{"id":49763,"date":"2025-07-30T19:33:42","date_gmt":"2025-07-30T11:33:42","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/49763.html"},"modified":"2025-07-30T19:33:42","modified_gmt":"2025-07-30T11:33:42","slug":"%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a002-%e6%95%b0%e6%8d%ae%e4%b8%8e%e7%ae%97%e6%b3%95%e5%88%9d%e6%ad%a5","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/49763.html","title":{"rendered":"\u673a\u5668\u5b66\u4e6002\u2014\u2014\u6570\u636e\u4e0e\u7b97\u6cd5\u521d\u6b65"},"content":{"rendered":"<h2>\u673a\u5668\u5b66\u4e60<\/h2>\n<p>\u673a\u5668\u5b66\u4e6001\u2014\u2014\u521d\u8bc6\u673a\u5668\u5b66\u4e60<\/p>\n<hr \/>\n<h4>\u6587\u7ae0\u76ee\u5f55<\/h4>\n<ul>\n<li>\u673a\u5668\u5b66\u4e60<\/li>\n<li>\u4e00\u3001\u6570\u636e\u964d\u7ef4<\/li>\n<li>\n<ul>\n<li>1.1 \u7279\u5f81\u9009\u62e9<\/li>\n<li>\n<ul>\n<li>(a) VarianceThreshold \u4f4e\u65b9\u5dee\u8fc7\u6ee4\u7279\u5f81\u9009\u62e9<\/li>\n<li>(b) \u6839\u636e\u76f8\u5173\u7cfb\u6570\u7684\u7279\u5f81\u9009\u62e9<\/li>\n<li>\n<ul>\n<li>&lt;1&gt;\u7406\u8bba<\/li>\n<li>&lt;2&gt;\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570:<\/li>\n<li>&lt;3&gt;api:<\/li>\n<li>&lt;4&gt;\u793a\u4f8b&#xff1a;<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>1.2 \u4e3b\u6210\u5206\u5206\u6790&#xff08;PCA&#xff09;<\/li>\n<li>\n<ul>\n<li>(a) \u539f\u7406<\/li>\n<li>(b) \u6b65\u9aa4<\/li>\n<li>api<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>\u4e8c\u3001KNN\u7b97\u6cd5<\/li>\n<li>\n<ul>\n<li>2.1 \u9884\u4f30\u5668<\/li>\n<li>2.2 KNN\u5206\u7c7b<\/li>\n<li>\n<ul>\n<li>2.2.1 \u6837\u672c\u8ddd\u79bb\u5206\u6790<\/li>\n<li>2.2.2 \u539f\u7406<\/li>\n<li>2.2.3 api\u4e0e\u793a\u4f8b<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>\u4e09\u3001\u6a21\u578b\u9009\u62e9\u4e0e\u8c03\u4f18<\/li>\n<li>\n<ul>\n<li>3.1 \u4ea4\u53c9\u9a8c\u8bc1<\/li>\n<li>\n<ul>\n<li>(1) \u4fdd\u7559\u4ea4\u53c9\u9a8c\u8bc1HoldOut<\/li>\n<li>(2) K-\u6298\u4ea4\u53c9\u9a8c\u8bc1(K-fold)<\/li>\n<li>(3) \u5206\u5c42k-\u6298\u4ea4\u53c9\u9a8c\u8bc1Stratified k-fold<\/li>\n<li>(4) api<\/li>\n<\/ul>\n<\/li>\n<li>3.2 \u8d85\u53c2\u6570\u641c\u7d22<\/li>\n<\/ul>\n<\/li>\n<li>\u56db\u3001\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b<\/li>\n<li>\n<ul>\n<li>4.1 \u8d1d\u53f6\u65af\u5206\u7c7b\u7406\u8bba<\/li>\n<li>4.2 \u6761\u4ef6\u6982\u7387<\/li>\n<li>4.3 \u5168\u6982\u7387\u516c\u5f0f<\/li>\n<li>4.4 \u8d1d\u53f6\u65af\u63a8\u65ad<\/li>\n<li>4.5 \u6734\u7d20\u8d1d\u53f6\u65af\u63a8\u65ad<\/li>\n<li>4.6 \u62c9\u666e\u62c9\u65af\u5e73\u6ed1\u7cfb\u6570<\/li>\n<li>4.7 api\u4e0e\u793a\u4f8b<\/li>\n<\/ul>\n<\/li>\n<li>\u603b\u7ed3<\/li>\n<\/ul>\n<hr \/>\n<h2>\u4e00\u3001\u6570\u636e\u964d\u7ef4<\/h2>\n<p>\u5b9e\u9645\u6570\u636e\u4e2d,\u6709\u65f6\u5019\u7279\u5f81\u5f88\u591a,\u4f1a\u589e\u52a0\u8ba1\u7b97\u91cf,\u964d\u7ef4\u5c31\u662f\u53bb\u6389\u4e00\u4e9b\u7279\u5f81,\u6216\u8005\u8f6c\u5316\u591a\u4e2a\u7279\u5f81\u4e3a\u5c11\u91cf\u4e2a\u7279\u5f81<\/p>\n<ul>\n<li>\u7279\u5f81\u964d\u7ef4\u5176\u76ee\u7684&#xff1a;\u662f\u51cf\u5c11\u6570\u636e\u96c6\u7684\u7ef4\u5ea6&#xff0c;\u540c\u65f6\u5c3d\u53ef\u80fd\u4fdd\u7559\u6570\u636e\u7684\u91cd\u8981\u4fe1\u606f\u3002<\/li>\n<li>\u7279\u5f81\u964d\u7ef4\u7684\u597d\u5904:\n<ul>\n<li>\u51cf\u5c11\u8ba1\u7b97\u6210\u672c&#xff1a;\u5728\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u5904\u7406\u6570\u636e\u53ef\u80fd\u975e\u5e38\u8017\u65f6\u4e14\u8ba1\u7b97\u5bc6\u96c6\u3002\u964d\u7ef4\u53ef\u4ee5\u7b80\u5316\u6a21\u578b&#xff0c;\u964d\u4f4e\u8bad\u7ec3\u65f6\u95f4\u548c\u8d44\u6e90\u9700\u6c42\u3002<\/li>\n<li>\u53bb\u9664\u566a\u58f0&#xff1a;\u9ad8\u7ef4\u6570\u636e\u53ef\u80fd\u5305\u542b\u8bb8\u591a\u65e0\u5173\u6216\u5197\u4f59\u7279\u5f81&#xff0c;\u8fd9\u4e9b\u7279\u5f81\u53ef\u80fd\u5f15\u5165\u566a\u58f0\u5e76\u5bfc\u81f4\u8fc7\u62df\u5408\u3002\u964d\u7ef4\u53ef\u4ee5\u5e2e\u52a9\u53bb\u9664\u8fd9\u4e9b\u4e0d\u5fc5\u8981\u7684\u7279\u5f81\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u7279\u5f81\u964d\u7ef4\u7684\u65b9\u5f0f:\n<ul>\n<li>\u7279\u5f81\u9009\u62e9&#xff1a;\u4ece\u539f\u59cb\u7279\u5f81\u96c6\u4e2d\u6311\u9009\u51fa\u6700\u76f8\u5173\u7684\u7279\u5f81<\/li>\n<li>\u4e3b\u6210\u4efd\u5206\u6790(PCA)&#xff1a;\u4e3b\u6210\u5206\u5206\u6790\u5c31\u662f\u628a\u4e4b\u524d\u7684\u7279\u5f81\u901a\u8fc7\u4e00\u7cfb\u5217\u6570\u5b66\u8ba1\u7b97&#xff0c;\u5f62\u6210\u65b0\u7684\u7279\u5f81&#xff0c;\u65b0\u7684\u7279\u5f81\u6570\u91cf\u4f1a\u5c0f\u4e8e\u4e4b\u524d\u7279\u5f81\u6570\u91cf<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>1.1 \u7279\u5f81\u9009\u62e9<\/h3>\n<h4>(a) VarianceThreshold \u4f4e\u65b9\u5dee\u8fc7\u6ee4\u7279\u5f81\u9009\u62e9<\/h4>\n<p>\u5982\u679c\u4e00\u4e2a\u7279\u5f81\u7684\u65b9\u5dee\u5f88\u5c0f&#xff0c;\u8bf4\u660e\u8fd9\u4e2a\u7279\u5f81\u7684\u503c\u5728\u6837\u672c\u4e2d\u51e0\u4e4e\u76f8\u540c\u6216\u53d8\u5316\u4e0d\u5927&#xff0c;\u5305\u542b\u7684\u4fe1\u606f\u91cf\u5f88\u5c11&#xff0c;\u6a21\u578b\u5f88\u96be\u901a\u8fc7\u8be5\u7279\u5f81\u533a\u5206\u4e0d\u540c\u7684\u5bf9\u8c61,\u6bd4\u5982\u533a\u5206\u751c\u74dc\u5b50\u548c\u54b8\u74dc\u5b50\u8fd8\u662f\u849c\u9999\u74dc\u5b50,\u5982\u679c\u6709\u4e00\u4e2a\u7279\u5f81\u662f\u957f\u5ea6,\u8fd9\u4e2a\u7279\u5f81\u76f8\u5dee\u4e0d\u5927\u53ef\u4ee5\u53bb\u6389\u3002<\/p>\n<li>\u8ba1\u7b97\u65b9\u5dee&#xff1a;\u5bf9\u4e8e\u6bcf\u4e2a\u7279\u5f81&#xff0c;\u8ba1\u7b97\u5176\u5728\u8bad\u7ec3\u96c6\u4e2d\u7684\u65b9\u5dee(\u6bcf\u4e2a\u6837\u672c\u503c\u4e0e\u5747\u503c\u4e4b\u5dee\u7684\u5e73\u65b9,\u5728\u6c42\u5e73\u5747)\u3002<\/li>\n<li>\u8bbe\u5b9a\u9608\u503c&#xff1a;\u9009\u62e9\u4e00\u4e2a\u65b9\u5dee\u9608\u503c&#xff0c;\u4efb\u4f55\u4f4e\u4e8e\u8fd9\u4e2a\u9608\u503c\u7684\u7279\u5f81\u90fd\u5c06\u88ab\u89c6\u4e3a\u4f4e\u65b9\u5dee\u7279\u5f81\u3002<\/li>\n<li>\u8fc7\u6ee4\u7279\u5f81&#xff1a;\u79fb\u9664\u6240\u6709\u65b9\u5dee\u4f4e\u4e8e\u8bbe\u5b9a\u9608\u503c\u7684\u7279\u5f81<\/li>\n<p>api:<\/p>\n<p># \u521b\u5efa\u5bf9\u8c61&#xff0c;\u51c6\u5907\u628a\u65b9\u5dee\u4e3a\u7b49\u4e8e\u5c0f\u4e8e2\u7684\u53bb\u6389&#xff0c;threshold\u7684\u7f3a\u7701\u503c\u4e3a2.0<br \/>\nsklearn.feature_selection.VarianceThreshold(threshold&#061;2.0)<\/p>\n<p># \u628ax\u4e2d\u4f4e\u65b9\u5dee\u7279\u5f81\u53bb\u6389, x\u7684\u7c7b\u578b\u53ef\u4ee5\u662fDataFrame\u3001ndarray\u548clist<br \/>\nVananceThreshold.fit_transform(x)<br \/>\n# fit_transform\u51fd\u6570\u7684\u8fd4\u56de\u503c\u4e3andarray<\/p>\n<p>\u793a\u4f8b&#xff1a;<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>feature_selection <span class=\"token keyword\">import<\/span> VarianceThreshold<br \/>\n<span class=\"token keyword\">import<\/span> numpy <span class=\"token keyword\">as<\/span> np<\/p>\n<p><span class=\"token comment\"># \u751f\u6210\u4e00\u4e2a4*5\u5217\u8868&#xff0c;\u8981\u6c42\u6570\u5b57\u4e3a\u6574\u6570&#xff0c;\u8303\u56f4\u4e3a1-9<\/span><br \/>\ndata<span class=\"token operator\">&#061;<\/span>np<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>randint<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>data<span class=\"token punctuation\">)<\/span><br \/>\ntransfer<span class=\"token operator\">&#061;<\/span>VarianceThreshold<span class=\"token punctuation\">(<\/span>threshold<span class=\"token operator\">&#061;<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">)<\/span><br \/>\ndata<span class=\"token operator\">&#061;<\/span>transfer<span class=\"token punctuation\">.