65b9\u6cd5\u8ba4\u4e3a\u5728\u4f4e\u566a\u58f0\u6c34\u5e73\u56e0\u679c\u6d8c\u73b0\u59cb\u7ec8\u53d1\u751f\uff0c\u800c\u56e0\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c3<\/span><\/mi>=<\/span><\/mo>10<\/span><\/mn><\/mo><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u2212<\/span><\/sup><\/span><\/mo>3<\/span><\/sup><\/span><\/mn><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u540e\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a8<\/span><\/mi>><\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u8868\u660eRosas\u7684\u65b9\u6cd5\u8ba4\u4e3a\u56e0\u679c\u6d8c\u73b0\u59cb\u7ec8\u53d1\u751f\u3002NIS+\u7684\u7ed3\u679c\u66f4\u5408\u7406\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u4ece\u6709\u566a\u58f0\u7684\u6570\u636e\u4e2d\u63d0\u53d6\u51fa\u7c7b\u4f3c\u4e8e\u771f\u5b9e\u5b8f\u89c2\u673a\u5236\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\uff0c\u5e76\u4e14\u8fd9\u79cd\u786e\u5b9a\u6027\u52a8\u529b\u5b66\u5e94\u8be5\u6bd4\u6709\u566a\u58f0\u7684\u5fae\u89c2\u52a8\u529b\u5b66\u5177\u6709\u66f4\u5927\u7684EI\u3002\u4f5c\u8005\u8fd8\u5206\u522b\u7ed8\u5236\u4e86\u5b8f\u89c2\u548c\u5fae\u89c2\u52a8\u529b\u5b66\u7684EI\u66f2\u7ebf<\/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-texatom><\/mjx-mstyle><\/mjx-math>J<\/span><\/mi>(<\/span><\/mo>f<\/span><\/mi>M<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>(\u7ea2\u8272\u865a\u7ebf)\u548c<\/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-texatom><\/mjx-mstyle><\/mjx-math>J<\/span><\/mi>(<\/span><\/mo>f<\/span><\/mi>m<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>(\u7eff\u8272\u865a\u7ebf)\u3002\u8fd9\u4e9b\u66f2\u7ebf\u968f\u7740\u03c3\u7684\u589e\u5927\u800c\u51cf\u5c0f\uff0c\u4f46<\/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-texatom><\/mjx-mstyle><\/mjx-math>J<\/span><\/mi>(<\/span><\/mo>f<\/span><\/mi>m<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u51cf\u5c0f\u901f\u5ea6\u66f4\u5feb\uff0c\u5bfc\u81f4\u89c2\u6d4b\u5230\u56e0\u679c\u6d8c\u73b0\u7684\u53d1\u751f\u3002\u4f46\u662f\uff0c\u5f53<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a8<\/span><\/mi><<\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\uff0c\u56e0\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03a8<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u53ea\u80fd\u4e3a\u56e0\u679c\u6d8c\u73b0\u63d0\u4f9b\u5145\u5206\u6761\u4ef6\uff0c\u4f5c\u8005\u4e0d\u80fd\u505a\u51fa\u660e\u786e\u7684\u5224\u65ad\u3002\u8fd9\u4e24\u4e2a\u6307\u6807\u5728<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c3<\/span><\/mi>=<\/span><\/mo>10<\/span><\/mn><\/mo><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u2212<\/span><\/sup><\/mo>2<\/span><\/sup><\/mn><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5904\u8fbe\u5230\u5cf0\u503c\uff0c\u8fd9\u4e0e\u4f5c\u8005\u6a21\u62df\u4e2d\u4f7f\u7528\u7684\u65f6\u95f4\u6b65\u957f\uff08<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>d<\/span><\/mi>t<\/span><\/mi>=<\/span><\/mo>0.01<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff09\u7684\u5927\u5c0f\u76f8\u5bf9\u5e94\uff0c\u53cd\u6620\u4e86\u5fae\u89c2\u72b6\u6001\u7684\u53d8\u5316\u6c34\u5e73\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u566a\u58f0\u8fc7\u5927\uff0c\u6709\u9650\u7684\u89c2\u6d4b\u6570\u636e\u5c06\u4f7fNIS+\u96be\u4ee5\u4ece\u6570\u636e\u4e2d\u51c6\u786e\u8bc6\u522b\u6b63\u786e\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u3002\u56e0\u6b64\uff0cCE\u7684\u7a0b\u5ea6\u964d\u81f3\u96f6\u3002\u867d\u7136NIS+\u5224\u5b9a<\/span><\/mjx-c><\/mjx-mi>\uff1e<\/span><\/mjx-utext><\/mjx-mi><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c3<\/span><\/mi>\uff1e<\/span><\/mi>10<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\u4e0d\u5b58\u5728\u56e0\u679c\u6d8c\u73b0\uff0c\u4f46\u8fd9\u4e00\u7ed3\u679c\u5e76\u4e0d\u53ef\u9760\uff0c\u56e0\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c3<\/span><\/mi>=<\/span><\/mo>10<\/span><\/mn><\/mo><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u2212<\/span><\/sup><\/mo>2<\/span><\/sup><\/mn><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u540e\u7684\u5f52\u4e00\u5316\u9884\u6d4b\u8bef\u5dee\u5df2\u7ecf\u8d85\u8fc7\u4e86\u6240\u9009\u9608\u503c0.3(\u5782\u76f4\u865a\u7ebf\u548c\u865a\u7ebf)\u3002<\/span><\/section>\n

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

      4.2.1.2 NIS+\u4e0e\u5176\u4ed6\u6a21\u578b\u6bd4\u8f83\u9884\u6d4b\u548c\u6cdb\u5316\u80fd\u529b<\/span><\/h4>\n

      <\/span><\/section>\n
      \u6bd4\u8f83\u7684\u6a21\u578b\u5305\u62ecNIS\u6a21\u578b\u3001\u524d\u9988\u795e\u7ecf\u7f51\u7edc<\/span>\uff08NN\uff09<\/span>\u3001\u53d8\u5206\u81ea\u7f16\u7801\u5668<\/span>\uff08VAE\uff09<\/span>\u3002\u4e3a\u4e86\u8fdb\u884c\u516c\u5e73\u6bd4\u8f83\uff0c\u4f5c\u8005\u786e\u4fdd\u6240\u6709\u6a21\u578b\u5177\u6709\u5927\u81f4\u76f8\u540c\u6570\u91cf\u7684\u53c2\u6570\uff0c\u4e14\u5c06\u6837\u672c\u91cd\u52a0\u6743\u6280\u672f\u548c\u53cd\u5411\u52a8\u529b\u5b66\u6280\u672f\u5e94\u7528\u4e8e\u524d\u9988\u795e\u7ecf\u7f51\u7edc<\/span>\uff08NN\uff09<\/span>\u548c\u53d8\u5206\u81ea\u7f16\u7801\u5668<\/span>\uff08VAE\uff09<\/span>\uff0c\u6784\u5efa\u51faNN+\u548cVAE+\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5728\u5355\u72ec\u7684\u6d4b\u8bd5\u6570\u636e\u96c6\u4e0a\u9884\u6d4b\u591a\u4e2a\u65f6\u95f4\u6b65\uff0810\u6b65\uff09\u7684\u672a\u6765\u72b6\u6001\uff0c\u4ee5\u6bd4\u8f83NIS+\u4e0e\u5176\u4ed6\u6a21\u578b\u7684\u9884\u6d4b\u672a\u6765\u72b6\u6001\u7684\u80fd\u529b\u3002\u4e4b\u540e\uff0c\u4ee5\u56fe(a)\u4e2d\u5e26\u70b9\u533a\u57df\u4e3a\u8bad\u7ec3\u6570\u636e\u96c6\uff0c\u5373<\/span><\/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-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>1\/<\/span><\/mn>3<\/span><\/mn><\/mfrac>\u2264<\/span><\/mo>S<\/span><\/mi>\u2264<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u90e8\u5206\u3002\u4ee5\u56fe(a)\u4e2d\u6574\u4e2a\u84dd\u8272\u4e09\u89d2\u5f62\u4e3a\u6d4b\u8bd5\u6570\u636e\u96c6\uff0c\u5373<\/span><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>0<\/span><\/mn>\u2264<\/span><\/mo>S<\/span><\/mi>\u2264<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u90e8\u5206\u3002\u8fd9\u6837\u8bad\u7ec3NIS+\u7684\u65f6\u5019\u4e0d\u4f1a\u7528\u5230<\/span><\/mjx-c><\/mjx-mn><\/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-texatom><\/mjx-mstyle><\/mjx-math>0<\/span><\/mn>\u2264<\/span><\/mo>S<\/span><\/mi>\u2264<\/span><\/mo>1\/<\/span><\/mn>3<\/span><\/mn><\/mfrac><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u6570\u636e\uff0c\u4f46\u662f\u6d4b\u8bd5NIS+\u7684\u65f6\u5019\u4f1a\u7528\u5230<\/span><\/mjx-c><\/mjx-mn><\/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-texatom><\/mjx-mstyle><\/mjx-math>0<\/span><\/mn>\u2264<\/span><\/mo>S<\/span><\/mi>\u2264<\/span><\/mo>1\/<\/span><\/mn>3<\/span><\/mn><\/mfrac><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u6570\u636e\uff0c\u53ef\u4ee5\u901a\u8fc7\u6d4b\u8bd5<\/span><\/mjx-c><\/mjx-mn><\/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-texatom><\/mjx-mstyle><\/mjx-math>0<\/span><\/mn>\u2264<\/span><\/mo>S<\/span><\/mi>\u2264<\/span><\/mo>1\/<\/span><\/mn>3<\/span><\/mn><\/mfrac><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u6570\u636e\u7684\u8bef\u5dee\u5927\u5c0f\u6765\u6bd4\u8f83\u5404\u4e2a\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u7ed3\u679c\u8868\u660e<\/span>\uff08\u56fe(d)\uff09<\/span>\uff0cNIS+\u548cNIS\u5728\u6574\u4f53\u6570\u636e\u96c6\u4e0a<\/span>\uff08\u7eff\u8272\u6761\uff09<\/span>\u8868\u73b0\u4f18\u4e8e\u5176\u4ed6\u6a21\u578b<\/span>\uff08NN\u3001NN+\u3001VAE\u3001VAE+\uff09<\/span>\u3002\u8fd9\u8bf4\u660e\u5728\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\u4e2d\u4f7f\u7528\u53ef\u9006\u795e\u7ecf\u7f51\u7edc\u4f1a\u66f4\u597d\u3002NIS+\u7684\u5206\u5e03\u5916\u6cdb\u5316\u80fd\u529b\u4f18\u4e8e\u5176\u4ed6\u6a21\u578b\uff0c\u5728\u90e8\u5206\u6570\u636e\u96c6\u4e0a\uff0c\u4e0d\u540c\u6a21\u578b\u4e4b\u95f4\u7684\u5dee\u5f02\u8f83\u5927\u3002<\/span><\/section>\n

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

      4.2.1.3 NIS+\u80fd\u5426\u53d1\u73b0\u771f\u6b63\u7684\u5b8f\u89c2\u52a8\u6001<\/span><\/h4>\n

      <\/span><\/section>\n
      \u5c06\u771f\u5b9e\u7684SIR\u52a8\u529b\u5b66\u7684\u5411\u91cf\u573a\uff08<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>d<\/span><\/mi>y<\/span><\/mi>\/<\/span><\/mo><\/mrow>d<\/span><\/mi>t<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff09\uff08\u7ea2\u8272\uff09\u3001\u57fa\u4e8e\u7f16\u7801\u5668\u7684\u96c5\u53ef\u6bd4\u77e9\u9635\u5f97\u5230\u7684\u7406\u8bba\u5411\u91cf\uff08\u84dd\u8272\uff09\u4e0e\u901a\u8fc7\u6a21\u578b\u5b66\u4e60\u5230\u7684\u5b8f\u89c2\u52a8\u6001\u7684\u5411\u91cf\uff08<\/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-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>d<\/span><\/mi>(<\/span><\/mo>h<\/span><\/mi><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>1<\/span><\/sub><\/span><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/msub>,<\/span><\/mo>h<\/span><\/mi><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>2<\/span><\/sub><\/span><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/msub>)<\/span><\/mo>\/<\/span><\/mo><\/mrow>d<\/span><\/mi>t<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff09\uff08\u7eff\u8272\uff09\u8fdb\u884c\u6bd4\u8f83\u3002<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u7ed3\u679c\u8868\u660e\uff08\u56fe(c)\u8868\u793aNIS+\uff0c\u56fe(f)\u8868\u793aNIS\uff09\uff0c\u5b66\u4e60\u5230\u7684\u5411\u91cf\u4e0e\u771f\u5b9e\u5411\u91cf\u5bf9\u9f50\u53ca\u7406\u8bba\u5411\u91cf\uff08\u7528\u96c5\u53ef\u6bd4\u77e9\u9635\u8ba1\u7b97\uff09\u5bf9\u9f50\u3002NIS+\u660e\u663e\u4f18\u4e8eNIS\uff0c\u5c24\u5176\u662f\u5728\u6ca1\u6709\u8bad\u7ec3\u6837\u672c\u7684\u5916\u56f4\u533a\u57df\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u7efc\u4e0a\u53ef\u77e5\uff0c\u901a\u8fc7\u6700\u5927\u5316EI\u548c\u5b66\u4e60\u72ec\u7acb\u7684\u56e0\u679c\u673a\u5236\uff0cNIS+\u53ef\u4ee5\u6709\u6548\u5730\u5ffd\u7565\u6570\u636e\u4e2d\u7684\u566a\u58f0\uff0c\u51c6\u786e\u5730\u5b66\u4e60\u771f\u5b9e\u5b8f\u89c2\u52a8\u6001\uff0c\u5e76\u6709\u826f\u597d\u7684\u6cdb\u5316\u80fd\u529b\u3002\u6b64\u5916\uff0cNIS+\u5728\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u65b9\u9762\u8868\u73b0\u51fa\u4f18\u8d8a\u7684\u6027\u80fd\u3002<\/span><\/section>\n


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

      4.2.2 Boids \u6a21\u578b\u6570\u636e<\/span><\/strong><\/h3>\n

      <\/span><\/section>\n
      Boids\u6a21\u578b\uff0c\u662f\u4e00\u4e2a\u8457\u540d\u7684\u591a\u4e3b\u4f53\u6a21\u578b\uff0c\u7528\u4e8e\u6a21\u62df\u9e1f\u7c7b\u7684\u96c6\u4f53\u884c\u4e3a[22]\u3002\u4f7f\u7528\u6b64\u6a21\u578b\u751f\u6210\u7684\u6570\u636e\u68c0\u6d4bNIS+\u5728\u4e0b\u9762\u56db\u4e2a\u65b9\u9762\u7684\u80fd\u529b\uff1a\u2460\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u7684\u80fd\u529b\uff1b\u2461\u7c97\u7c92\u5316\u7b56\u7565\u7684\u53ef\u89e3\u91ca\u6027\uff1b\u2462\u5206\u5e03\u5916\u6570\u636e\u6cdb\u5316\u80fd\u529b\uff1b\u2463\u5185\u5728\u566a\u97f3\u548c\u5916\u90e8\u566a\u97f3\u5bf9\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u7684\u5f71\u54cd\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u4f5c\u8005\u6839\u636eReynolds(1987)[22]\u7684\u65b9\u6cd5\u6a21\u62dfBoids\u6a21\u578b\uff0c\u5728300 \u00d7 300\u7684\u753b\u5e03\u4e0a\u7528N = 16\u4e2a\u9e1f\u751f\u6210\u8bad\u7ec3\u6570\u636e\u3002\u4e3a\u4e86\u8bc4\u4f30NIS+\u53d1\u73b0\u6709\u610f\u4e49\u7684\u5b8f\u89c2\u72b6\u6001\u7684\u80fd\u529b\uff0c\u4f5c\u8005\u5c06\u9e1f\u7fa4\u5206\u4e3a\u4e24\u7ec4\uff0c\u5e76\u4e3a\u6bcf\u7ec4\u5f15\u5165\u4e0d\u540c\u7684\u6052\u5b9a\u8f6c\u5411\u529b\u3002\u8fd9\u4e00\u4fee\u6539\u786e\u4fdd\u4e86\u4e24\u7ec4\u5206\u522b\u6cbf\u7740\u4e0d\u540c\u8f6c\u5f2f\u89d2\u5ea6\u7684\u8f68\u8ff9\u8fd0\u52a8\uff0c\u5982\u56fe(a)\u6240\u793a\u3002\u4f5c\u8005\u901a\u8fc7\u6a21\u62df\u751f\u6210\u8bad\u7ec3\u548c\u6d4b\u8bd5\u6570\u636e\u3002\u5728\u6bcf\u4e2a\u65f6\u95f4\u6b65\u957ft\u4e0a\uff0c\u5fae\u89c2\u72b6\u6001\u4e3a4N\u7ef4\u5411\u91cf\uff1a<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u5176\u4e2d<\/span><\/sub><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u7b2ci\u53ea\u9e1f\u5728t\u65f6\u523b\u7684\u4f4d\u7f6e\u5750\u6807\uff0c<\/span><\/sub><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662fi\u5728\u65f6\u523bt\u7684\u901f\u5ea6\u5411\u91cf\uff0c\u5176\u4e2d<\/span><\/mjx-c><\/mjx-mi><\/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-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>i<\/span><\/mi>=<\/span><\/mo>1<\/span><\/mn>,<\/span><\/mo>2<\/span><\/mn>,<\/span><\/mo>\u2026<\/span><\/mo>,<\/span><\/mo>16<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/section>\n

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


      <\/span><\/h4>\n

      4.2.2.1NIS+\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u7684\u80fd\u529b<\/span><\/h4>\n