<\/span>fit_transform<span class=\"token punctuation\">(<\/span>data<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>data<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>transfer<span class=\"token punctuation\">.<\/span>variances_<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u4f7f\u7528\u4e0a\u4e00\u6b21\u7279\u5f81\u503c\u6765\u8fc7\u6ee4\u7279\u5f81&#xff0c;\u5373\u76f4\u63a5\u8ba4\u4e3a\u65b0\u6570\u636e\u7684\u65b9\u5dee\u5c31\u662f\u4e0a\u4e00\u6b21\u8ba1\u7b97\u51fa\u6765\u7684\u65b9\u5dee<\/span><br \/>\ndata1<span class=\"token operator\">&#061;<\/span>np<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>randint<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>data1<span class=\"token punctuation\">)<\/span><br \/>\ndata1<span class=\"token operator\">&#061;<\/span>transfer<span class=\"token punctuation\">.<\/span>transform<span class=\"token punctuation\">(<\/span>data1<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>data1<span class=\"token punctuation\">)<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113330-688a030a4910c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>(b) \u6839\u636e\u76f8\u5173\u7cfb\u6570\u7684\u7279\u5f81\u9009\u62e9<\/h4>\n<h5>&lt;1&gt;\u7406\u8bba<\/h5>\n<p>\u6b63\u76f8\u5173\u6027&#xff08;Positive Correlation&#xff09;\u662f\u6307\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u4e00\u79cd\u7edf\u8ba1\u5173\u7cfb&#xff0c;\u5176\u4e2d\u4e00\u4e2a\u53d8\u91cf\u7684\u589e\u52a0\u901a\u5e38\u4f34\u968f\u7740\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u589e\u52a0&#xff0c;\u53cd\u4e4b\u4ea6\u7136\u3002\u5728\u6b63\u76f8\u5173\u7684\u5173\u7cfb\u4e2d&#xff0c;\u4e24\u4e2a\u53d8\u91cf\u7684\u53d8\u5316\u8d8b\u52bf\u662f\u540c\u5411\u7684\u3002\u5f53\u6211\u4eec\u8bf4\u4e24\u4e2a\u53d8\u91cf\u6b63\u76f8\u5173\u65f6&#xff0c;\u610f\u5473\u7740&#xff1a;<\/p>\n<ul>\n<li>\u5982\u679c\u7b2c\u4e00\u4e2a\u53d8\u91cf\u589e\u52a0&#xff0c;\u7b2c\u4e8c\u4e2a\u53d8\u91cf\u4e5f\u6709\u5f88\u5927\u7684\u6982\u7387\u4f1a\u589e\u52a0\u3002<\/li>\n<li>\u540c\u6837&#xff0c;\u5982\u679c\u7b2c\u4e00\u4e2a\u53d8\u91cf\u51cf\u5c11&#xff0c;\u7b2c\u4e8c\u4e2a\u53d8\u91cf\u4e5f\u5f88\u53ef\u80fd\u4f1a\u51cf\u5c11\u3002<\/li>\n<\/ul>\n<p>\u6b63\u76f8\u5173\u6027\u5e76\u4e0d\u610f\u5473\u7740\u4e00\u4e2a\u53d8\u91cf\u7684\u53d8\u5316\u76f4\u63a5\u5f15\u8d77\u4e86\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u53d8\u5316&#xff0c;\u5b83\u4ec5\u4ec5\u6307\u51fa\u4e86\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u7684\u4e00\u79cd\u7edf\u8ba1\u4e0a\u7684\u5173\u8054\u6027\u3002\u8fd9\u79cd\u5173\u8054\u6027\u53ef\u4ee5\u662f\u56e0\u679c\u5173\u7cfb&#xff0c;\u4e5f\u53ef\u4ee5\u662f\u7531\u7b2c\u4e09\u4e2a\u672a\u89c2\u5bdf\u5230\u7684\u53d8\u91cf\u5f15\u8d77\u7684&#xff0c;\u6216\u8005\u662f\u7eaf\u5c5e\u5de7\u5408\u3002<\/p>\n<p>\u5728\u6570\u5b66\u4e0a&#xff0c;\u6b63\u76f8\u5173\u6027\u901a\u5e38\u7528\u6b63\u503c\u7684\u76f8\u5173\u7cfb\u6570\u6765\u8868\u793a&#xff0c;\u8fd9\u4e2a\u503c\u4ecb\u4e8e0\u548c1\u4e4b\u95f4\u3002\u5f53\u76f8\u5173\u7cfb\u6570\u7b49\u4e8e1\u65f6&#xff0c;\u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u5b8c\u7f8e\u7684\u6b63\u76f8\u5173\u5173\u7cfb&#xff0c;\u5373\u4e00\u4e2a\u53d8\u91cf\u7684\u503c\u53ef\u4ee5\u5b8c\u5168\u7531\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u503c\u9884\u6d4b\u3002<\/p>\n<p>\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570&#xff08;Pearson correlation coefficient)\u662f\u4e00\u79cd\u5ea6\u91cf\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7ebf\u6027\u76f8\u5173\u6027\u7684\u7edf\u8ba1\u91cf\u3002\u5b83\u63d0\u4f9b\u4e86\u4e24\u4e2a\u53d8\u91cf\u95f4\u5173\u7cfb\u7684\u65b9\u5411&#xff08;\u6b63\u76f8\u5173\u6216\u8d1f\u76f8\u5173&#xff09;\u548c\u5f3a\u5ea6\u7684\u4fe1\u606f\u3002\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u7684\u53d6\u503c\u8303\u56f4\u662f[\u22121,1]&#xff0c;\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          \u03c1<\/p>\n<p>          &#061;<\/p>\n<p>          1<\/p>\n<p>         \\\\rho&#061;1<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u5b8c\u5168\u6b63\u76f8\u5173&#xff0c;\u5373\u968f\u7740\u4e00\u4e2a\u53d8\u91cf\u7684\u589e\u52a0&#xff0c;\u53e6\u4e00\u4e2a\u53d8\u91cf\u4e5f\u7ebf\u6027\u589e\u52a0\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          \u03c1<\/p>\n<p>          &#061;<\/p>\n<p>          \u2212<\/p>\n<p>          1<\/p>\n<p>         \\\\rho&#061;-1<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u5b8c\u5168\u8d1f\u76f8\u5173&#xff0c;\u5373\u968f\u7740\u4e00\u4e2a\u53d8\u91cf\u7684\u589e\u52a0&#xff0c;\u53e6\u4e00\u4e2a\u53d8\u91cf\u7ebf\u6027\u51cf\u5c11\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          \u03c1<\/p>\n<p>          &#061;<\/p>\n<p>          0<\/p>\n<p>         \\\\rho&#061;0<\/p>\n<p>      <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u4e0d\u5b58\u5728\u7ebf\u6027\u5173\u7cfb\u3002<\/li>\n<\/ul>\n<p>\u76f8\u5173\u7cfb\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u03c1<\/p>\n<p>        \\\\rho<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03c1<\/span><\/span><\/span><\/span><\/span>\u7684\u7edd\u5bf9\u503c\u4e3a0-1\u4e4b\u95f4&#xff0c;\u7edd\u5bf9\u503c\u8d8a\u5927&#xff0c;\u8868\u793a\u8d8a\u76f8\u5173&#xff0c;\u5f53\u4e24\u7279\u5f81\u5b8c\u5168\u76f8\u5173\u65f6&#xff0c;\u4e24\u7279\u5f81\u7684\u503c\u8868\u793a\u7684\u5411\u91cf\u662f\u540c\u4e00\u6761\u76f4\u7ebf\u4e0a&#xff1b;\u5f53\u4e24\u7279\u5f81\u7684\u76f8\u5173\u7cfb\u6570\u7edd\u5bf9\u503c\u5f88\u5c0f\u65f6&#xff0c;\u4e24\u7279\u5f81\u503c\u8868\u793a\u7684\u5411\u91cf\u63a5\u8fd1\u5728\u540c\u4e00\u6761\u76f4\u7ebf\u4e0a\u3002\u5f53\u76f8\u5173\u7cfb\u503c\u4e3a\u8d1f\u6570\u65f6&#xff0c;\u8868\u793a\u8d1f\u76f8\u5173\u3002<\/p>\n<h5>&lt;2&gt;\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570:<\/h5>\n<p>\u5bf9\u4e8e\u4e24\u7ec4\u6570\u636e &#x1d44b;&#061;{&#x1d465;1,&#x1d465;2,\u2026,&#x1d465;&#x1d45b;} \u548c &#x1d44c;&#061;{&#x1d466;1,&#x1d466;2,\u2026,&#x1d466;&#x1d45b;}&#xff0c;\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u53ef\u4ee5\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u03c1<\/p>\n<p>         &#061;<\/p>\n<p>           Cos<\/p>\n<p>           \u2061<\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           ,<\/p>\n<p>           y<\/p>\n<p>           )<\/p>\n<p>             D<\/p>\n<p>             x<\/p>\n<p>           \u22c5<\/p>\n<p>             D<\/p>\n<p>             y<\/p>\n<p>         &#061;<\/p>\n<p>           E<\/p>\n<p>           [<\/p>\n<p>           (<\/p>\n<p>            x<\/p>\n<p>            \u2212<\/p>\n<p>           E<\/p>\n<p>           x<\/p>\n<p>           )<\/p>\n<p>           (<\/p>\n<p>           y<\/p>\n<p>           \u2212<\/p>\n<p>           E<\/p>\n<p>           y<\/p>\n<p>           )<\/p>\n<p>           ]<\/p>\n<p>             D<\/p>\n<p>             x<\/p>\n<p>           \u22c5<\/p>\n<p>             D<\/p>\n<p>             y<\/p>\n<p>        \\\\rho&#061;\\\\frac{\\\\operatorname{Cos}(x, y)}{\\\\sqrt{D x} \\\\cdot \\\\sqrt{D y}}&#061;\\\\frac{E[(x_-E x)(y-E y)]}{\\\\sqrt{D x} \\\\cdot \\\\sqrt{D y}}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4542em;vertical-align: -1.0272em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.1833em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9267em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8867em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1133em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8294em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">Dy<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7894em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2106em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mord mathrm\">Cos<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0272em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4542em;vertical-align: -1.0272em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.1833em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9267em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8867em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1133em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8294em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">Dy<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7894em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2106em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mopen\">[(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2583em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u2212<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2083em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mclose\">)]<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0272em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         &#061;<\/p>\n<p>            \u2211<\/p>\n<p>             i<\/p>\n<p>             &#061;<\/p>\n<p>             1<\/p>\n<p>            n<\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           \u2212<\/p>\n<p>            x<\/p>\n<p>            ~<\/p>\n<p>           )<\/p>\n<p>           (<\/p>\n<p>           y<\/p>\n<p>           \u2212<\/p>\n<p>            y<\/p>\n<p>            \u02c9<\/p>\n<p>           )<\/p>\n<p>           \/<\/p>\n<p>           (<\/p>\n<p>           n<\/p>\n<p>           \u2212<\/p>\n<p>           1<\/p>\n<p>           )<\/p>\n<p>              \u2211<\/p>\n<p>               i<\/p>\n<p>               &#061;<\/p>\n<p>               1<\/p>\n<p>              n<\/p>\n<p>             (<\/p>\n<p>             x<\/p>\n<p>             \u2212<\/p>\n<p>              x<\/p>\n<p>              \u02c9<\/p>\n<p>              )<\/p>\n<p>              2<\/p>\n<p>             \/<\/p>\n<p>             (<\/p>\n<p>             n<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>             )<\/p>\n<p>           \u22c5<\/p>\n<p>              \u2211<\/p>\n<p>               i<\/p>\n<p>               &#061;<\/p>\n<p>               1<\/p>\n<p>              n<\/p>\n<p>             (<\/p>\n<p>             y<\/p>\n<p>             \u2212<\/p>\n<p>              y<\/p>\n<p>              \u02c9<\/p>\n<p>              )<\/p>\n<p>              2<\/p>\n<p>             \/<\/p>\n<p>             (<\/p>\n<p>             n<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>             )<\/p>\n<p>         &#061;<\/p>\n<p>           cov<\/p>\n<p>           (<\/p>\n<p>           X<\/p>\n<p>           ,<\/p>\n<p>           Y<\/p>\n<p>           )<\/p>\n<p>            \u03c3<\/p>\n<p>            X<\/p>\n<p>            \u03c3<\/p>\n<p>            Y<\/p>\n<p>        &#061;\\\\frac{\\\\sum_{i&#061;1}^{n}(x-\\\\tilde{x})(y-\\\\bar{y}) \/(n-1)}{\\\\sqrt{\\\\sum_{i&#061;1}^{n}(x-\\\\bar{x})^{2} \/(n-1)} \\\\cdot \\\\sqrt{\\\\sum_{i&#061;1}^{n}(y-\\\\bar{y})^{2} \/(n-1)}} &#061; \\\\frac{\\\\text{cov}(X,Y)}{\\\\sigma_X \\\\sigma_Y}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.3669em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.624em;vertical-align: -1.13em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.494em\"><span class=\"\" style=\"top: -2.1727em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9373em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8043em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8973em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3027em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9373em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8043em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8973em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/p>\n<p>                   <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3027em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.6897em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8043em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6679em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3.35em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.13em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.263em;vertical-align: -0.836em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0785em\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.2222em\">Y<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">cov<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">Y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.836em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         \u02c9<\/p>\n<p>       \\\\bar{x}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5678em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.2222em\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         y<\/p>\n<p>         \u02c9<\/p>\n<p>       \\\\bar{y}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7622em;vertical-align: -0.1944em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5678em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5206\u522b\u662f&#x1d44b;\u548c&#x1d44c;\u7684\u5e73\u5747\u503c\u3002<\/p>\n<p>\u8be5\u516c\u5f0f\u53ef\u4ee5\u770b\u4f5c\u5bf9x,y\u7684\u534f\u65b9\u5dee\u4f5c\u6807\u51c6\u5316&#xff0c;\u5373\u5c06\u5176\u534f\u65b9\u5dee\u9664\u4ee5\u5404\u81ea\u7684\u6807\u51c6\u5dee\u3002<\/p>\n<p>|\u03c1|&lt;0.4\u4e3a\u4f4e\u5ea6\u76f8\u5173; 0.4&lt;&#061;|\u03c1|&lt;0.7\u4e3a\u663e\u8457\u76f8\u5173&#xff1b; 0.7&lt;&#061;|\u03c1|&lt;1\u4e3a\u9ad8\u5ea6\u76f8\u5173\u3002<\/p>\n<h5>&lt;3&gt;api:<\/h5>\n<p>scipy.stats.personr(x, y) # \u8ba1\u7b97\u4e24\u7279\u5f81\u4e4b\u95f4\u7684\u76f8\u5173\u6027<\/p>\n<p>\u8fd4\u56de\u5bf9\u8c61\u6709\u4e24\u4e2a\u5c5e\u6027:<\/p>\n<ul>\n<li>statistic\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570[-1,1]\u3002<\/li>\n<li>pvalue\u96f6\u5047\u8bbe(\u4e86\u89e3),\u7edf\u8ba1\u4e0a\u8bc4\u4f30\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u6027,\u8d8a\u5c0f\u8d8a\u76f8\u5173\u3002<\/li>\n<\/ul>\n<h5>&lt;4&gt;\u793a\u4f8b&#xff1a;<\/h5>\n<p><span class=\"token keyword\">from<\/span> scipy<span class=\"token punctuation\">.<\/span>stats <span class=\"token keyword\">import<\/span> pearsonr<br \/>\nx<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">7<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">9<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">]<\/span><br \/>\ny<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">7<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">9<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">11<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">12<\/span><span class=\"token punctuation\">]<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>pearsonr<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>pearsonr<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">:<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113330-688a030ac40f8.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u5f00\u53d1\u4e2d\u4e00\u822c\u4e0d\u4f7f\u7528\u6c42\u76f8\u5173\u7cfb\u6570\u7684\u65b9\u6cd5&#xff0c;\u4e00\u822c\u4f7f\u7528\u4e3b\u6210\u5206\u5206\u6790&#xff0c;\u56e0\u4e3a\u4e3b\u6210\u5206\u5206\u6837\u8fc7\u7a0b\u4e2d\u5c31\u5305\u62ec\u4e86\u6c42\u76f8\u5173\u7cfb\u6570\u4e86\u3002<\/p>\n<h3>1.2 \u4e3b\u6210\u5206\u5206\u6790&#xff08;PCA&#xff09;<\/h3>\n<p>PCA\u7684\u6838\u5fc3\u76ee\u6807\u662f\u4ece\u539f\u59cb\u7279\u5f81\u7a7a\u95f4\u4e2d\u627e\u5230\u4e00\u4e2a\u65b0\u7684\u5750\u6807\u7cfb\u7edf&#xff0c;\u4f7f\u5f97\u6570\u636e\u5728\u65b0\u5750\u6807\u8f74\u4e0a\u7684\u6295\u5f71\u80fd\u591f\u6700\u5927\u7a0b\u5ea6\u5730\u4fdd\u7559\u6570\u636e\u7684\u65b9\u5dee&#xff0c;\u540c\u65f6\u51cf\u5c11\u6570\u636e\u7684\u7ef4\u5ea6\u3002<\/p>\n<h4>(a) \u539f\u7406<\/h4>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113331-688a030b5bccf.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>       x_0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6295\u5f71\u5230L\u7684\u5927\u5c0f\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>        \u2217<\/p>\n<p>        c<\/p>\n<p>        o<\/p>\n<p>        s<\/p>\n<p>        \u03b1<\/p>\n<p>       x_0*cos \\\\alpha<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6153em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2217<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">cos<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><\/span><\/span><\/span><\/span> <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         y<\/p>\n<p>         0<\/p>\n<p>       y_0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6295\u5f71\u5230L\u7684\u5927\u5c0f\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         y<\/p>\n<p>         0<\/p>\n<p>        \u2217<\/p>\n<p>        s<\/p>\n<p>        i<\/p>\n<p>        n<\/p>\n<p>        \u03b1<\/p>\n<p>       y_0*sin\\\\alpha<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6597em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2217<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mord mathnormal\">in<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4f7f\u7528<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         0<\/p>\n<p>        ,<\/p>\n<p>         y<\/p>\n<p>         0<\/p>\n<p>        )<\/p>\n<p>       (x_0,y_0)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u4e00\u4e2a\u70b9&#xff0c; \u8868\u660e\u8be5\u70b9\u6709\u4e24\u4e2a\u7279\u5f81&#xff0c; \u800c\u6620\u5c04\u5230L\u4e0a\u6709\u4e00\u4e2a\u7279\u5f81\u5c31\u53ef\u4ee5\u8868\u793a\u8fd9\u4e2a\u70b9\u4e86\u3002\u8fd9\u5c31\u8fbe\u5230\u4e86\u964d\u7ef4\u7684\u529f\u80fd \u3002<\/p>\n<p>\u6295\u5f71\u5230L\u4e0a\u7684\u503c\u5c31\u662f\u964d\u7ef4\u540e\u4fdd\u7559\u7684\u4fe1\u606f&#xff0c;\u6295\u5f71\u5230\u4e0eL\u5782\u76f4\u7684\u8f74\u4e0a\u7684\u503c\u5c31\u662f\u4e22\u5931\u7684\u4fe1\u606f\u3002\u4fdd\u7559\u4fe1\u606f\/\u539f\u59cb\u4fe1\u606f&#061;\u4fe1\u606f\u4fdd\u7559\u7684\u6bd4\u4f8b<\/p>\n<h4>(b) \u6b65\u9aa4<\/h4>\n<li>\n<p>\u5f97\u5230\u77e9\u9635<\/p>\n<\/li>\n<li>\n<p>\u7528\u77e9\u9635P\u5bf9\u539f\u59cb\u6570\u636e\u8fdb\u884c\u7ebf\u6027\u53d8\u6362&#xff0c;\u5f97\u5230\u65b0\u7684\u6570\u636e\u77e9\u9635Z,\u6bcf\u4e00\u5217\u5c31\u662f\u4e00\u4e2a\u4e3b\u6210\u5206, \u5982\u4e0b\u56fe\u5c31\u662f\u628a10\u7ef4\u964d\u6210\u4e862\u7ef4,\u5f97\u5230\u4e86\u4e24\u4e2a\u4e3b\u6210\u5206 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113331-688a030be2c01.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<\/li>\n<li>\n<p>\u6839\u636e\u4e3b\u6210\u5206\u7684\u65b9\u5dee\u7b49&#xff0c;\u786e\u5b9a\u6700\u7ec8\u4fdd\u7559\u7684\u4e3b\u6210\u5206\u4e2a\u6570&#xff0c; \u65b9\u5dee\u5927\u7684\u8981\u7559\u4e0b\u3002\u4e00\u4e2a\u7279\u5f81\u7684\u591a\u4e2a\u6837\u672c\u7684\u503c\u5982\u679c\u90fd\u76f8\u540c&#xff0c;\u5219\u65b9\u5dee\u4e3a0&#xff0c; \u5219\u8bf4\u660e\u8be5\u7279\u5f81\u503c\u4e0d\u80fd\u533a\u522b\u6837\u672c&#xff0c;\u6240\u4ee5\u8be5\u7279\u5f81\u6ca1\u6709\u7528\u3002<\/p>\n<\/li>\n<p>\u6bd4\u5982\u4e0b\u56fe\u7684\u4e8c\u7ef4\u6570\u636e\u8981\u964d\u4e3a\u4e00\u7ef4\u6570\u636e&#xff0c;\u56fe\u5f62\u6cd5\u662f\u628a\u6240\u5728\u6570\u636e\u5728\u4e8c\u7ef4\u5750\u6807\u4e2d\u4ee5\u70b9\u7684\u5f62\u5f0f\u6807\u51fa&#xff0c;\u7136\u540e\u7ed9\u51fa\u4e00\u6761\u76f4\u7ebf&#xff0c;\u8ba9\u6240\u6709\u70b9\u5782\u76f4\u6620\u5c04\u5230\u76f4\u7ebf\u4e0a&#xff0c;\u8be5\u76f4\u7ebf\u6709\u5f88\u591a&#xff0c;\u53ea\u6709\u70b9\u5230\u7ebf\u7684\u8ddd\u79bb\u4e4b\u548c\u6700\u5c0f\u7684\u7ebf\u624d\u80fd\u8ba9\u4e4b\u524d\u4fe1\u606f\u635f\u5931\u6700\u5c0f\u3002<\/p>\n<p>\u8fd9\u6837\u4e4b\u524d\u6240\u6709\u7684\u4e8c\u7ef4\u8868\u793a\u7684\u70b9\u5c31\u5168\u90e8\u53d8\u6210\u4e00\u6761\u76f4\u7ebf\u4e0a\u7684\u70b9&#xff0c;\u4ece\u4e8c\u7ef4\u964d\u6210\u4e86\u4e00\u7ef4\u3002 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113332-688a030c001fc.