      <\/span><\/section>\n
      \u9884\u6d4b\u7684\u6d8c\u73b0\u96c6\u4f53\u98de\u884c\u884c\u4e3a<\/span>\uff0850\u6b65\uff09<\/span>\u4e0e\u4e24\u7ec4\u7684\u771f\u5b9e\u8f68\u8ff9\u5bc6\u5207\u76f8\u5173\uff0c\u7279\u522b\u662f\u5728\u521d\u59cb\u9636\u6bb5\u3002\u8fd9\u4e9b\u9884\u6d4b\u8f68\u8ff9\u662f\u901a\u8fc7\u5c06\u9884\u6d4b\u7684\u5b8f\u89c2\u72b6\u6001\u89e3\u7801\u4e3a\u76f8\u5e94\u7684\u5fae\u89c2\u72b6\u6001\u6765\u751f\u6210\u7684\uff0c\u4e24\u6761\u5b9e\u7ebf\u8868\u793a\u5b83\u4eec\u7684\u5e73\u5747\u503c\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5728\u4e0d\u540c\u5b8f\u89c2\u6001\u7ef4\u5ea6\u8d85\u53c2\u4e0b\uff0c\u7ed3\u679c\u8868\u660e<\/span>\uff08\u56fe(a)\uff09<\/span>\uff0c\u56e0\u679c\u6d8c\u73b0\u5728q = 8\u65f6\u8fbe\u5230\u6700\u5927\u503c\uff0c\u5982\u56fe(c)\u6240\u793a\uff0c\u8fd9\u4e0e\u4f5c\u8005\u9009\u62e9\u8d85\u53c2\u6570q = 8<\/span>\uff08\u5b8f\u89c2\u53d8\u91cf\u7684\u7ef4\u5ea6\uff09<\/span>\u76f8\u7b26\uff0c\u8fd9\u521a\u597d\u5bf9\u5e94\u4e24\u7ec4\u9e1f\u7684\u4e2d\u5fc3\u4ee3\u8868\u70b9\u7684\u72b6\u6001\u7a7a\u95f4\u7ef4\u6570<\/span>\uff08\u4e24\u4e2a\u7a7a\u95f4\u5750\u6807\u548c\u4e24\u4e2a\u65f6\u95f4\u5750\u6807\uff0c\u4e00\u5171\u4e24\u7ec4\uff0c\u6240\u4ee5\u5171\u67098\u4e2a\u7ef4\u5ea6\uff09<\/span>\u3002<\/span><\/section>\n

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


      <\/span><\/h4>\n

      4.2.2.2 NIS+\u7c97\u7c92\u5316\u7b56\u7565\u7684\u53ef\u89e3\u91ca\u6027<\/span><\/h4>\n

      <\/span><\/section>\n
      \u4f5c\u8005\u5229\u7528\u79ef\u5206\u68af\u5ea6(IG)[23]\u6765\u8bc6\u522b\u6bcf\u4e2a\u5b66\u5230\u7684\u6d8c\u73b0\u5b8f\u89c2\u72b6\u6001\u7ef4\u5ea6\u4e2d\u6700\u91cd\u8981\u7684\u5fae\u89c2\u72b6\u6001\uff0c\u5c06\u8ba1\u7b97\u7684IG\u5f52\u4e00\u5316\uff0c\u5e76\u5728\u6bcf\u4e2a\u5b8f\u89c2\u72b6\u6001\u4e2d\u63d0\u9ad8\u5fae\u89c2\u72b6\u6001\u7684\u6700\u5927\u68af\u5ea6\uff0c\u5e76\u4e14\u5ffd\u7565\u6bcf\u53ea\u9e1f\u7684\u901f\u5ea6\u7ef4\u5ea6<\/span>\uff08\u4e0e\u5b8f\u89c2\u72b6\u6001\u7684\u76f8\u5173\u6027\u8f83\u4f4e\uff09<\/span>\u3002\u6700\u540e\uff0c\u4f5c\u8005\u5c06\u5f52\u4e00\u5316\u7684IG\u7ed8\u5236\u6210\u56fe(d)\uff0c\u7528\u4ee5\u63cf\u8ff0\u6bcf\u4e2a\u5b8f\u89c2\u7ef4\u5ea6<\/span>\uff08\u7eb5\u8f74\uff09<\/span>\u548c\u6bcf\u53ea\u9e1f\u7a7a\u95f4\u5750\u6807<\/span>\uff08\u6a2a\u8f74\uff09<\/span>\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5e76\u7528\u6a59\u8272\u70b9\u8868\u793a\u6bcf\u4e2a\u5b8f\u89c2\u72b6\u6001\u4e2d\u6700\u91cd\u8981\u7684\u5fae\u89c2\u72b6\u6001\u3002<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u7ed3\u679c\u8868\u660e<\/span>\uff08\u56fe(d)\uff09<\/span>\uff0c\u5b8f\u89c2\u72b6\u6001\u7684\u7b2c1\u30012\u30015\u30016\u7ef4\u5206\u522b\u5bf9\u5e94\u7b2c\u4e00\u7ec4\u4e2d\u7684ID<\/span>\uff08ID<8\uff09\uff08\u56fe(d)\u4e2dgroup 1 \u7684\u6a59\u8272\u70b9\u5728\u7b2c1\u884c\u3001\u7b2c2\u884c\u3001\u7b2c5\u884c\u3001\u7b2c6\u884c\uff09<\/span>\uff0c\u7b2c3\u30014\u30017\u30018\u7ef4\u5bf9\u5e94\u7b2c\u4e8c\u7ec4\u4e2d\u7684ID<\/span>\uff08ID>=8\uff09\uff08\u56fe(d)\u4e2dgroup 2 \u7684\u6a59\u8272\u70b9\u5728\u7b2c3\u884c\u3001\u7b2c4\u884c\u3001\u7b2c7\u884c\u3001\u7b2c8\u884c\uff09<\/span>\u3002\u56e0\u6b64\uff0c\u5b66\u4e60\u5230\u7684\u7c97\u7c92\u5316\u7b56\u7565\u4f7f\u7528\u4e24\u4e2a\u4f4d\u7f6e\u5750\u6807\u6765\u8868\u793a\u6240\u6709\u5176\u4ed6\u4fe1\u606f\uff0c\u5f62\u6210\u4e00\u4e2a\u7ef4\u5ea6\u7684\u5b8f\u89c2\u72b6\u6001\u3002NIS+\u5b66\u4e60\u51fa\u6765\u7684\u7ef4\u5ea6\u5e76\u4e0d\u80fd\u521a\u597d\u5bf9\u5e94\u6bcf\u4e2a\u7ec4\u4e2d\u5fc3\u7684\u4f4d\u7f6e\u548c\u901f\u5ea6\uff0c\u800c\u662f\u4e0e\u7279\u5b9a\u9e1f\u7684\u4f4d\u7f6e\u6709\u5173<\/span>\uff08\u56fed\uff09<\/span>\u3002\u4f5c\u8005\u63a8\u6d4b\u8fd9\u53ea\u9e1f\u5b9e\u9645\u4e0a\u88abNIS+\u9009\u5b9a\u4e3a\u8fd9\u7fa4\u9e1f\u7684\u4ee3\u8868\uff0c\u89c2\u5bdf\u8fd9\u53ea\u9e1f\u7684\u60c5\u51b5\u53ef\u4ee5\u9884\u6d4b\u8fd9\u7fa4\u9e1f\u7684\u6574\u4f53\u8fd0\u52a8\u8d8b\u52bf\u3002NIS+\u5e76\u6ca1\u6709\u5229\u7528\u4efb\u4f55\u7684\u901f\u5ea6\u6570\u636e\uff0c\u800c\u4ec5\u4ec5\u4f7f\u7528\u4e86\u4f4d\u7f6e\u6570\u636e\uff0c\u4f5c\u8005\u8ba4\u4e3a\u8fd9\u662f\u56e0\u4e3aNIS+\u53ef\u4ee5\u901a\u8fc7\u989d\u5916\u7684\u81ea\u7531\u5ea6\u6765\u8868\u793a\u901f\u5ea6\uff0c\u56e0\u4e3a\u901a\u8fc7\u4e24\u4e2a\u8fde\u7eed\u65f6\u523b\u4e4b\u95f4\u7684\u4f4d\u7f6e\u5dee\u8ba1\u7b97\u51fa\u901f\u5ea6\u3002\u56e0\u6b64\uff0cNIS+\u4ecd\u7136\u9700\u8981\u516b\u4e2a\u81ea\u7531\u5ea6\u6765\u63cf\u8ff0\u4e24\u7ec4\u9e1f\u7684\u5b8f\u89c2\u72b6\u6001\u3002<\/span><\/section>\n

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

      4.2.2.3 NIS+\u7684\u6cdb\u5316\u80fd\u529b<\/span><\/h4>\n

      <\/span><\/section>\n
      \u4e3a\u4e86\u6bd4\u8f83\u4e0d\u540c\u6a21\u578b\u5728\u5206\u5e03\u5916\u6570\u636e\u4e0a\u7684\u6cdb\u5316\u80fd\u529b\uff0c\u4f5c\u8005\u5728\u751f\u6210\u8bad\u7ec3\u6570\u636e\u7684\u4eff\u771f\u8fc7\u7a0b\u4e2d\uff0c\u4ee4\u6240\u6709\u9e1f\u7684\u521d\u59cb\u4f4d\u7f6e\u88ab\u7ea6\u675f\u5728\u4e00\u4e2a\u534a\u5f84\u4e3ar\u7684\u5706\u5185\uff0c\u5982\u56fe(a)\u6240\u793a\u3002\u4f5c\u8005\u8bc4\u4f30\u5f53\u6d4b\u8bd5\u6570\u636e\u7684\u521d\u59cb\u4f4d\u7f6e\u53d6\u503c\u662f\u5728\u534a\u5f84\u66f4\u5927\u7684\u5706\u4e0a\u7684\u65f6\u5019\uff0c\u6a21\u578b\u7684\u6d4b\u8bd5\u8bef\u5dee\u5982\u4f55\u968f\u534a\u5f84\u53d8\u5316\uff1f<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u7ed3\u679c\u8868\u660e<\/span>\uff08\u56fe(b)\uff09<\/span>\uff0cNIS+\u548cNIS\u7684MAE\u503c\u90fd\u968f\u534a\u5f84r\u7684\u589e\u52a0\u800c\u589e\u52a0\uff0c\u800c\u9884\u6d4b\u8bef\u5deeMAE\u8d8a\u5c0f\uff0c\u6cdb\u5316\u80fd\u529b\u8d8a\u597d\u3002\u800c\u4e14\u4e0eNIS\u76f8\u6bd4\uff0cNIS+\u5728\u6240\u6709\u6d4b\u8bd5\u534a\u5f84r\u4e0a\u8bef\u5dee\u66f4\u5c0f\uff0c\u56e0\u6b64\u5b83\u5177\u6709\u66f4\u4f18\u8d8a\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/span><\/section>\n


      <\/span><\/h4>\n

      4.2.2.4 \u5185\u5728\u566a\u97f3\u548c\u5916\u90e8\u566a\u97f3\u5bf9NIS+\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u7684\u5f71\u54cd<\/span><\/h4>\n

      <\/span><\/section>\n
      \u901a\u8fc7\u5728\u6bcf\u4e2a\u65f6\u95f4\u6b65\u957f\u4e3a\u6bcf\u53ea\u9e1f\u589e\u52a0\u968f\u673a\u8f6c\u89d2\uff0c\u5f15\u5165\u5185\u5728\u566a\u58f0<\/span> (Intrinsic Noise)<\/span>\u3002\u8fd9\u4e9b\u89d2\u5ea6\u5747\u5300\u5206\u5e03\u5728\u533a\u95f4<\/span><\/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-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b1<\/span><\/mi>\u22c5<\/span><\/mo>[<\/span><\/mo>\u2212<\/span><\/mo>\u03c0<\/span><\/mi>,<\/span><\/mo>\u03c0<\/span><\/mi>]<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5185\uff0c\u5176\u4e2d<\/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-texatom><\/mjx-mstyle><\/mjx-math>\u03b1<\/span><\/mi>\u2208<\/span><\/mo>[<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo>1<\/span><\/mn>]<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u63a7\u5236\u5185\u5728\u566a\u58f0\u5f3a\u5ea6\u5927\u5c0f\u7684\u53c2\u6570\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5916\u90e8\u566a\u58f0<\/span>\uff08Extrinsic Noise\uff0c\u6216Observational Noise\uff09<\/span>\u662f\u6307\u5f71\u54cd\u89c2\u6d4b\u6570\u636e\u7684\u566a\u58f0\uff0c\u5728Boid\u6a21\u578b\u4e2d\uff0c\u5373\u662f\u52a0\u5230\u5fae\u89c2\u72b6\u6001\u4e0a\u7684\u566a\u58f0\uff0c\u4e5f\u5c31\u662f\u6700\u7ec8\u7684\u89c2\u6d4b\u6570\u636e\u662f\u5bf9\u6bcf\u4e00\u4e2a\u65f6\u523b\u7684\u5fae\u89c2\u6001\u90fd\u52a0\u4e0a\u5916\u90e8\u6216\u89c2\u6d4b\u566a\u58f0<\/span><\/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-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b4<\/span><\/mi>\u223c<\/span><\/mo>N<\/span><\/mi><\/mrow>(<\/span><\/mo>0<\/span><\/mn>,<\/span><\/mo>\u03b4<\/span><\/mi>m<\/span><\/sub><\/mi>a<\/span><\/sub><\/mi>x<\/span><\/sub><\/mi><\/mrow><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5176\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b4<\/span><\/mi>m<\/span><\/sub><\/mi>a<\/span><\/sub><\/mi>x<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u51b3\u5b9a\u8be5\u566a\u58f0\u5927\u5c0f\u7684\u53c2\u6570\u3002<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u7ed3\u679c\u8868\u660e\uff08\u56fe(f)\u548c\u56fe(g)\uff09\uff0c\u5728\u8fd9\u4e24\u79cd\u60c5\u51b5\u4e0b\uff0c\u5f52\u4e00\u5316MAE\u90fd\u589e\u52a0\u4e86\uff0c\u8fd9\u8868\u660e\u968f\u7740\u5185\u5728\u548c\u5916\u5728\u566a\u58f0\u7684\u589e\u52a0\uff0c\u9884\u6d4b\u4efb\u52a1\u66f4\u5177\u6311\u6218\u6027\u3002\u7136\u800c\uff0c\u8fd9\u4e24\u79cd\u7c7b\u578b\u7684\u566a\u58f0\u4e4b\u95f4\u7684\u5dee\u5f02\u53ef\u4ee5\u901a\u8fc7\u68c0\u67e5\u56e0\u679c\u6d8c\u73b0(<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u0394<\/span><\/mi>J<\/span><\/mi><\/mrow>><\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>)\u7684\u7a0b\u5ea6\u6765\u89c2\u5bdf\u3002\u4ece\u56fe(f)\u53ef\u4ee5\u770b\u51fa\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u0394<\/span><\/mi>J<\/span><\/mi><\/mrow>><\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u968f\u5916\u90e8\u566a\u58f0(<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b4<\/span><\/mi>m<\/span><\/sub><\/mi>a<\/span><\/sub><\/mi>x<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>)\u7684\u589e\u5927\u800c\u589e\u5927\uff0c\u8bf4\u660e\u7c97\u7c92\u5316\u7b56\u7565\u53ef\u4ee5\u5728\u4e00\u5b9a\u8303\u56f4\u5185\u51cf\u8f7b\u566a\u58f0\u5f71\u54cd\uff0c\u589e\u5f3a\u56e0\u679c\u6548\u5e94\u7684\u6548\u679c\u3002<\/span><\/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-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b4<\/span><\/mi>m<\/span><\/sub><\/mi>a<\/span><\/sub><\/mi>x<\/span><\/sub><\/mi><\/mrow><\/msub><<\/span><\/mo>0.1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\uff0c\u5f52\u4e00\u5316MAE\u5c0f\u4e8e0.3(\u9ed1\u8272\u865a\u7ebf)\uff0c\u6ee1\u8db3\u5f0f1\u7684\u7ea6\u675f\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u56e0\u679c\u6d8c\u73b0\u7684\u7a0b\u5ea6\u968f\u7740<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b4<\/span><\/mi>m<\/span><\/sub><\/mi>a<\/span><\/sub><\/mi>x<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u589e\u5927\u800c\u589e\u5927\u3002\u7136\u800c\uff0c\u5f53\u8d85\u8fc70.3\u7684\u9608\u503c\u65f6\uff0c\u5373\u4f7f<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u0394<\/span><\/mi>J<\/span><\/mi><\/mrow>><\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u51cf\u5c0f\uff0c\u539f\u5219\u4e0a\u6211\u4eec\u4e5f\u65e0\u6cd5\u5f97\u51fa\u6709\u610f\u4e49\u7684\u7ed3\u8bba<\/span>\uff08\u8fdd\u53cd\u4e86\u5f0f1\u4e2d\u7684\u7ea6\u675f\uff09<\/span>\uff0c\u7ed3\u679c\u7684\u53ef\u9760\u6027\u5c31\u4f1a\u964d\u4f4e\u3002\u4ece\u56fe(g)\u53ef\u4ee5\u770b\u51fa\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u0394<\/span><\/mi>J<\/span><\/mi><\/mrow>><\/span><\/mo>0<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u968f\u7740\u5185\u90e8\u566a\u58f0(\u03b1)\u6c34\u5e73\u7684\u589e\u52a0\u800c\u51cf\u5c0f\u3002\u8fd9\u662f\u7531\u4e8e\u5b8f\u89c2\u5c42\u9762\u7684\u52a8\u529b\u5b66\u5b66\u4e60\u5668\u8bd5\u56fe\u5728\u8fd9\u4e00\u9636\u6bb5\u6355\u6349\u6bcf\u4e2a\u7fa4\u4f53\u7684\u7fa4\u4f53\u884c\u4e3a\u3002\u7136\u800c\uff0c\u968f\u7740\u5185\u90e8\u566a\u58f0\u7684\u589e\u52a0\uff0c\u7fa4\u4f53\u884c\u4e3a\u9010\u6e10\u51cf\u5f31\uff0c\u5bfc\u81f4\u56e0\u679c\u6d8c\u73b0\u964d\u4f4e\u3002\u56e0\u4e3a\u5f52\u4e00\u5316MAE\u8d85\u8fc70.3\u7684\u9608\u503c\u65f6\u8fdd\u53cd\u4e86\u5f0f1\u4e2d\u7684\u7ea6\u675f\u3002\u56fe(e)\u663e\u793a\u4e86\u5f53\u5185\u5728\u566a\u58f0<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b1<\/span><\/mi>=<\/span><\/mo>0.4<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\u5019\u7684\u771f\u5b9e\u8f68\u8ff9\u548c\u9884\u6d4b\u3002\u53ef\u4ee5\u89c2\u5bdf\u5230\uff0c\u5728\u65e9\u671f\u53ef\u4ee5\u9884\u6d4b\u76f4\u7ebf\u8d8b\u52bf\uff0c\u4f46\u968f\u7740\u566a\u58f0\u5f15\u8d77\u7684\u504f\u5dee\u9010\u6e10\u589e\u5927\uff0c\u8bef\u5dee\u4e5f\u968f\u4e4b\u589e\u5927\uff0c\u56e0\u679c\u6d8c\u73b0\u964d\u4f4e\u3002<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u7efc\u4e0a\u53ef\u77e5\uff0cNIS+\u5177\u6709\u8bc6\u522b\u6d8c\u73b0\u96c6\u4f53\u884c\u4e3a\u548c\u566a\u58f0\u5bf9\u6d8c\u73b0\u96c6\u4f53\u884c\u4e3a\u7684\u5f71\u54cd\u7a0b\u5ea6\u7684\u80fd\u529b\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      NIS+\u53ef\u4ee5\u5b66\u4e60\u6700\u4f18\u5b8f\u89c2\u52a8\u6001\u548c\u7c97\u7c92\u5ea6\u7b56\u7565\uff0c\u5177\u6709\u826f\u597d\u7684\u6cdb\u5316\u80fd\u529b\u3002\u5b66\u4e60\u5230\u7684\u5b8f\u89c2\u72b6\u6001\u6709\u6548\u5730\u8bc6\u522b\u4e86\u5e73\u5747\u7fa4\u4f53\u884c\u4e3a\uff0c\u5e76\u4e14\u53ef\u4ee5\u4f7f\u7528IG\u65b9\u6cd5\u5c06\u5176\u5f52\u56e0\u4e8e\u4e2a\u4f53\u4e4b\u4e0a\u3002\u6b64\u5916\uff0c\u56e0\u679c\u6d8c\u73b0\u7684\u7a0b\u5ea6\u968f\u5916\u5728\u566a\u58f0\u7684\u589e\u52a0\u800c\u589e\u52a0\uff0c\u968f\u5185\u5728\u566a\u58f0\u7684\u589e\u5927\u800c\u51cf\u5c11\u3002\u8fd9\u4e00\u89c2\u5bdf\u7ed3\u679c\u8868\u660e\uff0c\u901a\u8fc7\u7c97\u7c92\u5316\u53ef\u4ee5\u6d88\u9664\u5916\u5728\u566a\u58f0\uff0c\u800c\u4e0d\u80fd\u6d88\u9664\u5185\u5728\u566a\u58f0\u3002<\/span><\/section>\n