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>api<\/h4>\n<p>\u793a\u4f8b&#xff1a;<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>decomposition <span class=\"token keyword\">import<\/span> PCA<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> train_test_split<br \/>\n<span class=\"token comment\"># \u751f\u6210\u4e00\u4e2a10*10\u5217\u8868&#xff0c;\u8981\u6c42\u6570\u5b57\u4e3a\u6574\u6570&#xff0c;\u8303\u56f4\u4e3a1-9<\/span><br \/>\ndata<span class=\"token operator\">&#061;<\/span>np<span class=\"token punctuation\">.<\/span>random<span class=\"token punctuation\">.<\/span>randint<span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>data<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u5212\u5206\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6<\/span><br \/>\nx_train<span class=\"token punctuation\">,<\/span> x_test <span class=\"token operator\">&#061;<\/span> train_test_split<span class=\"token punctuation\">(<\/span>data<span class=\"token punctuation\">,<\/span> test_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span>random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">22<\/span><span class=\"token punctuation\">,<\/span>shuffle<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u503c\u4e3a\u6574\u6570\u8868\u793a\u964d\u5230\u591a\u5c11\u7ef4&#xff0c;\u4e3a\u5c0f\u6570\u8868\u793a\u4fdd\u7559\u591a\u5c11\u6bd4\u4f8b\u7684\u4fe1\u606f<\/span><br \/>\ntransfer<span class=\"token operator\">&#061;<\/span>PCA<span class=\"token punctuation\">(<\/span>n_components<span class=\"token operator\">&#061;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><br \/>\ntrain<span class=\"token operator\">&#061;<\/span>transfer<span class=\"token punctuation\">.<\/span>fit_transform<span class=\"token punctuation\">(<\/span>x_train<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>train<span class=\"token punctuation\">)<\/span><br \/>\ntest<span class=\"token operator\">&#061;<\/span>transfer<span class=\"token punctuation\">.<\/span>transform<span class=\"token punctuation\">(<\/span>x_test<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>test<span class=\"token punctuation\">)<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113332-688a030c1f2e8.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h2>\u4e8c\u3001KNN\u7b97\u6cd5<\/h2>\n<h3>2.1 \u9884\u4f30\u5668<\/h3>\n<p>\u83b7\u53d6\u6570\u636e\u3001\u6570\u636e\u5904\u7406\u3001\u7279\u5f81\u5de5\u7a0b\u540e&#xff0c;\u5c31\u53ef\u4ee5\u4ea4\u7ed9\u9884\u4f30\u5668\u8fdb\u884c\u673a\u5668\u5b66\u4e60&#xff0c;\u6d41\u7a0b\u548c\u5e38\u7528API\u5982\u4e0b\u3002<\/p>\n<p>1.\u5b9e\u4f8b\u5316\u9884\u4f30\u5668(\u4f30\u8ba1\u5668)\u5bf9\u8c61(estimator)&#xff0c; \u9884\u4f30\u5668\u5bf9\u8c61\u5f88\u591a,\u90fd\u662festimator\u7684\u5b50\u7c7b<br \/>\n&#xff08;1&#xff09;\u7528\u4e8e\u5206\u7c7b\u7684\u9884\u4f30\u5668<br \/>\nsklearn.neighbors.KNeighborsClassifier k-\u8fd1\u90bb<br \/>\nsklearn.naive_bayes.MultinomialNB \u8d1d\u53f6\u65af<br \/>\nsklearn.linear_model.LogisticRegressioon \u903b\u8f91\u56de\u5f52<br \/>\nsklearn.tree.DecisionTreeClassifier \u51b3\u7b56\u6811<br \/>\nsklearn.ensemble.RandomForestClassifier \u968f\u673a\u68ee\u6797<br \/>\n(2)\u7528\u4e8e\u56de\u5f52\u7684\u9884\u4f30\u5668<br \/>\nsklearn.linear_model.LinearRegression \u7ebf\u6027\u56de\u5f52<br \/>\nsklearn.linear_model.Ridge \u5cad\u56de\u5f52<br \/>\n(3)\u7528\u4e8e\u65e0\u76d1\u7763\u5b66\u4e60\u7684\u9884\u4f30\u5668<br \/>\nsklearn.cluster.KMeans \u805a\u7c7b<br \/>\n2.\u8fdb\u884c\u8bad\u7ec3&#xff0c;\u8bad\u7ec3\u7ed3\u675f\u540e\u751f\u6210\u6a21\u578b<br \/>\nestimator.fit(x_train, y_train)<br \/>\n3.\u6a21\u578b\u8bc4\u4f30<br \/>\n(1)\u65b9\u5f0f1&#xff0c;\u76f4\u63a5\u5bf9\u6bd4<br \/>\ny_predict &#061; estimator.predict(x_test)<br \/>\ny_test &#061;&#061; y_predict<br \/>\n  (2)\u65b9\u5f0f2, \u8ba1\u7b97\u51c6\u786e\u7387<br \/>\n  accuracy &#061; estimator.score(x_test, y_test)<br \/>\n4.\u4f7f\u7528\u6a21\u578b(\u9884\u6d4b)<br \/>\ny_predict &#061; estimator.predict(x_true)<\/p>\n<h3>2.2 KNN\u5206\u7c7b<\/h3>\n<h4>2.2.1 \u6837\u672c\u8ddd\u79bb\u5206\u6790<\/h4>\n<p>\u901a\u5e38\u6211\u4eec\u53ef\u4ee5\u5c06\u4e00\u4e2a\u6709\u7740n\u4e2a\u7279\u5f81\u503c\u7684\u6837\u672c\u770b\u4f5c\u4e00\u4e2an\u7ef4\u5411\u91cf\u3002\u800c\u6837\u672c\u95f4\u7684\u76f8\u4f3c\u5ea6\u5c31\u53ef\u4ee5\u7528\u6837\u672c\u95f4\u7684\u8ddd\u79bb\u6765\u5ea6\u91cf\u3002<\/p>\n<p>\u800c\u7528\u6765\u5ea6\u91cf\u6837\u672c\u95f4\u76f8\u4f3c\u5ea6\u7684\u5e38\u7528\u8ddd\u79bb\u6709\u4ee5\u4e0b\u51e0\u79cd&#xff1a;<\/p>\n<ul>\n<li>\u95f5\u53ef\u592b\u65af\u57fa\u8ddd\u79bb \u8ba1\u7b97\u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           (<\/p>\n<p>            \u2211<\/p>\n<p>             i<\/p>\n<p>             &#061;<\/p>\n<p>             1<\/p>\n<p>            n<\/p>\n<p>           \u2223<\/p>\n<p>            x<\/p>\n<p>            i<\/p>\n<p>           \u2212<\/p>\n<p>            y<\/p>\n<p>            i<\/p>\n<p>            \u2223<\/p>\n<p>            p<\/p>\n<p>           )<\/p>\n<p>           1<\/p>\n<p>           \/<\/p>\n<p>           p<\/p>\n<p>        d(\\\\mathbf{x}, \\\\mathbf{y}) &#061; \\\\left( \\\\sum_{i&#061;1}^n |x_i &#8211; y_i|^p \\\\right)^{1\/p}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.3819em;vertical-align: -0.2997em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">(<\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8043em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\">\u2223<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6644em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">)<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0822em\"><span class=\"\" style=\"top: -3.2572em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1\/<\/span><span class=\"mord mathnormal mtight\">p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u6b27\u6c0f\u8ddd\u79bb \u8ba1\u7b97\u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>            \u2211<\/p>\n<p>             i<\/p>\n<p>             &#061;<\/p>\n<p>             1<\/p>\n<p>            n<\/p>\n<p>           (<\/p>\n<p>            x<\/p>\n<p>            i<\/p>\n<p>           \u2212<\/p>\n<p>            y<\/p>\n<p>            i<\/p>\n<p>            )<\/p>\n<p>            2<\/p>\n<p>        d(\\\\mathbf{x}, \\\\mathbf{y}) &#061; \\\\sqrt{\\\\sum_{i&#061;1}^n (x_i &#8211; y_i)^2}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24em;vertical-align: -0.3027em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9373em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8043em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.8973em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/p>\n<p>            <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3027em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u95f5\u53ef\u592b\u65af\u57fa\u8ddd\u79bb\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         p<\/p>\n<p>         &#061;<\/p>\n<p>         2<\/p>\n<p>        p&#061;2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>\u7684\u7279\u6b8a\u60c5\u51b5\u3002<\/li>\n<li>\u66fc\u54c8\u987f\u8ddd\u79bb \u8ba1\u7b97\u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          \u2211<\/p>\n<p>           i<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          n<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>          i<\/p>\n<p>         \u2212<\/p>\n<p>          y<\/p>\n<p>          i<\/p>\n<p>         \u2223<\/p>\n<p>        d(\\\\mathbf{x}, \\\\mathbf{y}) &#061; \\\\sum_{i&#061;1}^n |x_i &#8211; y_i|<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em;vertical-align: -0.2997em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8043em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u95f5\u53ef\u592b\u65af\u57fa\u8ddd\u79bb\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         p<\/p>\n<p>         &#061;<\/p>\n<p>         1<\/p>\n<p>        p&#061;1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u7684\u7279\u6b8a\u60c5\u51b5\u3002<\/li>\n<li>\u5207\u6bd4\u96ea\u592b\u8ddd\u79bb \u8ba1\u7b97\u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           max<\/p>\n<p>           \u2061<\/p>\n<p>          i<\/p>\n<p>         \u2223<\/p>\n<p>          x<\/p>\n<p>          i<\/p>\n<p>         \u2212<\/p>\n<p>          y<\/p>\n<p>          i<\/p>\n<p>         \u2223<\/p>\n<p>        d(\\\\mathbf{x}, \\\\mathbf{y}) &#061; \\\\max_{i} |x_i &#8211; y_i|<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mop\"><span class=\"mop\">max<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u95f5\u53ef\u592b\u65af\u57fa\u8ddd\u79bb\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         p<\/p>\n<p>        p<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span>\u8d8b\u4e8e\u65e0\u7a77\u7684\u7279\u6b8a\u60c5\u51b5\u3002<\/li>\n<li>\u4f59\u5f26\u76f8\u4f3c\u5ea6 \u8ba1\u7b97\u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         sim<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           x<\/p>\n<p>           \u22c5<\/p>\n<p>           y<\/p>\n<p>           \u2225<\/p>\n<p>           x<\/p>\n<p>           \u2225<\/p>\n<p>           \u2225<\/p>\n<p>           y<\/p>\n<p>           \u2225<\/p>\n<p>        \\\\text{sim}(\\\\mathbf{x}, \\\\mathbf{y}) &#061; \\\\frac{\\\\mathbf{x} \\\\cdot \\\\mathbf{y}}{\\\\|\\\\mathbf{x}\\\\| \\\\|\\\\mathbf{y}\\\\|}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord\">sim<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2772em;vertical-align: -0.52em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7572em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2225<\/span><span class=\"mord mathbf mtight\">x<\/span><span class=\"mord mtight\">\u2225\u2225<\/span><span class=\"mord mathbf mtight\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mord mtight\">\u2225<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.4461em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathbf mtight\">x<\/span><span class=\"mbin mtight\">\u22c5<\/span><span class=\"mord mathbf mtight\" style=\"margin-right: 0.016em\">y<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.52em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;&#xff08;\u8ddd\u79bb\u5e38\u5b9a\u4e49\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         d<\/p>\n<p>         &#061;<\/p>\n<p>         1<\/p>\n<p>         \u2212<\/p>\n<p>         s<\/p>\n<p>         i<\/p>\n<p>         m<\/p>\n<p>        d&#061;1\u2212sim<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mord mathnormal\">im<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002<\/li>\n<li>\u6c49\u660e\u8ddd\u79bb \u8ba1\u7b97\u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>          \u2211<\/p>\n<p>           i<\/p>\n<p>           &#061;<\/p>\n<p>           1<\/p>\n<p>          n<\/p>\n<p>         1<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          i<\/p>\n<p>         \u2260<\/p>\n<p>          y<\/p>\n<p>          i<\/p>\n<p>         )<\/p>\n<p>        d(\\\\mathbf{x}, \\\\mathbf{y}) &#061; \\\\sum_{i&#061;1}^n \\\\mathbb{1}(x_i \\\\neq y_i)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em;vertical-align: -0.2997em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8043em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">1<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">&#061;<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8ba1\u7b97\u7b49\u957f\u5b57\u7b26\u4e32\u7684\u5dee\u5f02\u4f4d\u7f6e\u6570\u3002<\/li>\n<li>\u9a6c\u6c0f\u8ddd\u79bb \u8ba1\u7b97\u516c\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         d<\/p>\n<p>         (<\/p>\n<p>         x<\/p>\n<p>         ,<\/p>\n<p>         y<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           \u2212<\/p>\n<p>           y<\/p>\n<p>            )<\/p>\n<p>            T<\/p>\n<p>            \u03a3<\/p>\n<p>             \u2212<\/p>\n<p>             1<\/p>\n<p>           (<\/p>\n<p>           x<\/p>\n<p>           \u2212<\/p>\n<p>           y<\/p>\n<p>           )<\/p>\n<p>        d(\\\\mathbf{x}, \\\\mathbf{y}) &#061; \\\\sqrt{(\\\\mathbf{x} &#8211; \\\\mathbf{y})^T \\\\Sigma^{-1} (\\\\mathbf{x} &#8211; \\\\mathbf{y})}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24em;vertical-align: -0.2963em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9437em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7673em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\">\u03a3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -2.9037em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/p>\n<p>            <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2963em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u901a\u8fc7\u534f\u65b9\u5dee\u77e9\u9635\u8003\u8651\u7279\u5f81\u95f4\u7684\u76f8\u5173\u6027\u3002<\/li>\n<\/ul>\n<h4>2.2.2 \u539f\u7406<\/h4>\n<p>K-\u8fd1\u90bb\u7b97\u6cd5&#xff08;K-Nearest Neighbors&#xff0c;\u7b80\u79f0KNN&#xff09;,\u6839\u636eK\u4e2a\u90bb\u5c45\u6837\u672c\u7684\u7c7b\u522b\u6765\u5224\u65ad\u5f53\u524d\u6837\u672c\u7684\u7c7b\u522b&#xff1b;\u5982\u679c\u4e00\u4e2a\u6837\u672c\u5728\u7279\u5f81\u7a7a\u95f4\u4e2d\u7684k\u4e2a\u6700\u76f8\u4f3c(\u6700\u90bb\u8fd1)\u6837\u672c\u4e2d\u7684\u5927\u591a\u6570\u5c5e\u4e8e\u67d0\u4e2a\u7c7b\u522b&#xff0c;\u5219\u8be5\u7c7b\u672c\u4e5f\u5c5e\u4e8e\u8fd9\u4e2a\u7c7b\u522b\u3002 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113332-688a030ca9b1f.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113333-688a030d80144.