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

      4.2.3 \u751f\u547d\u6e38\u620f\u6a21\u578b\u6570\u636e<\/span><\/strong><\/h3>\n

      <\/span><\/section>\n
      \u5eb7\u5a01\u7684\u751f\u547d\u6e38\u620f\u662f\u4e00\u4e2a\u8457\u540d\u7684\u4e8c\u7ef4\u5143\u80de\u81ea\u52a8\u673a\u6a21\u578b\uff0c\u5728\u8fd9\u4e2a\u6a21\u578b\u4e0a\u51fa\u73b0\u4e86\u6ed1\u7fd4\u673a\u3001\u6b63\u65b9\u5f62\u3001\u82b1\u6735\u3001\u4fe1\u53f7\u706f\u3001\u8702\u7a9d\u3001\u4ea4\u901a\u706f\u7b49\u5404\u79cd\u6709\u8da3\u7684\u52a8\u6001\u6a21\u5f0f\u3002\u4e0eSIR\u6a21\u578b\u548cBoids\u6a21\u578b\u4e0d\u540c\u7684\u662f\uff0c\u5728\u89c4\u5219\u7f51\u683c\u4e0a\uff0c\u751f\u547d\u6e38\u620f\u6a21\u578b\u5728\u6bcf\u4e2a\u65f6\u95f4\u6b65\u957f\u7684\u5fae\u89c2\u72b6\u6001\u662f\u79bb\u6563\u7684<\/span>\uff080\u62161\uff09<\/span>\u3002\u6b64\u5916\uff0c\u5fae\u89c2\u52a8\u529b\u5b66\u4e0d\u80fd\u7528\u5fae\u5206\u65b9\u7a0b\u6216\u5dee\u5206\u65b9\u7a0b\u6765\u8868\u793a\uff0c\u800c\u662f\u7528\u89c4\u5219\u8868\u6765\u8868\u793a\u3002<\/span><\/section>\n

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

      4.2.3.1 NIS+\u7684\u62d3\u5c55<\/span><\/h4>\n


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

      \u4e3a\u4e86\u4f7f\u7528\u6b64\u6570\u636e\uff0c\u4f5c\u8005\u5728\u7a7a\u95f4\u548c\u65f6\u95f4\u7ef4\u5ea6\u4e0a\u5bf9\u5143\u80de\u81ea\u52a8\u673a\u7684\u5fae\u89c2\u72b6\u6001\u8fdb\u884c\u7c97\u7c92\u5316\u5904\u7406\u3002\u4e3a\u6b64\uff0c\u4f5c\u8005\u5f15\u5165\u4e86\u65f6\u7a7a\u5377\u79ef\u7684\u6982\u5ff5\u3002<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u4f5c\u8005\u4f7f\u7528\u7684\u4f53\u7cfb\u7ed3\u6784\u5982\u56fe(e)\u6240\u793a\u3002\u6574\u4e2a\u7c97\u7c92\u5316\u8fc7\u7a0b\u53ef\u5206\u4e3a\u4e24\u4e2a\u6b65\u9aa4\uff1a\u2460\u5728\u56fa\u5b9a\u5927\u5c0f\u7684\u7a97\u53e3<\/span>\uff08\u672c\u6587\u4e3a3×3\u7a97\u53e3\uff09<\/span>\u5185\u805a\u5408\u4fe1\u606f\uff0c\u83b7\u5f97\u7a7a\u95f4\u7c97\u7c92\u5316\u7ed3\u679c\uff1b\u2461\u5c06\u8fd9\u4e9b\u7ed3\u679c\u5728\u591a\u4e2a\u8fde\u7eed\u7684\u65f6\u95f4\u6b65\u957f\u4e0a\u805a\u5408\uff0c\u5f62\u6210\u4e00\u4e2a\u65f6\u7a7a\u7c97\u7c92\u5316\u7684\u5b8f\u89c2\u72b6\u6001\u3002\u6240\u6709\u8fd9\u4e9b\u8fc7\u7a0b\u90fd\u662f\u901a\u8fc7NIS+\u4e2d\u7684\u5e76\u884c\u7f16\u7801\u5668\u5b9e\u73b0\u7684\u3002<\/span><\/section>\n

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

      4.2.3.2 NIS+\u6355\u83b7\u6a21\u5f0f\u7684\u80fd\u529b<\/span><\/h4>\n

      <\/span><\/section>\n
      \u4f5c\u8005\u4f7f\u7528\u968f\u673a\u521d\u59cb\u6761\u4ef6\u4e0b\u6a21\u62df\u751f\u6210\u7684\u6570\u636e\u6765\u8bad\u7ec3NIS+\uff0c\u5e76\u63d0\u53d6\u4ece\u7b2c100\u6b65\u5230\u7b2c120\u6b65\u7684\u72b6\u6001\u65f6\u95f4\u5e8f\u5217\u3002\u56fe(a)\u3001(b)\u548c(c)\u663e\u793a\u4e86\u7531\u771f\u5b9e\u5b8f\u89c2\u673a\u5236\u6a21\u62df<\/span> (\u7b2c\u4e00\u884c) <\/span>\u548cNIS+\u9884\u6d4b<\/span> (\u7b2c\u4e09\u884c) <\/span>\u751f\u6210\u7684\u52a8\u6001\u6a21\u5f0f\uff0c\u4ee5\u53ca\u53ef\u4ee5\u8fdb\u884c\u8fd9\u4e9b\u9884\u6d4b\u7684\u6d8c\u73b0\u5b8f\u89c2\u72b6\u6001<\/span> (\u7b2c\u4e8c\u884c) <\/span>\u3002\u4f5c\u8005\u5c06\u4e24\u4e2a\u8fde\u7eed\u65f6\u95f4\u6b65\u957f\u7684\u56fe\u50cf\u8f93\u5165\u5230NIS+\u4e2d\uff0c\u518d\u7528\u4e24\u4e2a\u8fde\u7eed\u65f6\u95f4\u6b65\u957f\u5f97\u5230\u53e6\u4e00\u4e2a\u56fe\u50cf\u5bf9\u3002\u628a\u4e0a\u9762\u7684\u56fe\u7247\u548c\u4e0b\u9762\u7684\u56fe\u7247\u6bd4\u8f83\u4e00\u4e0b\uff0c\u56fe\u6848\u662f\u76f8\u4f3c\u7684\u3002\u7136\u800c\uff0c\u7531\u4e8e\u5728\u968f\u673a\u521d\u59cb\u6761\u4ef6\u4e0b\u5177\u6709\u67d0\u4e9b\u6a21\u5f0f\u7684\u8bad\u7ec3\u6837\u672c\u51fa\u73b0\u6709\u9650\uff0c\u7b2c\u4e09\u5217\u7684\u5b66\u4e60\u548c\u9884\u6d4b\u6a21\u5f0f\u6709\u4e9b<\/span>\uff08\u7279\u522b\u662f\u201c\u6ed1\u7fd4\u673a\u201d\u6a21\u5f0f\uff09<\/span>\u663e\u5f97\u6a21\u7cca\u3002\u4e3a\u4e86\u63d0\u9ad8\u9884\u6d4b\u7684\u8d28\u91cf\uff0c\u4f5c\u8005\u751f\u6210\u4e00\u7ec4\u5305\u542b\u4e24\u4e2a\u201c\u6ed1\u7fd4\u673a\u201d\u521d\u59cb\u6761\u4ef6\u7684\u65b0\u8bad\u7ec3\u6837\u672c\u3002<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u7ed3\u679c\u5982\u56fe(d)\u6240\u793a\uff0c\u5c3d\u7ba1\u8fd9\u4e2a\u6d4b\u8bd5\u73af\u5883\u4e2d\u7684\u6ed1\u7fd4\u673a\u6570\u91cf\u662f3\u4e2a\uff0c\u9884\u6d4b\u4e5f\u66f4\u52a0\u6e05\u6670\u3002\u8fd9\u610f\u5473\u7740\uff0cNIS+\u53ef\u4ee5\u6355\u83b7\u5305\u62ec\u79fb\u52a8\u3001\u9759\u6001\u548c\u632f\u8361\u7ed3\u6784\u5728\u5185\u7684\u6a21\u5f0f\u3002<\/span><\/section>\n

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

      4.2.3.3 NIS+\u7684\u6cdb\u5316\u80fd\u529b<\/span><\/h4>\n

      <\/span><\/section>\n
      \u4f5c\u8005\u6bd4\u8f83\u4e86\u5728\u4e0d\u540c\u4e8e\u521d\u59cb\u968f\u673a\u6a21\u5f0f\u4e0b\uff0cNIS\u548cNIS+\u5bf98\u79cd\u4e0d\u540c\u6a21\u5f0f\u7c7b\u578b\u7684\u591a\u6b65\u9884\u6d4b\u6027\u80fd\u3002<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u7ed3\u679c\u8868\u660e<\/span>\uff08\u56fe(f)\uff09<\/span>\uff0c\u5bf9\u4e8e\u6240\u6709\u6a21\u5f0f\u7c7b\u578b\uff0cNIS+\u59cb\u7ec8\u6bd4NIS\u5177\u6709\u66f4\u9ad8\u7684AUC<\/span> (\u66f2\u7ebf\u4e0b\u9762\u79ef) <\/span>\u3002\u5176\u4e2d\uff0c\u5728x\u5750\u6807\u7684\u523b\u5ea6\u6807\u7b7e\u4e2d\uff0c\u4f5c\u8005\u91c7\u7528\u201c\u6a21\u5f0f\u540d\u79f0<\/span> (\u6570\u91cf) <\/span>\u201d\u7684\u683c\u5f0f\u6765\u8868\u793a\u5404\u79cd\u521d\u59cb\u6761\u4ef6\u3002\u4f8b\u5982\uff0c\u201c\u6ed1\u7fd4\u673a(2)\u201d\u8868\u793a\u5305\u542b\u4e24\u4e2a\u6ed1\u7fd4\u673a\u7684\u521d\u59cb\u914d\u7f6e\u3002\u7ed3\u679c\u8868\u660e\uff0cNIS+\u5728\u6355\u83b7\u8fd9\u4e9b\u6a21\u5f0f\u65b9\u9762\u5177\u6709\u4f18\u8d8a\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/span><\/section>\n

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

      4.2.3.4 NIS+\u8bc6\u522bCE\u7684\u80fd\u529b<\/span><\/h4>\n

      <\/span><\/section>\n
      \u5728\u6bd4\u8f83\u8fc7\u7a0b\u4e2d\uff0c\u4f5c\u8005\u4f7f\u7528\u76f8\u540c\u7684\u6a21\u5f0f\u4f5c\u4e3a\u521d\u59cb\u6761\u4ef6\u3002<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u7ed3\u679c\u8868\u660e<\/span>\uff08\u56fe(g)\uff09<\/span>\uff0c\u9664\u201c\u968f\u673a\u201d\u60c5\u51b5\u5916\uff0c\u5176\u4f598\u4f8b\u5747\u53d1\u751f\u56e0\u679c\u6d8c\u73b0\u3002\u7531\u4e8e\u51fa\u73b0\u201c\u6ed1\u7fd4\u673a\u201d\u7684\u8bad\u7ec3\u6837\u672c\u6709\u9650\uff0cNIS+\u5728\u6b64\u90e8\u5206\u8bad\u7ec3\u4e0d\u5145\u5206\uff0c\u6545\u201c\u6ed1\u7fd4\u673a\u201d\u578b\u9884\u6d4b\u4e0d\u826f\uff0c\u56e0\u679c\u6d8c\u73b0\uff08<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-math>\u0394<\/span><\/mi>J<\/span><\/mi><\/mrow><\/mjx-assistive-mml><\/mjx-container>\uff09\u7a0b\u5ea6\u6700\u4f4e<\/span>\uff08\u89c1\u56fe(c)\uff09<\/span>\u3002\u5176\u4f597\u79cd\u6a21\u5f0f\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u0394<\/span><\/mi>J<\/span><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u503c\u76f8\u4f3c\u3002\u8fd9\u4e9b\u7ed3\u679c\u8868\u660e\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u0394<\/span><\/mi>J<\/span><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u63d0\u4f9b\u4e86\u56e0\u679c\u6d8c\u73b0\u53d1\u751f\u7684\u66f4\u5408\u7406\u7684\u6307\u793a\u3002\u4f46\u662f\uff0c\u5bf9\u4e8e\u03a8\uff0c\u6240\u6709\u60c5\u51b5\u4ea7\u751f\u7684\u503c\u90fd\u5c0f\u4e8e\u6216\u7b49\u4e8e0\uff0c\u8fd9\u53ef\u80fd\u662f\u56e0\u4e3a\u6b64\u7cfb\u7edf\u662f\u4e00\u4e2a\u9ad8\u7ef4\u7684\u590d\u6742\u7cfb\u7edf\uff0c\u5197\u4f59\u4fe1\u606f\u66f4\u591a\uff0c\u800c\u03a8\u7684\u8fd1\u4f3c\u5ffd\u7565\u4e86\u8bb8\u591a\u5197\u4f59\u4fe1\u606f\uff0c\u4f7f\u5f97\u03a8\u65e0\u6cd5\u786e\u5b9a\u56e0\u679c\u6d8c\u73b0\u662f\u5426\u53d1\u751f\u3002\u56e0\u6b64\uff0c\u672c\u6587\u63d0\u51fa\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u0394<\/span><\/mi>J<\/span><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u4e00\u79cd\u8f83\u597d\u7684\u9274\u522b\u56e0\u679c\u6d8c\u73b0\u7684\u65b9\u6cd5\u3002<\/span><\/section>\n

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

      4.2.4 \u5927\u8111fMRI \u771f\u5b9e\u6570\u636e<\/span><\/strong><\/h3>\n

      <\/span><\/section>\n
      \u4f5c\u8005\u5728830\u540d\u53d7\u8bd5\u8005<\/span> (AOMIC ID1000) <\/span>\u7684\u5927\u8111fMRI\u771f\u5b9e\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u4e0a\u6d4b\u8bd5\u4e86NIS+[24]\u3002fMRI\u626b\u63cf\u6570\u636e\u662f\u5728\u53d7\u8bd5\u8005\u89c2\u770b\u540c\u4e00\u6bb5\u7535\u5f71\u65f6\u6536\u96c6\u7684\uff0c\u8fd9\u5bf9\u5e94\u4e8e\u5177\u6709\u4e0d\u540c\u521d\u59cb\u6761\u4ef6\u7684\u76f8\u540c\u52a8\u529b\u5b66\u7684\u65f6\u95f4\u5e8f\u5217\u3002\u91c7\u6837\u7387<\/span>\uff08\u91cd\u590d\u65f6\u95f4\uff09<\/span>\u4e3a\uff1aID1000\u4e3a2.2s\uff0cPIOP2\u4e3a2s\u3002\u4f5c\u8005\u901a\u8fc7Schaefer atlas\u65b9\u6cd5\u5bf9\u539f\u59cb\u6570\u636e\u8fdb\u884c\u9884\u5904\u7406[25]\uff0c\u5c06\u6bcf\u4e2a\u53d7\u8bd5\u8005\u7684\u65f6\u95f4\u5e8f\u5217\u7ef4\u6570\u4ece\u5927\u7ea6140,000<\/span>\uff08\u4e0d\u540c\u53d7\u8bd5\u8005\u7684\u7ef4\u6570\u4e0d\u540c\uff09<\/span>\u964d\u81f3100\uff0c\u4f7fNIS+\u80fd\u591f\u8fd0\u884c\u5e76\u83b7\u5f97\u66f4\u6e05\u6670\u7684\u7ed3\u679c\u3002\u7136\u540e\uff0c\u9009\u53d6\u524d800\u4e2a\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u8fdb\u884c\u8bad\u7ec3\uff0c\u5269\u4e0b\u768430\u4e2a\u65f6\u95f4\u5e8f\u5217\u8fdb\u884c\u6d4b\u8bd5\u3002\u4f5c\u8005\u8fd8\u5c06\u7ed3\u679c\u4e0e\u53e6\u4e00\u4e2afMRI\u6570\u636e\u96c6AOMIC PIOP2[24]\u8fdb\u884c\u4e86\u6bd4\u8f83\uff0c\u5176\u4e2d50\u540d\u53d7\u8bd5\u8005\u5904\u4e8e\u9759\u606f\u72b6\u6001\u3002<\/span><\/section>\n

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

      4.2.4.1 \u5bf9\u5fae\u89c2\u72b6\u6001\u7684\u9884\u6d4b\u80fd\u529b<\/span><\/h4>\n


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

      <\/section>\n

      <\/span><\/section>\n
      \u7ed3\u679c\u8868\u660e<\/span>\uff08\u56fe(a)\uff09<\/span>\uff0c\u5f53q = 27\u548cq = 1\u65f6\uff0cNIS+\u7684\u9884\u6d4b\u6548\u679c\u66f4\u597d\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u968f\u7740\u9884\u6d4b\u6b65\u9aa4\u7684\u589e\u52a0\uff0c\u4e0eq = 1\u7684\u66f2\u7ebf\u76f8\u6bd4\uff0cq = 27\u7684\u66f2\u7ebf\u663e\u793a\u51fa\u8f83\u6162\u7684\u589e\u957f\u7387\u3002\u8fd9\u8868\u660e\u9009\u62e9\u8d85\u53c2\u6570q\u4e3a27\u53ef\u80fd\u6bd41\u66f4\u5408\u9002\u3002<\/span><\/section>\n

      <\/section>\n

      <\/span><\/section>\n
      \u7136\u800c\uff0c\u56fe(b)\u663e\u793a\u4e86\u4e0d\u540c\u7684\u7ed3\u679c\u3002\u56fe(b)\u4e2d\u7eff\u8272\u67f1\u5b50\u5c31\u662fNIS+\u5e94\u7528\u4e8e\u7b2c\u4e00\u7ec4\u5b9e\u9a8c\u6570\u636e<\/span>\uff08\u975e\u9759\u606f\u6570\u636e\uff09<\/span>\u6240\u8ba1\u7b97\u51fa\u4e0d\u540c\u7ef4\u5ea6q\u4e0b\u7684\u56e0\u679c\u6d8c\u73b0\u6570\u503c\u3002\u53ef\u4ee5\u770b\u51faq=1\u7684\u65f6\u5019<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u0394<\/span><\/mi>J<\/span><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u6570\u503c\u6700\u9ad8\u3002\u4e3a\u4e86\u6bd4\u5bf9\uff0c\u4f5c\u8005\u4e5f\u7528NIS\u6846\u67b6\u5206\u6790\u4e86\u540c\u6837\u7684\u6570\u636e\uff0c\u5982\u56fe(b)\u4e2d\u7684\u7ea2\u8272\u67f1\u5b50\u6240\u793a\uff0c\u53ef\u4ee5\u770b\u51fa\u5b83\u5728\u4e0d\u540c\u7ef4\u5ea6\u4e0a\u7684\u5206\u5e03\u4e0e\u7eff\u8272\u67f1\u5b50\u8fd1\u4f3c\u76f8\u540c\uff0c\u4f46\u662f\u56e0\u679c\u6d8c\u73b0\u5ea6\u91cf\u90fd\u6bd4\u8f83\u5c0f\u3002\u8fd9\u8bf4\u660e\uff0cq=1 \u7ef4\u80fd\u591f\u5c55\u73b0\u56e0\u679c\u6d8c\u73b0\u662f\u4e00\u4e2a\u7a33\u5b9a\u5ba2\u89c2\u7684\u7ed3\u679c\uff0c\u5176\u6b21\uff0cNIS+\u7531\u4e8e\u6700\u5927\u5316\u4e86EI\uff0c\u56e0\u800c\u4f1a\u8ba9\u8fd9\u4e00\u7ed3\u679c\u66f4\u52a0\u7a81\u51fa\u3002\u53cd\u4e4b\uff0c\u5f53q = 27\u65f6\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u0394<\/span><\/mi>J<\/span><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u503c\u4e3a\u8d1f\u3002\u8fd9\u8868\u660e\uff0c\u5f53q = 27\u65f6\uff0c\u9884\u6d4b\u7ed3\u679c\u7684\u6539\u5584\u53ef\u80fd\u662f\u7531\u4e8e\u8fc7\u62df\u5408\u3002\u7efc\u5408\u6765\u770b\uff0c\u5f53\u88ab\u8bd5\u5728\u770b\u540c\u4e00\u7ec4\u89c6\u9891\u7684\u65f6\u5019\uff0c\u5b83\u4eec\u7684fMRI\u6570\u636e\u7528\u4e00\u4e2a\u7ef4\u5ea6\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u5c31\u53ef\u4ee5\u5f88\u597d\u5730\u6982\u62ec\u5927\u8111\u7684\u6d3b\u52a8\u4e86\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u6b64\u5916\uff0c\u4f5c\u8005\u8fd8\u5c06NIS+\u6a21\u578b\u548cNIS\u6a21\u578b\u5e94\u7528\u4e8e\u9759\u606f\u6570\u636e\uff0c\u89c2\u5bdf\u5230NIS<\/span>\uff08\u6df1\u84dd\u8272\u6761\uff09<\/span>\u548cNIS+<\/span>\uff08\u9ec4\u8272\u6761\uff09<\/span>\u5728q = 3\u6216q = 7\u5904\u8fbe\u5230\u5cf0\u503c\uff0c\u6b64\u65f6\uff0c\u5927\u8111\u7684\u52a8\u6001\u8868\u73b0\u65e0\u6cd5\u7b80\u5316\u4e3a\u4e00\u4e2a\u4e00\u7ef4\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\uff0c\u800c\u81f3\u5c11\u9700\u89813~7\u4e2a\u7ef4\u5ea6\u624d\u80fd\u5bf9\u5927\u8111\u7684\u6d3b\u52a8\u8fdb\u884c\u6982\u62ec\u3002<\/span><\/section>\n

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

      4.2.4.2 \u5c1d\u8bd5\u7814\u7a76\u7c97\u7c92\u5316\u5982\u4f55\u5c06\u8f93\u5165\u6570\u636e\u8f6c\u5316\u4e3a\u4e00\u7ef4\u5b8f\u89c2\u72b6\u6001<\/span><\/h4>\n


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

      <\/section>\n

      <\/span><\/section>\n
      \u4f5c\u8005\u5229\u7528\u5f52\u56e0\u5206\u6790\u6280\u672f\uff0c\u8ffd\u8e2a\u8fd9\u4e00\u4e2a\u7ef4\u5ea6\u7684\u5b8f\u89c2\u6001\u6570\u636e\u5230\u5e95\u548c\u54ea\u4e9b\u539f\u59cb\u6570\u636e\u7ef4\u5ea6\u6709\u5173<\/span>\uff08\u56fe(c)\uff09<\/span>\uff0c\u5e76\u628a\u5f52\u56e0\u5206\u6790\u7684\u5f3a\u5ea6\u503c\u5206\u914d\u5230\u8fd9100\u4e2a\u539f\u59cb\u5fae\u89c2\u6001\u7ef4\u5ea6\u6240\u5bf9\u5e94\u7684\u8111\u533a\u3002\u7ed3\u679c\u5982\u56fe(d)\u6240\u793a\uff0c\u53ef\u4ee5\u770b\u51fa\uff0c\u989c\u8272\u8f83\u6df1\u7684\u533a\u57df\u5927\u591a\u90fd\u662f\u8d1f\u8d23\u89c6\u89c9\u4fe1\u53f7\u52a0\u5de5\u7684\u8111\u533a\u3002<\/span><\/section>\n

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

      <\/span><\/section>\n
      \u7efc\u4e0a\uff0cNIS+\u662f\u53ef\u4ee5\u76f4\u63a5\u4ecefMRI\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u63ed\u793a\u51fa\u5927\u8111\u5728\u4e0d\u540c\u5c3a\u5ea6\u7684\u52a8\u529b\u5b66\uff0c\u5e76\u53d1\u73b0\u56e0\u679c\u6d8c\u73b0\u4e3b\u8981\u53d1\u751f\u5728\u54ea\u4e2a\u5c3a\u5ea6\uff1b\u5f53\u88ab\u8bd5\u96c6\u4e2d\u770b\u89c6\u9891\u7684\u65f6\u5019\uff0c\u5927\u8111\u6d3b\u52a8\u53ef\u4ee5\u88ab\u4e00\u4e2a\u7ef4\u5ea6\u7684\u5b8f\u89c2\u4fe1\u53f7\u6240\u6982\u62ec\uff0c\u8fd9\u4e00\u7ef4\u5ea6\u4e3b\u8981\u4ee3\u8868\u7684\u662f\u89c6\u89c9\u533a\u57df\u7684\u6d3b\u52a8\u72b6\u6001\uff0c\u5927\u8111\u53d1\u751f\u4e86\u975e\u5e38\u660e\u663e\u7684\u56e0\u679c\u6d8c\u73b0\u73b0\u8c61\uff1b\u800c\u5728\u9759\u606f\u6001\u4e0b\uff0c\u88ab\u8bd5\u5927\u8111\u867d\u7136\u4e5f\u53d1\u751f\u4e86\u56e0\u679c\u6d8c\u73b0\u73b0\u8c61\uff0c\u4f46\u5f3a\u5ea6\u660e\u663e\u4f4e\u4e8e\u524d\u8005\u3002\u5927\u8111\u7684\u4e3b\u8981\u6d3b\u52a8\u5219\u76f8\u5bf9\u7b2c\u4e00\u7ec4\u66f4\u590d\u6742\uff0c\u56e0\u4e3a\u5b83\u4e0d\u80fd\u7b80\u5355\u5730\u88ab\u4e00\u4e2a\u7ef4\u5ea6\u7684\u5b8f\u89c2\u6001\u6240\u6982\u62ec\uff0c\u800c\u662f\u96c6\u4e2d\u5728\u4e00\u4e2a3~7\u7ef4\u7684\u4ecb\u89c2\u5c3a\u5ea6\u4e0a\u3002<\/span><\/section>\n


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

      4.3 \u5173\u952e\u5b9a\u7406\u4e0e\u8bc1\u660e<\/span><\/strong><\/span><\/h2>\n

      <\/span><\/section>\n
      \u4e3a\u4e86\u4fdd\u8bc1NIS+\u7684\u6b63\u786e\u8fd0\u8f6c\uff0c\u4f5c\u8005\u4eec\u901a\u8fc7\u7406\u8bba\u5206\u6790\uff0c\u8bc1\u660e\u4e86\u51e0\u4e2a\u5173\u952e\u6570\u5b66\u5b9a\u7406\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u9996\u5148\uff0c\u5f0f1\u4e2d\u7684\u6570\u5b66\u5f62\u5f0f\u662f\u4e00\u4e2a\u6cdb\u51fd\u4f18\u5316\u95ee\u9898\uff0c\u5f88\u96be\u76f4\u63a5\u8fdb\u884c\u4f18\u5316\u3002\u4e8e\u662f\uff0c\u4f5c\u8005\u5c06\u901a\u8fc7\u8ba1\u7b97\u5e76\u4f18\u5316\u8be5\u76ee\u6807\u51fd\u6570\u7684\u4e00\u4e2a\u53d8\u5206\u4e0b\u754c\u6765\u95f4\u63a5\u89e3\u51b3\u6cdb\u51fd\u4f18\u5316\u95ee\u9898\u3002\u540c\u65f6\uff0c\u5728NIS+\u6846\u67b6\u4e2d\uff0c\u4f5c\u8005\u4f7f\u7528\u4e86\u7f16\u7801\u5668\u5c06p\u7ef4\u7684\u8f93\u5165\u6570\u636e\u8fdb\u884c\u7c97\u7c92\u5316\uff0c\u5f97\u5230q\u7ef4\u7684\u5b8f\u89c2\u6570\u636e\uff0c\u4e0b\u9762\u7f16\u7801\u5668\u7684\u901a\u7528\u903c\u8fd1\u5b9a\u7406\u5c06\u8bc1\u660e\u7f16\u7801\u5668\u662f\u53ef\u4ee5\u8fd1\u4f3c\u4efb\u610f\u590d\u6742\u7684\u7c97\u7c92\u5316\u51fd\u6570\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5728\u6b64\u7ae0\u8282\uff0c\u4f5c\u8005\u5c06\u4f7f\u7528\u5927\u5199\u5b57\u6bcd\u6765\u8868\u793a\u76f8\u5e94\u7684\u968f\u673a\u53d8\u91cf\u3002\u4f8b\u5982\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>X<\/span><\/mi>t<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u65f6\u95f4t\u7684\u5fae\u89c2\u72b6\u6001<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u968f\u673a\u53d8\u91cf\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>Y<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u65f6\u95f4t+1\u7684\u5b8f\u89c2\u72b6\u6001<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5bf9\u5e94\u7684\u968f\u673a\u53d8\u91cf\u3002\u5bf9\u4e8e\u4efb\u610f\u968f\u673a\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>V<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c <\/span><\/sub><\/mo><\/mover><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>X<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u88ab\u5e72\u9884\u540e\u7684\u968f\u673a\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>V<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/sub><\/mo><\/mover><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u795e\u7ecf\u7f51\u7edc\u5bf9<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>X<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u9884\u6d4b\u3002<\/span><\/section>\n

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

      4.3.1 \u5b8f\u89c2EI\u7684\u53d8\u5206\u4e0b\u754c<\/span><\/strong><\/h3>\n


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

      \u5b9a\u74061<\/span>\uff08\u5b8f\u89c2EI\u7684\u53d8\u5206\u4e0b\u754c\uff09<\/span>\uff1a\u5bf9\u4e8e\u7ed9\u5b9a\u7684 q \u503c\uff0c\u7531\u5f0f3\u5b9a\u4e49\u7684\u65e0\u7ea6\u675f\u76ee\u6807\u51fd\u6570\u4f18\u5316\u7b49\u4ef7\u4e8e\u4f18\u5316\u5f0f1\u4e2d\u5b9a\u4e49\u7684\u65e0\u7ea6\u675f\u76ee\u6807\u51fd\u6570\u7684\u4e0b\u754c\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u4f18\u5316\u76ee\u6807\uff08\u5f0f1\uff09\u53ef\u8f6c\u5316\u4e3a\uff1a<\/span><\/section>\n

      <\/span><\/section>\n
       (3)<\/span><\/section>\n

      <\/span><\/section>\n
      \u5f0f\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3001<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u53ef\u89c2\u6d4b\u7684\u5fae\u89c2\u6570\u636e\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3001<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u7ecf\u8fc7\u7c97\u7c92\u5316\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5f97\u5230\u7684\u5b8f\u89c2\u6570\u636e\uff0c\u8fd9\u91cc<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math>\u03d5<\/span><\/mi>=<\/span><\/mo>\u03c8<\/span><\/mi>\u03c9<\/span><\/sub><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03c7<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5176\u4e2d<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-math>\u03c8<\/span><\/mi>\u03c9<\/span><\/sub><\/mi><\/mrow><\/msub><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u4e00\u4e2a\u53ef\u9006\u51fd\u6570\uff0c\u53c2\u6570\u4e3a<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03c9<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\uff1b<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03c7<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u6295\u5f71\u64cd\u4f5c\uff0c<\/span><\/mjx-c><\/mjx-mo><\/mjx-math>\u2218<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u51fd\u6570\u590d\u5408<\/span>\u3002<\/span><\/sub><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ecf\u8fc7\u5b8f\u89c2\u52a8\u529b\u5b66<\/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-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi>:<\/span><\/mo>R<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub>\u2192<\/span><\/mo>R<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5f97\u5230\u7684\u9884\u6d4b<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>t<\/span><\/mi>+<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\u523b\u5b8f\u89c2\u53d8\u91cf\u503c\uff0c<\/span><\/sub><\/mn><\/mjx-container><\/msub><\/mrow><\/mjx-container><\/msub><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a<\/span><\/sub><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ecf\u8fc7\u53cd\u7c97\u7c92\u5316\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>\u2020<\/span><\/mo><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff08\u8fd9\u91cc\u53cd\u7c97\u7c92\u5316\u51fd\u6570<\/span><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mo><\/mjx-math>\u2a01<\/span><\/mo><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u5411\u91cf\u62fc\u63a5\u8fd0\u7b97\u7b26\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03be<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u4e00\u4e2a\u6b63\u6001\u5206\u5e03\u968f\u673a\u6570\uff09\u5f97\u5230\u7684\u9884\u6d4b\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>t<\/span><\/mi>+<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\u523b\u5fae\u89c2\u53d8\u91cf\u503c\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-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>g<\/span><\/mi>:<\/span><\/mo>R<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub>\u2192<\/span><\/mo>R<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u53cd\u5b8f\u89c2\u52a8\u529b\u5b66\u51fd\u6570\uff0c\u53ef\u4ee5\u6839\u636e<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>t<\/span><\/mi>+<\/span><\/mo>1<\/span><\/mn><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\u523b\u5b8f\u89c2\u53d8\u91cf\u503c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u63a8\u51fa\u9884\u6d4b\u7684<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>t<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u65f6\u523b\u7684\u5b8f\u89c2\u53d8\u91cf<\/span><\/sub><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03bb<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4f5c\u4e3a\u62c9\u683c\u6717\u65e5\u4e58\u5b50\uff0c\u5728\u5b9e\u9a8c\u6846\u67b6\u5185\u88ab\u8ba4\u4e3a\u662f\u4e00\u4e2a\u53ef\u8c03\u7684\u8d85\u53c2\u6570\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-texatom><\/mjx-mstyle><\/mjx-math>w<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u9006\u6982\u7387\u6743\u91cd\u3002<\/span><\/section>\n

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

      <\/section>\n<\/section>\n
      \n
      \n
      \n
      \n
      \u8bc1\u660e\uff1a<\/span><\/section>\n