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>KNN\u7b97\u6cd5\u5177\u6709\u4ee5\u4e0b\u7f3a\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u5bf9\u4e8e\u5927\u89c4\u6a21\u6570\u636e\u96c6&#xff0c;\u8ba1\u7b97\u91cf\u5927&#xff0c;\u56e0\u4e3a\u9700\u8981\u8ba1\u7b97\u6d4b\u8bd5\u6837\u672c\u4e0e\u6240\u6709\u8bad\u7ec3\u6837\u672c\u7684\u8ddd\u79bb\u3002<\/li>\n<li>\u5bf9\u4e8e\u9ad8\u7ef4\u6570\u636e&#xff0c;\u8ddd\u79bb\u5ea6\u91cf\u53ef\u80fd\u53d8\u5f97\u4e0d\u90a3\u4e48\u6709\u610f\u4e49&#xff0c;\u8fd9\u5c31\u662f\u6240\u8c13\u7684\u201c\u7ef4\u5ea6\u707e\u96be\u201d\u3002<\/li>\n<li>\u9700\u8981\u9009\u62e9\u5408\u9002\u7684k\u503c\u548c\u8ddd\u79bb\u5ea6\u91cf&#xff0c;\u8fd9\u53ef\u80fd\u9700\u8981\u4e00\u4e9b\u5b9e\u9a8c\u548c\u8c03\u6574\u3002<\/li>\n<\/ul>\n<h4>2.2.3 api\u4e0e\u793a\u4f8b<\/h4>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>neighbors <span class=\"token keyword\">import<\/span> KNeighborsClassifier<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> load_iris<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> train_test_split<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>preprocessing <span class=\"token keyword\">import<\/span> StandardScaler<\/p>\n<p>iris <span class=\"token operator\">&#061;<\/span> load_iris<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx <span class=\"token operator\">&#061;<\/span> iris<span class=\"token punctuation\">.<\/span>data<br \/>\ny <span class=\"token operator\">&#061;<\/span> iris<span class=\"token punctuation\">.<\/span>target<br \/>\nx_train<span class=\"token punctuation\">,<\/span>x_test<span class=\"token punctuation\">,<\/span>y_train<span class=\"token punctuation\">,<\/span>y_test <span class=\"token operator\">&#061;<\/span> train_test_split<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">,<\/span>test_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span>random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">22<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u7279\u5f81\u5de5\u7a0b-\u6807\u51c6\u5316<\/span><br \/>\ntransfer <span class=\"token operator\">&#061;<\/span> StandardScaler<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx_train <span class=\"token operator\">&#061;<\/span> transfer<span class=\"token punctuation\">.<\/span>fit_transform<span class=\"token punctuation\">(<\/span>x_train<span class=\"token punctuation\">)<\/span><br \/>\nx_test <span class=\"token operator\">&#061;<\/span> transfer<span class=\"token punctuation\">.<\/span>transform<span class=\"token punctuation\">(<\/span>x_test<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u6a21\u578b\u8bad\u7ec3<\/span><br \/>\nmodel<span class=\"token operator\">&#061;<\/span>KNeighborsClassifier<span class=\"token punctuation\">(<\/span>n_neighbors<span class=\"token operator\">&#061;<\/span><span class=\"token number\">7<\/span><span class=\"token punctuation\">)<\/span><br \/>\nmodel<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>x_train<span class=\"token punctuation\">,<\/span>y_train<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u6a21\u578b\u4fdd\u5b58<\/span><br \/>\njoblib<span class=\"token punctuation\">.<\/span>dump<span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">,<\/span><span class=\"token string\">&#039;.\/ML\/model\/knn.pkl&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\njoblib<span class=\"token punctuation\">.<\/span>dump<span class=\"token punctuation\">(<\/span>transfer<span class=\"token punctuation\">,<\/span><span class=\"token string\">&#039;.\/ML\/model\/std.pkl&#039;<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u9884\u6d4b<\/span><br \/>\ny_p<span class=\"token operator\">&#061;<\/span>model<span class=\"token punctuation\">.<\/span>predict<span class=\"token punctuation\">(<\/span>x_test<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u9884\u6d4b\u7ed3\u679c\u4e3a&#xff1a;&#034;<\/span><span class=\"token punctuation\">,<\/span>y_p<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u5b9e\u9645\u7ed3\u679c\u4e3a&#xff1a;&#034;<\/span><span class=\"token punctuation\">,<\/span>y_test<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u6a21\u578b\u8bc4\u4f30<\/span><br \/>\n<span class=\"token keyword\">def<\/span> <span class=\"token function\">accuracy_score<\/span><span class=\"token punctuation\">(<\/span>y_true<span class=\"token punctuation\">,<\/span>y_predict<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token triple-quoted-string string\">&#034;&#034;&#034;\u51c6\u786e\u7387&#034;&#034;&#034;<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> np<span class=\"token punctuation\">.<\/span><span class=\"token builtin\">sum<\/span><span class=\"token punctuation\">(<\/span>y_true<span class=\"token operator\">&#061;&#061;<\/span>y_predict<span class=\"token punctuation\">)<\/span><span class=\"token operator\">\/<\/span><span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>y_true<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u51c6\u786e\u7387&#xff1a;&#034;<\/span><span class=\"token punctuation\">,<\/span>accuracy_score<span class=\"token punctuation\">(<\/span>y_test<span class=\"token punctuation\">,<\/span>y_p<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u51c6\u786e\u7387&#xff1a;&#034;<\/span><span class=\"token punctuation\">,<\/span>model<span class=\"token punctuation\">.<\/span>score<span class=\"token punctuation\">(<\/span>x_test<span class=\"token punctuation\">,<\/span>y_test<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token comment\"># \u65b0\u6570\u636e\u9884\u6d4b<\/span><br \/>\nnew_x<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1.1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">1.2<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0.3<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0.4<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n       <span class=\"token punctuation\">[<\/span><span class=\"token number\">0.5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0.6<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0.7<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0.8<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n       <span class=\"token punctuation\">[<\/span><span class=\"token number\">0.9<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">1.0<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0.1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><br \/>\nx_new<span class=\"token operator\">&#061;<\/span>transfer<span class=\"token punctuation\">.<\/span>transform<span class=\"token punctuation\">(<\/span>new_x<span class=\"token punctuation\">)<\/span><br \/>\ny_new<span class=\"token operator\">&#061;<\/span>model<span class=\"token punctuation\">.<\/span>predict<span class=\"token punctuation\">(<\/span>x_new<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u9884\u6d4b\u7ed3\u679c\u4e3a&#xff1a;&#034;<\/span><span class=\"token punctuation\">,<\/span>iris<span class=\"token punctuation\">.