      <\/span><\/section>\n
      \u539f\u59cb\u7684\u6709\u7ea6\u675f\u7684\u76ee\u6807\u4f18\u5316\u516c\u5f0f\u5982\u5f0f1\u6240\u793a\u3002\u5728\u6b64\u65b9\u7a0b\u4e2d<\/span><\/sub><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5176\u4e2d<\/sub>\u662f\u53ef\u9006\u6620\u5c04\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-math>\u03be<\/span><\/mi><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u4e00\u4e2a\u6b63\u6001\u5206\u5e03\u968f\u673a\u6570\uff0c\u6839\u636e\u5f15\u74061\u548c\u5f15\u74062\u4ee5\u53ca\u4e92\u4fe1\u606f\u7684\u6027\u8d28\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/span><\/section>\n
      \u5176\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>I<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u4e92\u4fe1\u606f\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>H<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u71b5\uff0c\u4ee4<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>U<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u5b8f\u89c2\u53d8\u91cf\u7684\u5747\u5300\u5206\u5e03\uff0c\u90a3\u4e48<\/span><\/sub><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u6545\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/span><\/section>\n
      \u5176\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>J<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u7ef4\u5ea6\u5e73\u5747\u7684\u6709\u6548\u4fe1\u606f\u3002\u7531\u4e8e<\/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-texatom><\/mjx-mstyle><\/mjx-math>H<\/span><\/mi>(<\/span><\/mo>U<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u5e38\u6570\uff0c\u6240\u4ee5<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>J<\/span><\/mi><\/mrow>(<\/span><\/mo>f<\/span><\/mi>q<\/span><\/sub><\/mi><\/mrow><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u4f18\u5316\u53ef\u4ee5\u8f6c\u5316\u4e3a\u6761\u4ef6\u71b5<\/span><\/sub><\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u6700\u5c0f\u5316\u4f18\u5316\u95ee\u9898\u3002\u6839\u636e\u5f15\u74063\u53ef\u4ee5\u5f97\u77e5\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/span><\/section>\n
      \u5f0f\u4e2d\uff0c<\/span><\/sub><\/span><\/mo><\/mover><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u968f\u673a\u53d8\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>Y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u88ab\u5e72\u9884\u60c5\u51b5\u4e0b\u7684\u6982\u7387\u5206\u5e03\u51fd\u6570\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u4f5c\u8005\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u6765\u62df\u5408\u5206\u5e03g<\/span>(<\/span><\/mo>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>|<\/span><\/mo><\/mrow>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>+<\/span><\/mo>1<\/span><\/mn>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u6839\u636e\u5f15\u74063\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-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>g<\/span><\/mi>(<\/span><\/mo>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>|<\/span><\/mo><\/mrow>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>+<\/span><\/mo>1<\/span><\/mn>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u53ef\u4ee5\u662f\u4efb\u4f55\u5206\u5e03\uff0c\u5728\u8fd9\u91cc\uff0c\u5047\u8bbe<\/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-texatom><\/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-mstyle><\/mjx-math>g<\/span><\/mi>(<\/span><\/mo>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>|<\/span><\/mo><\/mrow>x<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e3a\u6b63\u6001\u5206\u5e03\uff0c\u5373<\/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-texatom><\/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-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-mstyle><\/mjx-math>g<\/span><\/mi>(<\/span><\/mo>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>|<\/span><\/mo><\/mrow>x<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub>)<\/span><\/mo>\u223c<\/span><\/mo>N<\/span><\/mi>(<\/span><\/mo>\u03bc<\/span><\/mi>,<\/span><\/mo>\u03a3<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5176\u4e2d<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/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-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03bc<\/span><\/mi>=<\/span><\/mo>g<\/span><\/mi>\u03b8<\/span><\/sub><\/mi>\u2032<\/span><\/sub><\/mo><\/msup><\/mrow><\/msub>(<\/span><\/mo>\u03d5<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub>)<\/span><\/mo>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/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-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-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>\u03a3<\/span><\/mi>=<\/span><\/mo>d<\/span><\/mi>i<\/span><\/mi>a<\/span><\/mi>g<\/span><\/mi>(<\/span><\/mo>\u03c3<\/span><\/mi>1<\/span><\/sub><\/mn><\/msub>, <\/span><\/mo>\u03c3<\/span><\/mi>2<\/span><\/sub><\/mn><\/msub>, <\/span><\/mo>\u22c5<\/span><\/mo>\u22c5<\/span><\/mo>\u22c5<\/span><\/mo>,<\/span><\/mo>\u03c3<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u5e38\u6570\u5bf9\u89d2\u77e9\u9635\uff0c\u8fdb\u4e00\u6b65\uff0c\u5047\u8bbe<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c3<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u6709\u754c\u7684\uff0c\u5219<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/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-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c3<\/span><\/mi>i<\/span><\/sub><\/mi><\/msub>\u2208<\/span><\/mo>[<\/span><\/mo>\u03c3<\/span><\/mi>m<\/span><\/sub><\/mi><\/msub>,<\/span><\/mo>\u03c3<\/span><\/mi>M<\/span><\/sub><\/mi><\/msub>]<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5176\u4e2d<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c3<\/span><\/mi>m<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c3<\/span><\/mi>M<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5206\u522b\u662fMSE\u7684\u6700\u5c0f\u503c\u548c\u6700\u5927\u503c\u3002\u5219<\/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-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>g<\/span><\/mi>(<\/span><\/mo>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>|<\/span><\/mo><\/mrow>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>+<\/span><\/mo>1<\/span><\/mn>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u5bf9\u6570\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/section>\n
      \u5982\u679c\u8bad\u7ec3\u8db3\u591f\u5145\u5206\uff0c\u90a3\u4e48<\/span><\/mrow><\/mstyle><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u6545\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/section>\n
      \u5f0f\u4e2d\uff0c<\/span><\/sub><\/mi><\/msubsup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u7531\u4e8e<\/span><\/mrow><\/mstyle><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5176\u4e2d<\/span><\/sub><\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u76ee\u6807\u5206\u5e03\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi>(<\/span><\/mo>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/mrow><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u6570\u636e\u7684\u539f\u59cb\u5206\u5e03\u3002\u6211\u4eec\u5b9a\u4e49\u9006\u6982\u7387\u6743\u91cd<\/sub>\u3002\u4e14\u7531\u4e8e\u6211\u4eec\u4f7f\u7528\u79bb\u6563\u6837\u672c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u6765\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u6837\u672c\u5747\u503c\u4f5c\u4e3a\u671f\u671b\u7684\u8fd1\u4f3c\u4f30\u8ba1\u3002\u56e0\u6b64\uff0c<\/span><\/mrow><\/mstyle><\/sub><\/mo><\/mjx-assistive-mml><\/mjx-container>\u7684\u53d8\u5206\u4e0a\u754c\u53ef\u5199\u6210\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/section>\n
      \u8fdb\u800c\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u539f\u76ee\u6807\u51fd\u6570\u7684\u53d8\u5206\u4e0b\u754c\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/span><\/section>\n
      \u539f\u4f18\u5316\u95ee\u9898\uff08\u5f0f<\/span>1\uff09\u4fbf\u8f6c\u6362\u6210\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/section>\n
      \u5f0f\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c9<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b8<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c <\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b8<\/span><\/mi>\u2032<\/span><\/mo><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5206\u522b\u8868\u793aNIS+\u6846\u67b6\u4e2d\u4e09\u4e2a\u795e\u7ecf\u7f51\u7edc<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c8<\/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-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi>\u03b8<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c <\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>g<\/span><\/mi>\u03b8<\/span><\/sub><\/mi>\u2032<\/span><\/sub><\/mo><\/msup><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u53c2\u6570\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u7136\u540e\u6784\u9020\u62c9\u683c\u6717\u65e5\u51fd\u6570\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/section>\n
      \u4fbf\u5f97\u5230\u4e86\u5f0f<\/span>3\u3002<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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


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

      \n
      \n

      <\/section>\n<\/section>\n<\/section>\n
      \u76f8\u5173\u5f15\u7406\uff1a<\/span><\/section>\n

      <\/section>\n
      \u5f15\u74061\u2014\u2014\u53cc\u5c04\u6620\u5c04\u4e0d\u5f71\u54cd\u4e92\u4fe1\u606f[13]\uff1a<\/span><\/section>\n

      <\/span><\/section>\n
      \u5bf9\u4e8e\u4efb\u610f\u7ed9\u5b9a\u7684\u8fde\u7eed\u968f\u673a\u53d8\u91cfX\u548cZ\uff0c\u5982\u679c\u5b58\u5728\u4e00\u4e2a\u53cc\u5c04(\u4e00\u5bf9\u4e00)\u6620\u5c04f\u4e0e\u53e6\u4e00\u4e2a\u968f\u673a\u53d8\u91cfY\uff0c\u4f7f\u5f97\u5bf9\u4e8e\u4efb\u610f<\/span><\/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-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>\u2208<\/span><\/mo>D<\/span><\/mi>o<\/span><\/mi>m<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5b58\u5728\u4e00\u4e2a<\/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-mi><\/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>\u2208<\/span><\/mo>D<\/span><\/mi>o<\/span><\/mi>m<\/span><\/mi>(<\/span><\/mo>Y<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u53cd\u4e4b\u4ea6\u7136\uff0c\u5176\u4e2d<\/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-mstyle><\/mjx-math>D<\/span><\/mi>o<\/span><\/mi>m<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u53d8\u91cfX\u7684\u57df\uff0c\u5219X\u4e0eZ\u4e4b\u95f4\u7684\u4e92\u4fe1\u606f\u7b49\u4e8eY\u4e0eZ\u4e4b\u95f4\u7684\u4e92\u4fe1\u606f\uff0c\u5373\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-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-mstyle><\/mjx-math>I<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi>;<\/span><\/mo>Z<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>I<\/span><\/mi>(<\/span><\/mo>Y<\/span><\/mi>;<\/span><\/mo>Z<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

      <\/section>\n
      \u5f15\u74062\u2014\u2014\u8fde\u7eed\u81ea\u53d8\u91cf\u4e0d\u5f71\u54cd\u4e92\u4fe1\u606f[13]\uff1a<\/span><\/section>\n

      <\/span><\/section>\n
      \u82e5<\/span><\/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-texatom><\/mjx-mstyle><\/mjx-math>X<\/span><\/mi>\u2208<\/span><\/mo>D<\/span><\/mi>o<\/span><\/mi>m<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e0e<\/span><\/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-texatom><\/mjx-mstyle><\/mjx-math>Y<\/span><\/mi>\u2208<\/span><\/mo>D<\/span><\/mi>o<\/span><\/mi>m<\/span><\/mi>(<\/span><\/mo>Y<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u6784\u6210\u4e00\u6761\u9a6c\u5c14\u53ef\u592b\u94fe<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>X<\/span><\/mi>\u2192<\/span><\/mo>Y<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4e14<\/span><\/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-texatom><\/mjx-mstyle><\/mjx-math>Z<\/span><\/mi>\u2208<\/span><\/mo>D<\/span><\/mi>o<\/span><\/mi>m<\/span><\/mi>(<\/span><\/mo>Z<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u4e00\u4e2a\u4e0eX\u3001Y\u5747\u65e0\u5173\u7684\u968f\u673a\u53d8\u91cf\uff0c\u5219\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-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>I<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi>;<\/span><\/mo>Y<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>I<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi>;<\/span><\/mo>Y<\/span><\/mi>\u2a01<\/span><\/mo>Z<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

      <\/span><\/section>\n
      \u5f15\u74063\u2014\u2014\u6761\u4ef6\u71b5\u7684\u53d8\u5206\u4e0a\u754c\uff1a<\/span><\/section>\n

      <\/span><\/section>\n
      \u7ed9\u5b9a\u4e00\u4e2a\u6761\u4ef6\u71b5<\/span><\/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>H<\/span><\/mi>(<\/span><\/mo>y<\/span><\/mi>|<\/span><\/mo><\/mrow>x<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5176\u4e2d<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>\u2208<\/span><\/mo>R<\/span><\/mi><\/mrow>s<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/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>\u2208<\/span><\/mo>R<\/span><\/mi><\/mrow>q<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5219\u8be5\u6761\u4ef6\u71b5\u5b58\u5728\u4e00\u4e2a\u53d8\u5206\u4e0a\u754c\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/section>\n
      \u5176\u4e2d<\/span><\/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-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>H<\/span><\/mi>(<\/span><\/mo>Y<\/span><\/mi>|<\/span><\/mo><\/mrow>X<\/span><\/mi>)<\/span><\/mo>\u2208<\/span><\/mo>R<\/span><\/mi>q<\/span><\/sup><\/mi><\/msup>\u00d7<\/span><\/mi>R<\/span><\/mi>s<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u4efb\u610f\u5206\u5e03\u3002<\/span><\/section>\n


      <\/h3>\n

      \u7f16\u7801\u5668\u7684\u901a\u7528\u903c\u8fd1\u5b9a\u7406<\/span><\/strong><\/span><\/h3>\n

      <\/section>\n
      \u5b9a\u74062<\/span>\uff08\u7f16\u7801\u5668\u7684\u901a\u7528\u903c\u8fd1\u5b9a\u7406\uff09<\/span>\uff1a\u5bf9\u4e8e\u4efb\u4f55\u8fde\u7eed\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5b9a\u4e49\u5728<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>K<\/span><\/mi>\u00d7<\/span><\/mo>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>K<\/span><\/mi>\u2208<\/span><\/mo>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u4e00\u4e2a\u7d27\u96c6\uff0c<\/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-script><\/mjx-msup><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi>><\/span><\/mo>q<\/span><\/mi>\u2208<\/span><\/mo>Z<\/span><\/mi>+<\/span><\/sup><\/mo><\/msup><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5b58\u5728\u6574\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>s<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c\u6269\u5c55\u5806\u7f16\u7801\u5668<\/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-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/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>\u03d5<\/span><\/mi>p<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>s<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>q<\/span><\/sub><\/mi><\/mrow><\/msub>:<\/span><\/mo>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup>\u2192<\/span><\/mo>R<\/span><\/mi><\/mrow>q<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff08\u6709<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>s<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u9690\u85cf\u5c42\uff09\u548c\u6269\u5c55\u64cd\u4f5c<\/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>\u03b7<\/span><\/mi>p<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>s<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4f7f\u5f97\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-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>p<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>s<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>q<\/span><\/sub><\/mi><\/mrow><\/msub>\u2243<\/span><\/mo>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/section>\n

      <\/section>\n
      \u8fd9\u8868\u660e\u7f16\u7801\u5668\u53ef\u4ee5\u8fd1\u4f3c(\u6a21\u62df)\u4efb\u4f55\u5b9a\u4e49\u5728<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/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>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup>\u00d7<\/span><\/mo>R<\/span><\/mi><\/mrow>q<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7c97\u7c92\u5316\u51fd\u6570\u3002<\/span><\/section>\n

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

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

      \u8bc1\u660e\uff1a<\/span><\/p>\n


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

      \u9996\u5148\uff0c\u6211\u4eec\u6269\u5c55\u57fa\u672c\u7f16\u7801\u5668\u7684\u5b9a\u4e49\uff0c\u5f15\u5165\u4e00\u4e2a\u65b0\u7684\u8fd0\u7b97<\/span><\/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-mi><\/mjx-texatom><\/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>\u03b7<\/span><\/mi>p<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>s<\/span><\/sub><\/mi><\/mrow><\/msub>:<\/span><\/mo>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup>\u2192<\/span><\/mo>R<\/span><\/mi><\/mrow>s<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5b83\u8868\u793a\u539f\u59cb\u53d8\u91cf\u7684\u81ea\u590d\u5236\u3002<\/span><\/p>\n


      <\/span><\/p>\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-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-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b7<\/span><\/mi>p<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>s<\/span><\/sub><\/mi><\/mrow><\/msub>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>x<\/span><\/mi>\u2a01<\/span><\/mo>x<\/span><\/mi>s<\/span><\/sub><\/mi>\u2212<\/span><\/sub><\/mo>p<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/p>\n


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

      \u5411\u91cf<\/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>x<\/span><\/mi>s<\/span><\/sub><\/mi>\u2212<\/span><\/sub><\/mo>p<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>s<\/span><\/mi>\u2212<\/span><\/mo>p<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7ef4\uff0c\u5176\u4e2d\u6bcf\u4e2a\u7ef4\u90fd\u662fx\u4e2d\u7279\u5b9a\u7ef4\u7684\u91cd\u590d\u3002\u4f8b\u5982\uff0c\u82e5<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>x<\/span><\/mi>=<\/span><\/mo>(<\/span><\/mo>0.1<\/span><\/mn>,<\/span><\/mo>0.2<\/span><\/mn>,<\/span><\/mo>0.3<\/span><\/mn>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5219<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/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-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03b7<\/span><\/mi><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>2<\/span><\/sub><\/mn>,<\/span><\/sub><\/mo>5<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/mrow><\/msub>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>(<\/span><\/mo>0.1<\/span><\/mn>,<\/span><\/mo>0.2<\/span><\/mn>,<\/span><\/mo>0.3<\/span><\/mn>,<\/span><\/mo>0.1<\/span><\/mn>,<\/span><\/mo>0.2<\/span><\/mn>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/p>\n


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

      \u5b66\u8005\u4eec\u66fe\u63d0\u51fa\u4e00\u822c\u524d\u9988\u795e\u7ecf\u7f51\u7edc<\/span>[26][27]\u548c\u53ef\u9006\u795e\u7ecf\u7f51\u7edc<\/span>[28][29]\u7684\u901a\u7528\u903c\u8fd1\u5b9a\u7406\uff0c\u5c06\u5176\u4f5c\u4e3a\u6865\u6881\uff0c\u53ef\u4ee5\u8bc1\u660e\u4efb\u4f55\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u90fd\u53ef\u4ee5\u7528\u4e00\u7cfb\u5217\u53cc\u5c04\u6620\u5c04(\u03c8)\u3001\u6295\u5f71(\u03c7)\u548c\u5411\u91cf\u6269\u5c55(\u03b7)\u8fc7\u7a0b\u6765\u6a21\u62df\u3002\u5bf9\u5411\u91cf\u5c55\u5f00\u8fdb\u884c\u6269\u5c55\u540e\u7684\u57fa\u672c\u7f16\u7801\u5668\u53ef\u8868\u793a\u4e3a\uff1a<\/span><\/p>\n


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

      <\/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-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/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-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>=<\/span><\/mo>P<\/span><\/mi>r<\/span><\/mi>o<\/span><\/mi>j<\/span><\/mi>q<\/span><\/sub><\/mi><\/msub>\u2218<\/span><\/mo>\u03c8<\/span><\/mi>s<\/span><\/sub><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03b7<\/span><\/mi>p<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>s<\/span><\/sub><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03c8<\/span><\/mi>p<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/p>\n


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

      \u5f0f\u4e2d\uff0c\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/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>\u03c8<\/span><\/mi>s<\/span><\/sub><\/mi><\/msub>:<\/span><\/mo>R<\/span><\/mi><\/mrow>s<\/span><\/sup><\/mi><\/msup>\u2192<\/span><\/mo>R<\/span><\/mi><\/mrow>s<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/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>\u03c8<\/span><\/mi>p<\/span><\/sub><\/mi><\/msub>:<\/span><\/mo>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup>\u2192<\/span><\/mo>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u4e24\u4e2a\u53ef\u9006\u6620\u5c04\u3002\u4fdd\u7559\u7684\u6700\u7ec8\u7ef4\u6570q\u53ef\u80fd\u5927\u4e8e\u521d\u59cb\u7ef4\u6570p\u3002\u03c6\u4e3a\u964d\u7ef4\u7b97\u5b50\u3002<\/span><\/p>\n


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

      \u6839\u636e\u901a\u7528\u903c\u8fd1\u5b9a\u7406<\/span>[26][27]\uff0c\u5bf9\u4e8e\u5b9a\u4e49\u5728<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>K<\/span><\/mi>\u00d7<\/span><\/mo>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e0a\u7684\u4efb\u610f\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5176\u4e2d<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>K<\/span><\/mi>\u2208<\/span><\/mo>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u7d27\u96c6\uff0c\u4e14<\/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-script><\/mjx-msup><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi>><\/span><\/mo>q<\/span><\/mi>\u2208<\/span><\/mo>Z<\/span><\/mi>+<\/span><\/sup><\/mo><\/msup><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5219\u5b58\u5728\u6574\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>s<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/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-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>W<\/span><\/mi>\u2208<\/span><\/mo>R<\/span><\/mi><\/mrow>s<\/span><\/sup><\/mi>\u00d7<\/span><\/sup><\/mo>p<\/span><\/sup><\/mi><\/mrow><\/msup>,<\/span><\/mo>W<\/span><\/mi>\u2032<\/span><\/mo><\/msup>\u2208<\/span><\/mo>R<\/span><\/mi><\/mrow>q<\/span><\/sup><\/mi>\u00d7<\/span><\/sup><\/mo>s<\/span><\/sup><\/mi><\/mrow><\/msup>,<\/span><\/mo>b<\/span><\/mi>\u2208<\/span><\/mo>R<\/span><\/mi><\/mrow>s<\/span><\/sup><\/mi><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4f7f\u5f97:<\/span><\/p>\n


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

      <\/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-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>W<\/span><\/mi>\u2032<\/span><\/mo><\/msup>\u22c5<\/span><\/mo>\u03c3<\/span><\/mi>(<\/span><\/mo>W<\/span><\/mi>+<\/span><\/mo>b<\/span><\/mi>)<\/span><\/mo>\u2243<\/span><\/mo>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/p>\n


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

      \u5f0f\u4e2d\uff0c<\/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-texatom><\/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-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c3<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo>=<\/span><\/mo>1<\/span><\/mn>\/<\/span><\/mo><\/mrow>(<\/span><\/mo>1<\/span><\/mn>+<\/span><\/mo>exp<\/span><\/mi>\u2061<\/span><\/mo>(<\/span><\/mo>\u2212<\/span><\/mo>x<\/span><\/mi>)<\/span><\/mo>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u5411\u91cf\u4e0a\u7684sigmoid\u51fd\u6570\u3002<\/span><\/p>\n


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

      \u6839\u636e\u5f15\u74064\uff0c<\/span><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>+<\/span><\/mo>b<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c3<\/span><\/mi>(<\/span><\/mo>\u22c5<\/span><\/mo>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u90fd\u662f\u53ef\u9006\u7b97\u5b50\uff0c\u56e0\u6b64\uff0c\u5b58\u5728\u53ef\u9006\u795e\u7ecf\u7f51\u7edc<\/span><\/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-mo><\/mjx-spacer><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msubsup><\/mjx-c><\/mjx-mo><\/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-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c8<\/span><\/mi>q<\/span><\/sub><\/mi><\/mrow><\/msub>,<\/span><\/mo>\u03c8\u2032<\/span><\/span><\/mi>s<\/span><\/sub><\/mi><\/mrow><\/msubsup>,<\/span><\/mo>\u03c8<\/span><\/mi>s<\/span><\/sub><\/mi><\/mrow><\/msub>,<\/span><\/mo>\u03c8<\/span><\/mi>p<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c\u4e24\u4e2a\u6574\u6570<\/span><\/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-texatom><\/mjx-mstyle><\/mjx-math>s<\/span><\/mi>1<\/span><\/sub><\/mn><\/msub>,<\/span><\/mo>s<\/span><\/mi>2<\/span><\/sub><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff08\u77e9\u9635<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>W<\/span><\/mi>\u2032<\/span><\/mo><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>W<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u79e9\uff09\uff0c\u4f7f\u5f97\uff1a<\/span><\/p>\n


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

      <\/p>\n


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

      \u5f0f\u4e2d\uff0c<\/span><\/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-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/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-mn><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c8<\/span><\/mi>s<\/span><\/sub><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03b7<\/span><\/mi>s<\/span><\/sub><\/mi>1<\/span><\/sub><\/mn><\/msub>,<\/span><\/sub><\/mo>s<\/span><\/sub><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03c7<\/span><\/mi>p<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>s<\/span><\/sub><\/mi>1<\/span><\/sub><\/mn><\/msub><\/mrow><\/msub>\u2218<\/span><\/mo>\u03c8<\/span><\/mi>p<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8fd1\u4f3c(\u6a21\u62df)\u51fd\u6570<\/span><\/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>\u03c3<\/span><\/mi>(<\/span><\/mo>W<\/span><\/mi>\u22c5<\/span><\/mo>+<\/span><\/mo>b<\/span><\/mi>)<\/span><\/mo><\/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-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/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-mn><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-spacer><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msubsup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c8<\/span><\/mi>q<\/span><\/sub><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03b7<\/span><\/mi>s<\/span><\/sub><\/mi>2<\/span><\/sub><\/mn><\/msub>,<\/span><\/sub><\/mo>q<\/span><\/sub><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03c7<\/span><\/mi>s<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>s<\/span><\/sub><\/mi>2<\/span><\/sub><\/mn><\/msub><\/mrow><\/msub>\u2218<\/span><\/mo>\u03c8\u2032<\/span><\/span><\/mi>s<\/span><\/sub><\/mi><\/mrow><\/msubsup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8fd1\u4f3c(\u6a21\u62df)\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-script><\/mjx-msup><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>W<\/span><\/mi>\u2032<\/span><\/mo><\/msup>\u22c5<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/p>\n


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

      \u56e0\u6b64\uff0c\u5982\u679c\u4ee4<\/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-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>p<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>s<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>q<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub>=<\/span><\/mo>(<\/span><\/mo>\u03c8<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>q<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03b7<\/span><\/mi><\/mi><\/msub><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>s<\/span><\/sub><\/span><\/mi>2<\/span><\/sub><\/span><\/mn><\/msub>,<\/span><\/sub><\/span><\/mo>q<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03c7<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>s<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>s<\/span><\/sub><\/span><\/mi>2<\/span><\/sub><\/span><\/mn><\/msub><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/msub><\/mrow><\/msub>\u2218<\/span><\/mo>\u03c8\u2032<\/span><\/span><\/mi>s<\/span><\/sub><\/mi><\/mrow><\/span><\/mi><\/mrow><\/msubsup>)<\/span><\/mo>\u2218<\/span><\/mo>(<\/span><\/mo>\u03c8<\/span><\/mi>s<\/span><\/sub><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03b7<\/span><\/mi><\/mi><\/msub><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>s<\/span><\/sub><\/span><\/mi>1<\/span><\/sub><\/span><\/mn><\/msub>,<\/span><\/sub><\/span><\/mo>s<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03c7<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>p<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>s<\/span><\/sub><\/span><\/mi>1<\/span><\/sub><\/span><\/mn><\/msub><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/msub><\/mrow><\/msub>\u2218<\/span><\/mo>\u03c8<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>p<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u90a3\u4e48<\/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-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>p<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>s<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>q<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub>\u2243<\/span><\/mo>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/p>\n


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

      \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u867d\u7136\u57fa\u672c\u7f16\u7801\u5668\u548c\u6269\u5c55\u7248\u672c\u4e0d\u5305\u62ec\u5c55\u5f00\u8fd0\u7b97\u7b26\uff0c\u4f46\u6211\u4eec\u603b\u662f\u5728\u8f93\u5165\u5411\u91cf\u4e3a\u7f16\u7801\u5668\u8f93\u5165\u4e4b\u524d\u5c55\u5f00\u5b83\u3002\u56e0\u6b64\uff0c\u6709\u7406\u7531\u76f8\u4fe1\u6b64\u5b9a\u7406\u4ecd\u7136\u9002\u7528\u4e8e\u5806\u53e0\u7f16\u7801\u5668\u3002<\/span><\/p>\n


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

      \u5bf9\u4e8e\u4efb\u4f55\u8fde\u7eed\u51fd\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5b9a\u4e49\u5728<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>K<\/span><\/mi>\u00d7<\/span><\/mo>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>K<\/span><\/mi>\u2208<\/span><\/mo>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u662f\u4e00\u4e2a\u7d27\u96c6\uff0c<\/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-script><\/mjx-msup><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi>><\/span><\/mo>q<\/span><\/mi>\u2208<\/span><\/mo>Z<\/span><\/mi>+<\/span><\/sup><\/mo><\/msup><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5b58\u5728\u6574\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>s<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c\u6269\u5c55\u5806\u7f16\u7801\u5668<\/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-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/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>\u03d5<\/span><\/mi>p<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>s<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>q<\/span><\/sub><\/mi><\/mrow><\/msub>:<\/span><\/mo>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup>\u2192<\/span><\/mo>R<\/span><\/mi><\/mrow>q<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff08\u6709<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>s<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u9690\u85cf\u5c42\uff09\u548c\u6269\u5c55\u64cd\u4f5c<\/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>\u03b7<\/span><\/mi>p<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>s<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4f7f\u5f97\uff1a<\/span><\/p>\n


      <\/span><\/p>\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-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>p<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>s<\/span><\/sub><\/mi>,<\/span><\/sub><\/mo>q<\/span><\/sub><\/mi><\/mrow><\/msub>\u2243<\/span><\/mo>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/p>\n


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

      \u6b64\u540e\uff0c\u6269\u5c55\u5806\u53e0\u7f16\u7801\u5668\u5177\u6709\u901a\u7528\u903c\u8fd1\u6027\u8d28\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u53ef\u4ee5\u8fd1\u4f3c(\u6a21\u62df)\u4efb\u4f55\u5b9a\u4e49\u5728<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/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>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup>\u00d7<\/span><\/mo>R<\/span><\/mi><\/mrow>q<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7c97\u7c92\u5316\u51fd\u6570\u3002<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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


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

      \n
      \n
      \n

      \u76f8\u5173\u5f15\u7406\uff1a<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n


      <\/span><\/section>\n
      \u5f15\u74064\u2014\u2014\u7f16\u7801\u5668\u7684\u4fe1\u606f\u74f6\u9888\uff1a<\/span><\/section>\n

      <\/span><\/section>\n
      \u5bf9\u4e8e\u4efb\u610f\u5411\u91cf<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>X<\/span><\/mi>\u2208<\/span><\/mo>R<\/span><\/mi><\/mrow>p<\/span><\/sup><\/mi><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c\u77e9\u9635<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>W<\/span><\/mi>\u2208<\/span><\/mo>R<\/span><\/mi><\/mrow>s<\/span><\/sup><\/mi>\u00d7<\/span><\/sup><\/mo>p<\/span><\/sup><\/mi><\/mrow><\/msup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5176\u4e2d<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>s<\/span><\/mi>,<\/span><\/mo>p<\/span><\/mi>\u2208<\/span><\/mo>N<\/span><\/mi><\/mrow><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5b58\u5728\u4e00\u4e2a\u6574\u6570<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/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-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>s<\/span><\/mi><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>1<\/span><\/sub><\/span><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/msub>\u2264<\/span><\/mo>min<\/span><\/mo>(<\/span><\/mo>s<\/span><\/mi>,<\/span><\/mo>p<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c\u4e24\u4e2a\u7f16\u7801\u5668\u7684\u57fa\u672c\u5355\u4f4d\uff1a<\/span><\/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-mn><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c8<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>s<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03b7<\/span><\/mi><\/mi><\/msub><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>s<\/span><\/sub><\/span><\/mi>1<\/span><\/sub><\/span><\/mn><\/msub>,<\/span><\/sub><\/span><\/mo>s<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03c7<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>p<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>s<\/span><\/sub><\/span><\/mi>1<\/span><\/sub><\/span><\/mn><\/msub><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/msub><\/mrow><\/msub>\u2218<\/span><\/mo>\u03c8<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>p<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4f7f\u5f97\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-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/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-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-c><\/mjx-mo><\/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-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>W<\/span><\/mi>\u22c5<\/span><\/mo>X<\/span><\/mi>\u2243<\/span><\/mo>(<\/span><\/mo>\u03c8<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>s<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub>\u2218<\/span><\/mo>\u03b7<\/span><\/mi><\/mi><\/msub><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>s<\/span><\/sub><\/span><\/mi>1<\/span><\/sub><\/span><\/mn><\/msub>,<\/span><\/sub><\/span><\/mo>s<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub>)<\/span><\/mo>\u2218<\/span><\/mo>(<\/span><\/mo>\u03c7<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>p<\/span><\/sub><\/span><\/mi>,<\/span><\/sub><\/span><\/mo>s<\/span><\/sub><\/span><\/mi>1<\/span><\/sub><\/span><\/mn><\/msub><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mn><\/msub><\/mrow><\/msub>\u2218<\/span><\/mo>\u03c8<\/span><\/mi><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>p<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/mi><\/mrow><\/msub>)<\/span><\/mo>(<\/span><\/mo>X<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container><\/section>\n

      <\/span><\/section>\n
      \u5f0f\u4e2d\uff0c<\/span><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u2243<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8868\u793a\u8fd1\u4f3c\u6216\u6a21\u62df\u3002<\/span><\/section>\n


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

      4.4 \u673a\u5668\u5b66\u4e60\u7b97\u6cd5<\/span><\/strong><\/span><\/h2>\n


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

      4.4.1 \u6837\u672c\u91cd\u52a0\u6743<\/span><\/strong><\/span><\/h3>\n

      <\/span><\/section>\n
      \u8f93\u5165\u6570\u636e\u7684\u5206\u5e03\u4f1a\u5bf9\u7ed3\u679c\u4ea7\u751f\u4e00\u5b9a\u7684\u5f71\u54cd\uff0c\u4e3a\u4e86\u51cf\u5c11\u6b64\u5f71\u54cd\uff0c\u4f5c\u8005\u9700\u8981\u5bf9\u6837\u672c\u8fdb\u884c\u91cd\u52a0\u6743\uff0c\u4e5f\u5c31\u662f\u901a\u8fc7\u4e3a\u6570\u636e\u4e2d\u7684\u6bcf\u4e2a\u5355\u5143\u5206\u914d\u9002\u5f53\u7684\u6743\u91cd\u6765\u6539\u53d8\u8f93\u5165\u6570\u636e\u7684\u5206\u5e03\uff0c\u89e3\u51b3\u9009\u62e9\u504f\u5dee\u95ee\u9898\u3002\u5728\u56e0\u679c\u673a\u5668\u5b66\u4e60\u3001\u56e0\u679c\u63a8\u65ad\u9886\u57df\u3001\u56e0\u679c\u7279\u5f81\u5b66\u4e60<\/span>\uff08Causal feature learning\uff09<\/span>\u548c\u7a33\u5b9a\u5b66\u4e60<\/span>\uff08Stable learning\uff09<\/span>\u4e2d\u53d1\u6325\u7740\u91cd\u8981\u4f5c\u7528\u3002\u53ef\u4ee5\u4f7f\u7ed3\u679c\u51cf\u5c11\u504f\u89c1\u7684\u5f71\u54cd\uff0c\u63d0\u9ad8\u6a21\u578b\u5728\u672a\u77e5\u73af\u5883\u4e0b\u7684\u6cdb\u5316\u80fd\u529b[15]\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u4e3a\u4e86\u4f7f\u7528\u9006\u6982\u7387\u52a0\u6743\u6280\u672f\uff0c\u6211\u4eec\u9700\u8981\u4f30\u8ba1\u6837\u672c\u7684\u6982\u7387\u5206\u5e03\u3002KDE<\/span> (Kernel Density Estimation) <\/span>\u662f\u4e00\u79cd\u5e38\u7528\u7684\u4f30\u8ba1\u65b9\u6cd5\uff0c\u5b83\u53ef\u4ee5\u6709\u6548\u5730\u6d88\u9664\u79bb\u7fa4\u503c\u5bf9\u6574\u4f53\u6982\u7387\u5206\u5e03\u4f30\u8ba1\u7684\u5f71\u54cd\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5bf9\u4e8e\u4e00\u4e2a\u6837\u672c<\/span><\/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-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>(<\/span><\/mo>x<\/span><\/mi>1<\/span><\/sub><\/mn><\/msub>,<\/span><\/mo>x<\/span><\/mi>2<\/span><\/sub><\/mn><\/msub>,<\/span><\/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\u6211\u4eec\u6709\u5982\u4e0b\u7684\u6838\u5bc6\u5ea6\u4f30\u8ba1\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/span><\/section>\n
      \u5f0f\u4e2d\uff0cn\u8868\u793a\u6837\u672c\u6570\uff0c\u8d85\u53c2\u6570h\u8868\u793a\u5e26\u5bbd<\/span>\uff08\u6839\u636e\u6570\u636e\u7684\u7c97\u7565\u8303\u56f4\u786e\u5b9a\uff09<\/span>\uff0c\u6587\u7ae0\u4e2d\uff0c\u4f5c\u8005\u4e00\u822c\u8bbe\u4e3a0.05\u3002K\u662f\u6838\u51fd\u6570\uff0c\u5177\u4f53\u6765\u8bf4\u662f\u6807\u51c6\u6b63\u6001\u5bc6\u5ea6\u51fd\u6570\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5f97\u5230\u4f30\u8ba1\u51fd\u6570\u540e\uff0c\u5bf9\u6bcf\u4e2a\u6837\u672c\u70b9\u5355\u72ec\u6c42\u503c\uff0c\u5f97\u5230\u6bcf\u4e2a\u6837\u672c\u70b9\u5bf9\u5e94\u7684\u6982\u7387\u503c<\/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-texatom><\/mjx-mstyle><\/mjx-math>p<\/span><\/mi>(<\/span><\/mo>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u5c06\u76ee\u6807\u5206\u5e03<\/span> (\u5747\u5300\u5206\u5e03) <\/span>\u7684\u6982\u7387<\/span><\/sub><\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u9664\u4ee5\u6211\u4eec\u4f30\u8ba1\u7684\u6982\u7387\u503c\uff0c\u5f97\u5230\u6bcf\u4e2a\u6837\u672c\u70b9\u5bf9\u5e94\u7684\u9006\u6982\u7387\u6743\u503c<\/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-texatom><\/mjx-mstyle><\/mjx-math>w<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u4e3a\u4e86\u8986\u76d6\u6240\u6709\u7684\u6837\u672c\u70b9\uff0c\u9700\u8981\u7528\u53c2\u6570L\u6765\u9650\u5236\u5747\u5300\u5206\u5e03\u7684\u8303\u56f4\uff0c\u4ee5\u4fdd\u8bc1\u8fb9\u957f\u4e3a2L\u7684\u6b63\u65b9\u5f62\u53ef\u4ee5\u8986\u76d6\u6240\u6709\u7ef4\u5ea6\u7684\u6240\u6709\u6837\u672c\u70b9\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u6b64\u65f6\u83b7\u5f97\u7684\u6743\u91cd\u4e0e\u6837\u672c\u91cf\u6709\u5173\uff0c\u56e0\u6b64\u9700\u8981\u5bf9\u5b83\u4eec\u8fdb\u884c\u5f52\u4e00\u5316\u3002\u7136\u800c\uff0c\u8fd9\u5c06\u5bfc\u81f4\u4e0e\u6837\u672c\u5bf9\u5e94\u7684\u6743\u91cd\u503c\u975e\u5e38\u5c0f\u3002\u56e0\u6b64\uff0c\u6709\u5fc5\u8981\u5c06\u5b83\u4eec\u4e58\u4ee5\u6837\u672c\u6570\u91cf\u4ee5\u5c06\u6743\u91cd\u503c\u653e\u5927\u56de\u5176\u6b63\u5e38\u8303\u56f4\u3002\u7136\u540e\uff0c\u5c06\u8be5\u6743\u503c\u4e58\u4ee5\u6bcf\u4e2a\u6837\u672c\u7684\u8bad\u7ec3\u635f\u5931\uff0c\u589e\u5f3a\u7a00\u758f\u533a\u57df\u7684\u8bad\u7ec3\uff0c\u8fbe\u5230\u9006\u6982\u7387\u52a0\u6743\u7684\u76ee\u7684\u3002\u7531\u4e8e\u6bcf\u6b21\u8fed\u4ee3\u65f6\u7f16\u7801\u5668\u53c2\u6570\u90fd\u4f1a\u53d1\u751f\u53d8\u5316\uff0c\u5bfc\u81f4<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u7684\u5206\u5e03\u53d1\u751f\u53d8\u5316\uff0c\u56e0\u6b64\u4f5c\u8005\u5c06\u6bcf1000\u6b21\u8fed\u4ee3\u4f7f\u7528KDE\u91cd\u65b0\u4f30\u8ba1\u6574\u4e2a\u6837\u672c\u7684\u6982\u7387\u5206\u5e03\u3002<\/span><\/section>\n

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

      4.4.2 \u53cd\u5411\u52a8\u529b\u5b66<\/span><\/strong><\/h3>\n


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

      <\/section>\n

      <\/span><\/section>\n
      \u6b63\u5411\u52a8\u529b\u5b66<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u8bad\u7ec3\u662f\u6700\u5c0f\u5316\u9884\u6d4b\u8bef\u5dee<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>L<\/span><\/mi>1<\/span><\/sub><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5373<\/sub>\uff0c\u4fdd\u8bc1\u52a8\u529b\u5b66\u9884\u6d4b\u672a\u6765\u7684\u51c6\u786e\u6027\uff0c\u4f46\u662fEI\u4f5c\u4e3a\u4e00\u79cd\u7279\u6b8a\u7684\u4e92\u4fe1\u606f\uff0c\u4e0d\u4ec5\u4e0e\u786e\u5b9a\u6027\u6709\u5173\uff0c\u8fd8\u4e0e\u7b80\u5e76\u6027\u6709\u5173\u3002\u6211\u4eec\u9700\u8981\u5728\u63d0\u9ad8\u52a8\u529b\u5b66\u5b66\u4e60\u5668\u7684\u786e\u5b9a\u6027\u7684\u540c\u65f6\uff0c\u63d0\u9ad8\u5b83\u7684\u975e\u7b80\u5e76\u6027\u3002\u56e0\u6b64\uff0c\u4f5c\u8005\u5728NIS\u7684\u6846\u67b6<\/span>\uff08\u56fe(a)\uff09<\/span>\u57fa\u7840\u4e4b\u4e0a\uff0c\u52a0\u5165\u4e86\u53cd\u5411\u52a8\u529b\u5b66<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>g<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u7528\u4ee5\u53cd\u5411\u9884\u6d4b<\/span>\uff08\u56fe(b)\uff09<\/span>\u3002\u5373\u8f93\u5165<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u901a\u8fc7\u52a8\u529b\u5b66\u5b66\u4e60\u5668<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>g<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e4b\u540e\uff0c\u5f97\u5230\u5b8f\u89c2\u91cf\u7684\u53cd\u5411\u9884\u6d4b\u503c<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4f7f<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>y<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/sub><\/span><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u4e4b\u95f4\u7684\u8bef\u5dee\u503c<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mn><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>L<\/span><\/mi>2<\/span><\/sub><\/mn><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u6700\u5c0f\u5316\u3002\u901a\u8fc7\u8bad\u7ec3\u53cd\u5411\u52a8\u529b\u5b66\u5b66\u4e60\u5668<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>g<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c\u6211\u4eec\u53ef\u4ee5\u5f71\u54cd\u7f16\u7801\u5668\uff0c\u8fdb\u800c\u5f71\u54cd\u9690\u7a7a\u95f4\u4e2d\u7684\u6570\u636e\u5206\u5e03\uff0c\u4ece\u800c\u4f7f\u5f97\u52a8\u529b\u5b66\u5b66\u4e60\u5668<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>f<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u53ef\u4ee5\u5b66\u5230\u4e00\u4e2a\u7b80\u5e76\u6027\u4f4e\u7684\u52a8\u529b\u5b66\u3002<\/span><\/section>\n

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

      4.4.3 \u5206\u9636\u6bb5\u8bad\u7ec3<\/span><\/strong><\/h3>\n

      <\/span><\/section>\n
      \u5728\u5b9e\u8df5\u4e2d\uff0c\u4e3a\u4e86\u51cf\u8f7b\u673a\u5668\u5b66\u4e60\u7684\u538b\u529b\uff0c\u4f5c\u8005\u5148\u8ba9\u6a21\u578b\u5b66\u5230\u6bd4\u8f83\u9760\u8c31\u7684\u7f16\u7801\u7b56\u7565\uff0c\u7136\u540e\u901a\u8fc7\u53cd\u5411\u52a8\u529b\u5b66\u5c06\u7f16\u7801\u7b56\u7565\u8c03\u6574\u81f3\u6700\u4f18\u89e3\u3002NIS+\u7684\u8bad\u7ec3\u8fc7\u7a0b\u5206\u4e3a\u4e24\u4e2a\u9636\u6bb5\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u7b2c\u4e00\u9636\u6bb5\uff1a\u53ea\u8bad\u7ec3\u524d\u5411\u795e\u7ecf\u7f51\u7edc\uff0c\u6700\u5c0f\u5316\u9884\u6d4b\u8bef\u5dee<\/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-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-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-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>w<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo>\u2225<\/span><\/mo>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>\u2212<\/span><\/mo>g<\/span><\/mi>(<\/span><\/mo>y<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub>)<\/span><\/mo>\u2225<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u7b2c\u4e8c\u9636\u6bb5\uff0c\u8bad\u7ec3\u53cd\u5411\u795e\u7ecf\u7f51\u7edc\u548c\u524d\u5411\u795e\u7ecf\u7f51\u7edc\uff0c\u672c\u8d28\u4e0a\u662f\u7528\u4e8e\u8bad\u7ec3<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>\u03c9<\/span><\/sub><\/mi><\/mrow><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u5728\u6b64\u8fc7\u7a0b\u4e2d\uff0c\u7528<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03bb<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u6765\u5e73\u8861\u524d\u5411\u795e\u7ecf\u7f51\u7edc\u9884\u6d4b\u8bef\u5dee<\/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-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-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-mo><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>w<\/span><\/mi>(<\/span><\/mo>x<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>)<\/span><\/mo>\u2225<\/span><\/mo>y<\/span><\/mi>t<\/span><\/sub><\/mi><\/msub>\u2212<\/span><\/mo>g<\/span><\/mi>(<\/span><\/mo>y<\/span><\/mi>t<\/span><\/sub><\/mi>+<\/span><\/sub><\/mo>1<\/span><\/sub><\/mn><\/mrow><\/msub>)<\/span><\/mo>\u2225<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c\u53cd\u5411\u795e\u7ecf\u7f51\u7edc\u9884\u6d4b\u8bef\u5dee<\/span><\/sub><\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u3002\u5728\u4e0d\u540c\u7684\u5b9e\u9a8c\u4e2d\uff0c\u6839\u636e\u8d85\u53c2\u6570\u641c\u7d22\u6cd5\uff0c<\/span><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03bb<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u53d6\u4e0d\u540c\u7684\u503c\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5728\u6574\u4e2a\u6a21\u578b\u7684\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c\u603b\u7684\u76ee\u6807\u5982\u5f0f3\u3002<\/span><\/section>\n

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

      4.4.4 \u9762\u5bf9\u5927\u89c4\u6a21\u590d\u6742\u7cfb\u7edf\u7684\u62d3\u5c55<\/span><\/strong><\/h3>\n


      <\/span><\/strong><\/p>\n

      <\/section>\n

      <\/span><\/section>\n
      \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5982\u679c\u7cfb\u7edf\u4e0d\u662f\u5c0f\u89c4\u6a21\u7cfb\u7edf\uff0c\u800c\u662f\u7c7b\u4f3c\u5143\u80de\u81ea\u52a8\u673a\u7684\u5927\u89c4\u6a21\u7684\u590d\u6742\u7cfb\u7edf\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u6b64\u6846\u67b6\u8fdb\u884c\u62d3\u5c55\uff0c\u5c06\u7f16\u7801\u5668<\/span>\uff08\u89e3\u7801\u5668\uff09<\/span>\u8fdb\u884c\u7ec4\u5408\uff0c\u4ece\u800c\u51cf\u8f7b\u6a21\u578b\u8bad\u7ec3\u7684\u538b\u529b\u548c\u96be\u5ea6\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u9996\u5148\uff0c\u5728\u5904\u7406\u9ad8\u7ef4\u590d\u6742\u7cfb\u7edf\u65f6\uff0c\u4e00\u6b21\u4e22\u5f03\u591a\u4e2a\u7ef4\u5ea6\u4f1a\u7ed9\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u5e26\u6765\u5f88\u5927\u7684\u6311\u6218\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u4e00\u7cfb\u5217\u57fa\u672c\u7f16\u7801\u5668\u5806\u53e0<\/span>\uff08\u4e32\u8054\uff09<\/span>\u5728\u4e00\u8d77\u5e76\u9010\u6e10\u4e22\u5f03\u7ef4\u5ea6\uff0c\u964d\u4f4e\u8bad\u7ec3\u96be\u5ea6\u3002\u5982\u56fe(a)\u6240\u793a\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u6b64\u5916\uff0c\u4e00\u4e9b\u5927\u89c4\u6a21\u590d\u6742\u7cfb\u7edf\u5177\u6709\u5148\u9a8c\u77e5\u8bc6\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u5148\u9a8c\u77e5\u8bc6\u5bf9\u5fae\u89c2\u7ef4\u5ea6\u8fdb\u884c\u5206\u7ec4\uff0c\u5206\u7ec4\u4e4b\u540e\uff0c\u5bf9\u6bcf\u4e00\u7ec4\u90fd\u7528\u7f16\u7801\u5668\u8fdb\u884c\u7f16\u7801\uff0c\u76f8\u5f53\u4e8e\u628a\u7f16\u7801\u5668\u8fdb\u884c\u4e86\u5e76\u8054\u3002\u5e76\u884c\u7f16\u7801\u5668\u4e4b\u95f4\u5171\u4eab\u53c2\u6570\uff0c\u6545\u795e\u7ecf\u7f51\u7edc\u4f9d\u7136\u53ef\u4ee5\u9ad8\u6548\u3001\u51c6\u786e\u5730\u83b7\u5f97\u7c97\u7c92\u5316\u89c4\u5219\u3002\u6700\u540e\uff0c\u5c06\u4ece\u6240\u6709\u7f16\u7801\u5668\u83b7\u5f97\u7684\u5b8f\u89c2\u53d8\u91cf\u8fde\u63a5\u6210\u4e00\u4e2a\u5411\u91cf\uff0c\u4ee5\u5bfc\u51fa\u603b\u4f53\u7684\u5b8f\u89c2\u53d8\u91cf\u3002\u8fd9\u79cd\u5e76\u884c\u7ed3\u6784\u4e5f\u53ef\u4ee5\u4e0e\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u7b49\u67b6\u6784\u7ed3\u5408\u8d77\u6765\u3002\u5982\u56fe(b)\u6240\u793a\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u4e3a\u4e86\u63d0\u9ad8\u641c\u7d22\u6700\u4f18\u5c3a\u5ea6\u7684\u6548\u7387\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u5806\u53e0\u7f16\u7801\u5668\u83b7\u5f97\u9690\u85cf\u7a7a\u95f4\u7684\u591a\u4e2a\u5c3a\u5ea6\uff0c\u540c\u65f6\u8bad\u7ec3\u591a\u4e2a\u4e0d\u540c\u5c3a\u5ea6\u7684\u52a8\u529b\u5b66\u5b66\u4e60\u5668<\/span>\uff08\u76f8\u5f53\u4e8e\u641c\u7d22\u4e0d\u540cq\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\uff09<\/span>\uff0c\u4ece\u800c\u907f\u514d\u91cd\u65b0\u8bad\u7ec3\u7f16\u7801\u5668\uff0c\u63d0\u9ad8\u6a21\u578b\u6548\u7387\u3002\u5982\u56fe(c)\u6240\u793a\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5c06NIS+\u7684\u7f16\u7801\u5668\u66ff\u6362\u4e3a\u5806\u53e0\u7f16\u7801\u5668\u4e0e\u5e76\u884c\u7f16\u7801\u5668\u7684\u4efb\u610f\u7ec4\u5408\u65f6\uff0c\u5f0f3\u7684\u6700\u4f18\u5316\u51fd\u6570\u4f9d\u7136\u9002\u7528<\/span>\uff08\u5f15\u74065\u3001\u5f15\u74066\uff09<\/span>\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5f15\u74065\u2014\u2014\u5806\u53e0\u7f16\u7801\u5668\u4e0d\u5f71\u54cd\u4e92\u4fe1\u606f\uff1a<\/span><\/section>\n

      <\/span><\/section>\n
      \u82e5<\/span><\/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-texatom><\/mjx-mstyle><\/mjx-math>X<\/span><\/mi>\u2208<\/span><\/mo>D<\/span><\/mi>o<\/span><\/mi>m<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/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-texatom><\/mjx-mstyle><\/mjx-math>Y<\/span><\/mi>\u2208<\/span><\/mo>D<\/span><\/mi>o<\/span><\/mi>m<\/span><\/mi>(<\/span><\/mo>Y<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5f62\u6210\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>X<\/span><\/mi>\u2192<\/span><\/mo>Y<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c <\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>L<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/sub><\/span><\/mo><\/msubsup><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5206\u522b\u8868\u793aL\u5c42\u5806\u53e0\u7684\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\uff0c\u5219\uff1a<\/span><\/section>\n

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

      <\/p>\n


      <\/span><\/section>\n
      \u5f15\u74066\u2014\u2014\u5e76\u884c\u7f16\u7801\u5668\u4e0d\u5f71\u54cd\u4e92\u4fe1\u606f\uff1a<\/span><\/section>\n

      <\/span><\/section>\n
      \u82e5<\/span><\/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-texatom><\/mjx-mstyle><\/mjx-math>X<\/span><\/mi>\u2208<\/span><\/mo>D<\/span><\/mi>o<\/span><\/mi>m<\/span><\/mi>(<\/span><\/mo>X<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/span><\/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-texatom><\/mjx-mstyle><\/mjx-math>Y<\/span><\/mi>\u2208<\/span><\/mo>D<\/span><\/mi>o<\/span><\/mi>m<\/span><\/mi>(<\/span><\/mo>Y<\/span><\/mi>)<\/span><\/mo><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u5f62\u6210\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe<\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>X<\/span><\/mi>\u2192<\/span><\/mo>Y<\/span><\/mi><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\uff0c <\/span><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-script><\/mjx-msub><\/mjx-texatom><\/mjx-mstyle><\/mjx-math>\u03d5<\/span><\/mi>T<\/span><\/sub><\/mi><\/msub><\/mrow><\/mstyle><\/mjx-assistive-mml><\/mjx-container>\u548c<\/sub><\/span>\u5206\u522b\u8868\u793a\u7531T\u4e2a\u666e\u901a\u7f16\u7801\u5668\u6216\u89e3\u7801\u5668\u7ec4\u6210\u7684\u5e76\u884c\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\uff0c\u5219\uff1a<\/span><\/section>\n

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

       \u3002<\/p>\n


      <\/section>\n


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

      \n
      \n
      \n
      \n
      \n

      <\/section>\n

      <\/section>\n
      \n
      <\/svg><\/section>\n<\/section>\n<\/section>\n
      \n

      5. \u603b\u7ed3\u4e0e\u5c55\u671b<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

      \n

      <\/section>\n

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


      <\/p>\n

      5.1 \u603b\u7ed3<\/span><\/strong><\/h2>\n

      <\/span><\/section>\n
      \u53d7\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u7684\u542f\u53d1\uff0c\u4f5c\u8005\u6784\u5efa\u4e86\u4e00\u79cd\u65b0\u7684\u673a\u5668\u5b66\u4e60\u6846\u67b6Neural Information Squeezer Plus<\/span> (NIS+) <\/span>\u6765\u5b66\u4e60\u6d8c\u73b0\u5b8f\u89c2\u52a8\u529b\u5b66\uff0c\u5e76\u76f4\u63a5\u4ece\u6570\u636e\u4e2d\u627e\u5230\u5408\u9002\u7684\u7c97\u7c92\u5316\u7b56\u7565\u3001\u91cf\u5316\u5404\u79cd\u6761\u4ef6\u4e0bCE\u7684\u7a0b\u5ea6\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u4e0e\u5176\u4ed6\u673a\u5668\u5b66\u4e60\u6846\u67b6\u76f8\u6bd4\uff0cNIS+\u4e13\u6ce8\u4e8e\u5728\u4fdd\u6301\u6709\u6548\u6027\u7ea6\u675f\u7684\u540c\u65f6\u6700\u5927\u5316\u5b8f\u89c2\u52a8\u529b\u5b66\u7684\u6709\u6548\u4fe1\u606f<\/span>\uff08EI\uff09<\/span>\u3002\u8fd9\u4f7f\u5f97\u5b66\u4e60\u5230\u7684\u6d8c\u73b0\u5b8f\u89c2\u52a8\u529b\u5b66\u80fd\u591f\u6355\u83b7\u5c3d\u53ef\u80fd\u72ec\u7acb\u4e8e\u8f93\u5165\u6570\u636e\u5206\u5e03\u7684\u4e0d\u53d8\u56e0\u679c\u673a\u5236\u3002\u8fd9\u4e2a\u7279\u6027\u4e0d\u4ec5\u4f7fNIS+\u80fd\u591f\u8bc6\u522b\u4e0d\u540c\u73af\u5883\u4e2d\u7684\u6570\u636eCE\uff0c\u800c\u4e14\u8fd8\u589e\u5f3a\u4e86\u5b83\u5bf9\u4e0d\u540c\u4e8e\u8bad\u7ec3\u6570\u636e\u7684\u73af\u5883\u8fdb\u884c\u6cdb\u5316\u7684\u80fd\u529b\u3002\u901a\u8fc7\u5c06\u8bef\u5dee\u7ea6\u675f\u7eb3\u5165\u5f0f1\uff0c\u4f5c\u8005\u589e\u5f3a\u4e86EI\u6700\u5927\u5316\u6846\u67b6\u7684\u9c81\u68d2\u6027\uff0c\u89e3\u51b3\u4e86[30]\u4e2d\u63d0\u51fa\u7684\u91cd\u6574\u5316\u548c\u65f6\u95f4\u6f14\u5316\u7b97\u5b50\u7684\u4ea4\u6362\u6027\u95ee\u9898\u3002\u4f5c\u8005\u7684\u6846\u67b6\u786e\u4fdd\u5fae\u89c2\u52a8\u529b\u5b66\u6f14\u5316\u4e0e\u7f16\u7801\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u76f8\u5339\u914d\u3002\u7531\u4e8e\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\u6240\u4f7f\u7528\u7684\u795e\u7ecf\u7f51\u7edc\u4e92\u4e3a\u53ef\u9006\u51fd\u6570\u4e14\u53c2\u6570\u5171\u4eab\uff0c\u8fd9\u79cd\u5fae\u89c2\u72b6\u6001\u548c\u7f16\u7801\u6210\u7684\u5b8f\u89c2\u72b6\u6001\u4e4b\u95f4\u7684\u4e00\u81f4\u6027\u8bc1\u5b9e\u4e86\u5b66\u4e60\u5b8f\u89c2\u7684\u52a8\u529b\u5b66\u548c\u7c97\u7c92\u5316\u7b56\u7565\u662f\u53ef\u4ea4\u6362\u7684\u3002\u56e0\u6b64\uff0cNIS+\u6269\u5c55\u4e86Hoel[1]\u7684CE\u7406\u8bba\uff0c\u4f7f\u5176\u65e2\u9002\u7528\u4e8e\u79bb\u6563\u548c\u8fde\u7eed\u52a8\u529b\u7cfb\u7edf\uff0c\u4e5f\u9002\u7528\u4e8e\u5b9e\u9645\u6570\u636e\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u5b9e\u9a8c\u8868\u660e\uff0c\u2460\u901a\u8fc7\u6700\u5927\u5316EI\uff0cNIS+\u7684\u591a\u6b65\u9884\u6d4b\u80fd\u529b\u3001\u6cdb\u5316\u80fd\u529b\u3001\u6a21\u5f0f\u6355\u83b7\u80fd\u529b\u4f18\u4e8e\u5176\u4ed6\u673a\u5668\u5b66\u4e60\u6a21\u578b\uff0c\u53ef\u4ee5\u5728\u9690\u7a7a\u95f4\u4e2d\u83b7\u5f97\u66f4\u7a33\u5065\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u3002\u2461NIS+\u53ef\u4ee5\u6bd4\u03a8\u6307\u6807\u66f4\u5408\u7406\u5730\u8bc6\u522bCE\u3002NIS+\u53ef\u4ee5\u6709\u6548\u5730\u5b66\u4e60\u590d\u6742\u7cfb\u7edf\u7684\u7c97\u7c92\u5ea6\u5316\u8fc7\u7a0b\uff0c\u5e76\u4f7f\u7528\u79ef\u5206\u68af\u5ea6(IG)\u65b9\u6cd5\u53ef\u4ee5\u5c06\u5b8f\u89c2\u72b6\u6001\u548c\u5fae\u89c2\u72b6\u6001\u4e4b\u95f4\u7684\u5173\u7cfb\u53ef\u89c6\u5316\uff0c\u4ece\u800c\u53ef\u4ee5\u8bc6\u522b\u5fae\u89c2\u72b6\u6001\u4e2d\u6700\u91cd\u8981\u7684\u53d8\u91cf\u3002\u2462\u5916\u5728\u566a\u58f0\u4f1a\u589e\u52a0CE\uff0c\u800c\u5185\u5728\u566a\u58f0\u4f1a\u964d\u4f4eCE\u3002\u8fd9\u8868\u660e\uff0c\u7531\u89c2\u6d4b\u4e0d\u786e\u5b9a\u6027\u5f15\u8d77\u7684\u5916\u90e8\u566a\u58f0\u53ef\u4ee5\u901a\u8fc7\u5b66\u5230\u7684\u7c97\u7c92\u5316\u7b56\u7565\u51cf\u8f7b\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u7531\u4e8e\u52a8\u6001\u89c4\u5219\u7684\u5185\u5728\u4e0d\u786e\u5b9a\u6027\u800c\u4ea7\u751f\u7684\u56fa\u6709\u566a\u58f0\u65e0\u6cd5\u6d88\u9664\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u6b64\u5916\uff0cNIS+\u8fd8\u8c03\u548c\u4e86\u5173\u4e8e\u6d8c\u73b0\u662f\u4e00\u4e2a\u5ba2\u89c2\u6982\u5ff5\u8fd8\u662f\u4e00\u4e2a\u4f9d\u8d56\u4e8e\u89c2\u5bdf\u8005\u7684\u8ba4\u77e5\u6982\u5ff5\u7684\u4e89\u8bba\u3002\u901a\u8fc7\u8bbe\u8ba1\u4e00\u4e2a\u6700\u5927\u5316EI\u7684\u673a\u5668\uff0c\u6211\u4eec\u53ef\u4ee5\u63d0\u53d6\u51fa\u5ba2\u89c2\u7684\u6d8c\u73b0\u7279\u5f81\u548c\u52a8\u6001\u3002\u8fd9\u53f0\u673a\u5668\u5145\u5f53\u4e86\u4e00\u4e2a\u89c2\u5bdf\u8005\uff0c\u4f46\u5374\u662f\u4e00\u4e2a\u5ba2\u89c2\u7684\u89c2\u5bdf\u8005\u3002\u5982\u679c\u673a\u5668\u89c2\u5bdf\u8005\u5728\u6570\u636e\u4e2d\u68c0\u6d4b\u5230\u6709\u8da3\u7684\u6a21\u5f0f\uff0c\u5c31\u4f1a\u8ba4\u4e3a\u51fa\u73b0\u6d8c\u73b0\u3002<\/span><\/section>\n

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

      5.2 \u5c55\u671b<\/span><\/strong><\/span><\/h2>\n


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

      NIS+\u4e5f\u5b58\u5728\u4e00\u4e9b\u5c40\u9650\u6027\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u2460NIS+\u9700\u8981\u5927\u91cf\u7684\u8bad\u7ec3\u6570\u636e\u6765\u5b66\u4e60\u5b8f\u89c2\u52a8\u6001\u548c\u7c97\u7c92\u5316\u7b56\u7565\uff0c\u8fd9\u5728\u5f88\u591a\u73b0\u5b9e\u60c5\u51b5\u4e0b\u53ef\u80fd\u662f\u4e0d\u53ef\u884c\u7684\u3002\u5982\u679c\u8bad\u7ec3\u4e0d\u5145\u5206\uff0c\u53ef\u80fd\u5bfc\u81f4CE\u7684\u9519\u8bef\u8bc6\u522b\u3002\u56e0\u6b64\uff0c\u6709\u5fc5\u8981\u7ed3\u5408\u5176\u4ed6\u6570\u503c\u65b9\u6cd5\uff0c\u5982\u03a6ID[3]\uff0c\u4ee5\u4f5c\u51fa\u51c6\u786e\u7684\u5224\u65ad\u3002NIS+\u7684\u4e00\u4e2a\u4f18\u70b9\u662f\u5b83\u80fd\u591f\u8bc6\u522b\u7c97\u7c92\u5316\u7684\u5b8f\u89c2\u72b6\u6001\uff0c\u7136\u540e\u53ef\u4ee5\u5c06\u5176\u7528\u4f5c\u03a6ID[3]\u7684\u8f93\u5165\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u2461\u795e\u7ecf\u7f51\u7edc\u7684\u53ef\u89e3\u91ca\u6027\u3002\u589e\u5f3a\u5b66\u4e60\u6a21\u578b\u7684\u53ef\u89e3\u91ca\u6027\u53ef\u4ee5\u63d0\u4f9b\u5bf9\u6f5c\u5728\u673a\u5236\u7684\u6709\u4ef7\u503c\u7684\u89c1\u89e3\uff0c\u5e76\u63d0\u9ad8\u7ed3\u679c\u7684\u53ef\u4fe1\u5ea6\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u2462\u4f5c\u8005\u7684\u5de5\u4f5c\u662f\u5bf9[1][2]\u4e2d\u63d0\u51fa\u7684\u7814\u7a76\u7684\u5ef6\u4f38\uff0c\u8fd9\u4e9b\u7814\u7a76\u5047\u8bbe\u52a8\u529b\u5b66\u662f\u9a6c\u5c14\u53ef\u592b\u7684\u3002\u7136\u800c\uff0c\u5f53\u52a8\u6001\u8868\u73b0\u51fa\u5f3a\u70c8\u7684\u975e\u9a6c\u5c14\u53ef\u592b\u7279\u5f81\u65f6\uff0c\u5176\u4ed6\u91cf\u5316\u6d8c\u73b0\u7684\u6846\u67b6\uff0c\u5982[3][5]\u4e2d\u63d0\u51fa\u7684\u6846\u67b6\uff0c\u53ef\u80fd\u5177\u6709\u66f4\u5927\u7684\u4f18\u52bf\u3002<\/span><\/section>\n

      <\/section>\n


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

      \n
      \n
      \n

      \u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

      \n
      \n
      \n
      \n
        \n
      1. \n

         Hoel E P, Albantakis L, Tononi G. Quantifying causal emergence shows that macro can beat micro[J]. Proceedings of the National Academy of Sciences, 2013, 110(49): 19790-19795.<\/p>\n<\/li>\n

      2. \n

         Hoel E P. When the map is better than the territory[J]. Entropy, 2017, 19(5): 188.<\/p>\n<\/li>\n

      3. \n

         Rosas F E, Mediano P A, Jensen H J, et al. Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data[J]. PLoS computational biology, 2020, 16(12): e1008289.<\/p>\n<\/li>\n

      4. \n

         Zhang J, Tao R, Yuan B. Dynamical Reversibility and A New Theory of Causal Emergence. arXiv preprint arXiv:2402.15054. 2024 Feb 23.<\/p>\n<\/li>\n

      5. \n

         Barnett L, Seth AK. Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems. Physical Review E. 2023 Jul;108(1):014304.<\/p>\n<\/li>\n

      6. \n

         Vlachas P-R, Arampatzis G and Uhler C et al. Multiscale simulations of complex systems by learning their effective dynamics. Nat Mach Intell 2022; 4: 359\u2013366.<\/p>\n<\/li>\n

      7. \n

         Kemeth F-P, Bertalan T and Thiem T et al. Learning emergent partial differential equations in a learned emergent space. Nat Commun 2022; 13: 3318.<\/p>\n<\/li>\n

      8. \n

         Floryan D and Graham M-D. Data-driven discovery of intrinsic dynamics. Nat Mach Intell 2022; 4: 1113\u20131120.<\/p>\n<\/li>\n

      9. \n

         Cai L and Ji S. A multi-scale approach for graph link prediction. Proceedings of the AAAI Conference on Artificial Intelligence, New York, 20-27 February 2020.<\/p>\n<\/li>\n

      10. \n

         Chen Z, Li S and Yang B et al. Multi-scale spatial temporal graph convolutional network for skeleton-based action recognition. Proceedings of the AAAI Conference on Artificial Intelligence, New York, 22 February – 1 March 2022.<\/p>\n<\/li>\n

      11. \n

         P. A. Mediano, F. Rosas, R. L. Carhart-Harris, A. K. Seth, A. B. Barrett, Beyond integrated information: A taxonomy of information dynamics phenomena, arXiv preprint arXiv:1909.02297 (2019).<\/p>\n<\/li>\n

      12. \n

         Kaplanis Christos, Mediano Pedro, Rosas Fernando. Learning Causally Emergent Representations. NeurIPS 2023 workshop: Information-Theoretic Principles in Cognitive Systems<\/p>\n<\/li>\n

      13. \n

         Zhang J, Liu K. Neural information squeezer for causal emergence[J]. Entropy, 2022, 25(1): 26.<\/p>\n<\/li>\n

      14. \n

         Dinh, L.; Sohl-Dickstein, J.; Bengio, S. Density estimation using real nvp. arXiv 2016, arXiv:1605.08803.<\/p>\n<\/li>\n

      15. \n

         Cui, Peng, Athey, et al. Stable learning establishes some common ground between causal inference and machine learning. nature machine intelligence, 2022, 4(2): 110-115<\/p>\n<\/li>\n

      16. \n

         Wang F ,Wei Z ,Zhang W . Sliding homoclinic orbits and chaotic dynamics in a class of 3D piecewise-linear Filippov systems [J]. Nonlinear Dynamics, 2024, (prepublish): 1-21.<\/p>\n<\/li>\n

      17. \n

         Arjovsky, M.; Bottou, L.; Gulrajani, I.; Lopez-Paz, D. Invariant risk minimization. arXiv 2019, arXiv:1907.02893<\/p>\n<\/li>\n

      18. \n

         Stan S ,Rostami M . Source-free domain adaptation for semantic image segmentation using internal representations [J]. Frontiers in Big Data, 2024, 7 1359317-1359317.<\/p>\n<\/li>\n

      19. \n

         L G M ,S A D ,M C S . Variability in training unlocks generalization in visual perceptual learning through invariant representations. [J]. Current biology : CB, 2023, 33 (5): 817-826.e3.<\/p>\n<\/li>\n

      20. \n

         Zhang B ,Gao B ,Liang S , et al. A classification algorithm based on improved meta learning and transfer learning for few\u2010shot medical images [J]. IET Image Processing, 2023, 17 (12): 3589-3598.<\/p>\n<\/li>\n

      21. \n

         Mingzhe Yang, Zhipeng Wang, Kaiwei Liu, et al. Finding emergence in data by maximizing effective information. National Science Review, 2024, nwae279<\/p>\n<\/li>\n

      22. \n

         Reynolds C-W. Flocks, herds and schools: A distributed behavioral model. Proceedings of the 14th annual conference on Computer graphics and interactive techniques, Denver, 27 July – 1 August 1987.<\/p>\n<\/li>\n

      23. \n

         Sundararajan M, Taly A and Yan Q. Axiomatic attribution for deep networks. Proceedings of the 34th International Conference on Machine Learning, Sydney, 6-11 August 2017.<\/p>\n<\/li>\n

      24. \n

         Snoek L, Miesen M and Beemsterboer T et al. The amsterdam open mri collection, a set of multimodal mri datasets for individual difference analyses. Sci Data 2021; 8: 03.<\/p>\n<\/li>\n

      25. \n

         Schaefer A, Kong R and Gordon E-M et al. Local-Global Parcellation of the Human Cerebral Cortex from Intrinsic Functional Connectivity MRI. Cereb Cortex 2017; 28:3095\u20133114.<\/p>\n<\/li>\n

      26. \n

         Shalizi C and Moore C. What is a macrostate? subjective observations and objective dynamics. arXiv: cond-mat\/0303625.<\/p>\n<\/li>\n

      27. \n

         Fisch D, J\u00e4nicke M and Sick B et al. Quantitative emergence\u2013a refined approach based on divergence measures. Fourth IEEE International Conference on Self-Adaptive and Self-Organizing Systems, 2010.<\/p>\n<\/li>\n

      28. \n

         Mnif M and M\u00fcller-Schloer C. Quantitative emergence. In: M\u00fcller-Schloer C, Schmeck H and Ungerer T(ed.). Organic Computing\u2014A Paradigm Shift for Complex Systems. Berlin: Springer, 2011, 39-52.<\/p>\n<\/li>\n

      29. \n

         Fisch D, J\u00e4nicke M and M\u00fcller-Schloer C et al. Divergence measures as a generalised approach to quantitative emergence. In: M\u00fcller-Schloer C, Schmeck H and Ungerer T(ed.). Organic Computing\u2014A Paradigm Shift for Complex Systems. Berlin: Springer, 2011, 53-66.<\/p>\n<\/li>\n

      30. \n

         Eberhardt F and Lee L-L. Causal emergence: When distortions in a map obscure the territory. Philosophies 2022; 7: 30.<\/p>\n<\/li>\n<\/ol>\n

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

        \n
        \n

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


        <\/p>\n


        <\/p>\n


        <\/p>\n

        <\/section>\n


        <\/p>\n

        \n
        \n
        \n
        \n

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


        <\/section>\n

        \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\u4ece2021\u5e74\u590f\u5929\u81f3\u4eca\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u5df2\u7ecf\u9646\u7eed\u4e3e\u529e\u4e86\u56db\u5b63\u300c\u56e0\u679c\u6d8c\u73b0\u300d\u8bfb\u4e66\u4f1a\uff0c\u7cfb\u7edf\u68b3\u7406\u4e86\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u7684\u53d1\u5c55\u8109\u7edc\uff0c\u6df1\u5165\u63a2\u8ba8\u4e86\u4fe1\u606f\u6574\u5408\u4e0e\u4fe1\u606f\u5206\u89e3\u7684\u672c\u8d28\uff0c\u5e76\u63a2\u7d22\u4e86\u5728\u751f\u7269\u7f51\u7edc\u3001\u8111\u7f51\u7edc\u3001\u673a\u5668\u5b66\u4e60\u7b49\u8de8\u5b66\u79d1\u9886\u57df\u7684\u5e94\u7528\u3002\u6b64\u6b21\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u4e94\u5b63<\/a>\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\u5df2\u5b8c\u7ed3\uff0c\u73b0\u5728\u62a5\u540d\u53ef\u52a0\u5165\u793e\u7fa4\u5e76\u89e3\u9501<\/span>\u56de\u653e<\/span>\u89c6\u9891\u6743\u9650\u3002<\/span><\/span><\/p>\n


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

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


        <\/p>\n


        <\/p>\n

        \n
        \n
        \n
        \n

        \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


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

        <\/section>\n

        \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


        <\/p>\n


        <\/p>\n

        \u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/strong><\/p>\n

        1. <\/strong>\u201c\u6d8c\u73b0\u201d\u53d1\u73b0\u4e4b\u65c5\uff1a\u4eba\u5de5\u667a\u80fd\u89c2\u5bdf\u8005\u4e0e\u6d8c\u73b0\u7684\u91cf\u5316\uff5c\u96c6\u667a\u79d1\u5b66\u7814\u7a76\u4e2d\u5fc3NSR\u6700\u65b0\u6210\u679c<\/a><\/strong><\/span><\/section>\n
        2. <\/strong>\u673a\u5668\u5b66\u4e60\u6846\u67b6NIS+\uff1a\u901a\u8fc7\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\u8bc6\u522b\u201c\u56e0\u679c\u6d8c\u73b0\u201d | NSR<\/a><\/strong><\/span><\/section>\n
        3. <\/strong>\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<\/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
        <\/strong>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><\/p>\n


        <\/p>\n


        <\/p>\n

        \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":"

        \u5bfc\u8bed NIS+\uff08Neural Information Squeezer Plus\uff09\u662f\u4e00\u4e2a\u673a\u5668\u5b66\u4e60\u6846\u67b6\uff0c\u53ef\u4ee5\u4ece\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u4e2d\u5b66\u4e60\u51fa\u7cfb\u7edf\u5728\u5fae\u89c2\u3001\u5b8f\u89c2\u4e0d\u540c\u5c3a\u5ea6\u7684\u52a8\u529b\u5b66\uff0c\u5e76\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\u3002\u8be5\u6846\u67b6\u901a\u8fc7\u6700\u5927\u5316\u6709\u6548\u4fe1\u606f\uff0c\u5f97\u5230\u4e00\u4e2a\u5b8f\u89c2\u52a8\u6001\u6a21\u578b\uff0c\u5b83\u662f\u5bf9NIS\u6846\u67b6\u7684\u63a8\u5e7f\u3002\u6a21\u62df\u548c\u5b9e\u9645\u6570\u636e\u4e0a\u7684\u591a\u9879\u5b9e\u9a8c\u53ef\u4ee5\u8bc1\u660e\u8be5\u6846\u67b6\u7684\u6709\u6548\u6027\uff0c…<\/p>\n","protected":false},"author":0,"featured_media":53841,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/53932"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=53932"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/53932\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/53841"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=53932"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=53932"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=53932"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=53932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}