<\/span>target_names<span class=\"token punctuation\">[<\/span>y_new<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113336-688a0310d3c71.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h2>\u4e09\u3001\u6a21\u578b\u9009\u62e9\u4e0e\u8c03\u4f18<\/h2>\n<h3>3.1 \u4ea4\u53c9\u9a8c\u8bc1<\/h3>\n<h4>(1) \u4fdd\u7559\u4ea4\u53c9\u9a8c\u8bc1HoldOut<\/h4>\n<p>\u5728\u8fd9\u79cd\u4ea4\u53c9\u9a8c\u8bc1\u6280\u672f\u4e2d&#xff0c;\u6574\u4e2a\u6570\u636e\u96c6\u88ab\u968f\u673a\u5730\u5212\u5206\u4e3a\u8bad\u7ec3\u96c6\u548c\u9a8c\u8bc1\u96c6\u3002\u6839\u636e\u7ecf\u9a8c\u6cd5\u5219&#xff0c;\u6574\u4e2a\u6570\u636e\u96c6\u7684\u8fd170%\u88ab\u7528\u4f5c\u8bad\u7ec3\u96c6&#xff0c;\u5176\u4f5930%\u88ab\u7528\u4f5c\u9a8c\u8bc1\u96c6\u3002\u4e5f\u5c31\u662f\u6211\u4eec\u6700\u5e38\u4f7f\u7528\u7684&#xff0c;\u76f4\u63a5\u5212\u5206\u6570\u636e\u96c6\u7684\u65b9\u6cd5\u3002<\/p>\n<ul>\n<li>\u4f18\u70b9&#xff1a;\u5f88\u7b80\u5355\u5f88\u5bb9\u6613\u6267\u884c\u3002<\/li>\n<li>\u7f3a\u70b91&#xff1a;\u4e0d\u9002\u7528\u4e8e\u4e0d\u5e73\u8861\u7684\u6570\u636e\u96c6\u3002\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u4e0d\u5e73\u8861\u7684\u6570\u636e\u96c6&#xff0c;\u67090\u7c7b\u548c1\u7c7b\u3002\u5047\u8bbe80%\u7684\u6570\u636e\u5c5e\u4e8e \u201c0 \u201c\u7c7b&#xff0c;\u5176\u4f5920%\u7684\u6570\u636e\u5c5e\u4e8e \u201c1 \u201c\u7c7b\u3002\u8fd9\u79cd\u60c5\u51b5\u4e0b&#xff0c;\u8bad\u7ec3\u96c6\u7684\u5927\u5c0f\u4e3a80%&#xff0c;\u6d4b\u8bd5\u6570\u636e\u7684\u5927\u5c0f\u4e3a\u6570\u636e\u96c6\u768420%\u3002\u53ef\u80fd\u53d1\u751f\u7684\u60c5\u51b5\u662f&#xff0c;\u6240\u670980%\u7684 \u201c0 \u201c\u7c7b\u6570\u636e\u90fd\u5728\u8bad\u7ec3\u96c6\u4e2d&#xff0c;\u800c\u6240\u6709 \u201c1 \u201c\u7c7b\u6570\u636e\u90fd\u5728\u6d4b\u8bd5\u96c6\u4e2d\u3002\u56e0\u6b64&#xff0c;\u6211\u4eec\u7684\u6a21\u578b\u5c06\u4e0d\u80fd\u5f88\u597d\u5730\u6982\u62ec\u6211\u4eec\u7684\u6d4b\u8bd5\u6570\u636e&#xff0c;\u56e0\u4e3a\u5b83\u4e4b\u524d\u6ca1\u6709\u89c1\u8fc7 \u201c1 \u201c\u7c7b\u7684\u6570\u636e\u3002<\/li>\n<li>\u7f3a\u70b92&#xff1a;\u4e00\u5927\u5757\u6570\u636e\u88ab\u5265\u593a\u4e86\u8bad\u7ec3\u6a21\u578b\u7684\u673a\u4f1a\u3002<\/li>\n<\/ul>\n<p>\u5728\u5c0f\u6570\u636e\u96c6\u7684\u60c5\u51b5\u4e0b&#xff0c;\u6709\u4e00\u90e8\u5206\u6570\u636e\u5c06\u88ab\u4fdd\u7559\u4e0b\u6765\u7528\u4e8e\u6d4b\u8bd5\u6a21\u578b&#xff0c;\u8fd9\u4e9b\u6570\u636e\u53ef\u80fd\u5177\u6709\u91cd\u8981\u7684\u7279\u5f81&#xff0c;\u800c\u6211\u4eec\u7684\u6a21\u578b\u53ef\u80fd\u4f1a\u56e0\u4e3a\u6ca1\u6709\u5728\u8fd9\u4e9b\u6570\u636e\u4e0a\u8fdb\u884c\u8bad\u7ec3\u800c\u9519\u8fc7\u3002\u4f46\u5728\u5927\u6570\u636e\u96c6\u4e0a&#xff0c;\u8fd9\u79cd\u65b9\u6cd5\u4ecd\u7136\u662f\u6700\u4f18\u5148\u8003\u8651\u7684\u3002<\/p>\n<h4>(2) K-\u6298\u4ea4\u53c9\u9a8c\u8bc1(K-fold)<\/h4>\n<p>K-Fold\u4ea4\u53c9\u9a8c\u8bc1\u6280\u672f\u4e2d&#xff0c;\u6574\u4e2a\u6570\u636e\u96c6\u88ab\u5212\u5206\u4e3aK\u4e2a\u5927\u5c0f\u76f8\u540c\u7684\u90e8\u5206\u3002\u6bcf\u4e2a\u5206\u533a\u88ab\u79f0\u4e3a \u4e00\u4e2a\u201dFold\u201d\u3002\u6240\u4ee5\u6211\u4eec\u6709K\u4e2a\u90e8\u5206&#xff0c;\u6211\u4eec\u79f0\u4e4b\u4e3aK-Fold\u3002\u4e00\u4e2aFold\u88ab\u7528\u4f5c\u9a8c\u8bc1\u96c6&#xff0c;\u5176\u4f59\u7684K-1\u4e2aFold\u88ab\u7528\u4f5c\u8bad\u7ec3\u96c6\u3002<\/p>\n<p>\u8be5\u6280\u672f\u91cd\u590dK\u6b21&#xff0c;\u76f4\u5230\u6bcf\u4e2aFold\u90fd\u88ab\u7528\u4f5c\u9a8c\u8bc1\u96c6&#xff0c;\u5176\u4f59\u7684\u4f5c\u4e3a\u8bad\u7ec3\u96c6\u3002\u6a21\u578b\u7684\u6700\u7ec8\u51c6\u786e\u5ea6\u662f\u901a\u8fc7\u53d6k\u4e2a\u6a21\u578b\u9a8c\u8bc1\u6570\u636e\u7684\u5e73\u5747\u51c6\u786e\u5ea6\u6765\u8ba1\u7b97\u7684\u3002<\/p>\n<p>\u7531\u4e8eknn\u7b97\u6cd5\u6027\u8d28&#xff0c;\u5176\u4e0d\u9002\u7528K-fold\u9a8c\u8bc1\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113337-688a03110443e.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>(3) \u5206\u5c42k-\u6298\u4ea4\u53c9\u9a8c\u8bc1Stratified k-fold<\/h4>\n<p>K-\u6298\u4ea4\u53c9\u9a8c\u8bc1\u7684\u53d8\u79cd&#xff0c; \u5206\u5c42\u7684\u610f\u601d\u662f\u8bf4\u5728\u6bcf\u4e00\u6298\u4e2d\u90fd\u4fdd\u6301\u7740\u539f\u59cb\u6570\u636e\u4e2d\u5404\u4e2a\u7c7b\u522b\u7684\u6bd4\u4f8b\u5173\u7cfb&#xff0c;\u6bd4\u5982\u8bf4&#xff1a;\u539f\u59cb\u6570\u636e\u67093\u7c7b&#xff0c;\u6bd4\u4f8b\u4e3a1:2:1&#xff0c;\u91c7\u75283\u6298\u5206\u5c42\u4ea4\u53c9\u9a8c\u8bc1&#xff0c;\u90a3\u4e48\u5212\u5206\u76843\u6298\u4e2d&#xff0c;\u6bcf\u4e00\u6298\u4e2d\u7684\u6570\u636e\u7c7b\u522b\u4fdd\u6301\u77401:2:1\u7684\u6bd4\u4f8b&#xff0c;\u8fd9\u6837\u7684\u9a8c\u8bc1\u7ed3\u679c\u66f4\u52a0\u53ef\u4fe1\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113337-688a03113c216.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<ul>\n<li>\u5176\u5b83\u9a8c\u8bc1<\/li>\n<\/ul>\n<p>\u53bb\u9664p\u4ea4\u53c9\u9a8c\u8bc1\u3001\u7559\u4e00\u4ea4\u53c9\u9a8c\u8bc1\u3001\u8499\u7279\u5361\u7f57\u4ea4\u53c9\u9a8c\u8bc1\u3001\u65f6\u95f4\u5e8f\u5217\u4ea4\u53c9\u9a8c\u8bc1\u3002<\/p>\n<h4>(4) api<\/h4>\n<p>from sklearn.model_selection import StratifiedKFold<br \/>\n\u8bf4\u660e:\u666e\u901aK\u6298\u4ea4\u53c9\u9a8c\u8bc1\u548c\u5206\u5c42K\u6298\u4ea4\u53c9\u9a8c\u8bc1\u7684\u4f7f\u7528\u662f\u4e00\u6837\u7684  \u53ea\u662f\u5f15\u5165\u7684\u7c7b\u4e0d\u540c<\/p>\n<p>from sklearn.model_selection import KFold<br \/>\n\u4f7f\u7528\u65f6\u53ea\u662fKFold\u8fd9\u4e2a\u7c7b\u540d\u4e0d\u4e00\u6837\u5176\u4ed6\u4ee3\u7801\u5b8c\u5168\u4e00\u6837<\/p>\n<p>strat_k_fold&#061;sklearn.model_selection.StratifiedKFold(n_splits&#061;5, shuffle&#061;True, random_state&#061;42)<br \/>\n\u200bn_splits\u5212\u5206\u4e3a\u51e0\u4e2a\u6298\u53e0<br \/>\n\u200bshuffle\u662f\u5426\u5728\u62c6\u5206\u4e4b\u524d\u88ab\u6253\u4e71(\u968f\u673a\u5316),False\u5219\u6309\u7167\u987a\u5e8f\u62c6\u5206<br \/>\n\u200brandom_state\u968f\u673a\u56e0\u5b50<\/p>\n<p>indexs&#061;strat_k_fold.split(X,y)<br \/>\n\u200b\u8fd4\u56de\u4e00\u4e2a\u53ef\u8fed\u4ee3\u5bf9\u8c61,\u4e00\u5171\u67095\u4e2a\u6298\u53e0,\u6bcf\u4e2a\u6298\u53e0\u5bf9\u5e94\u7684\u662f\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6\u7684\u4e0b\u6807<br \/>\n\u200b\u7136\u540e\u53ef\u4ee5\u7528for\u5faa\u73af\u53d6\u51fa\u6bcf\u4e00\u4e2a\u6298\u53e0\u5bf9\u5e94\u7684X\u548cy\u4e0b\u6807\u6765\u8bbf\u95ee\u5230\u5bf9\u5e94\u7684\u6d4b\u8bd5\u6570\u636e\u96c6\u548c\u8bad\u7ec3\u6570\u636e\u96c6 \u4ee5\u53ca\u6d4b\u8bd5\u76ee\u6807\u96c6\u548c\u8bad\u7ec3\u76ee\u6807\u96c6<\/p>\n<p>for train_index, test_index in indexs:<br \/>\n\u200bX[train_index]    y[train_index]   X[test_index ]  y[test_index ]<\/p>\n<h3>3.2 \u8d85\u53c2\u6570\u641c\u7d22<\/h3>\n<p>\u8d85\u53c2\u6570\u641c\u7d22\u4e5f\u53eb\u7f51\u683c\u641c\u7d22(Grid Search)&#xff0c;\u6bd4\u5982\u5728KNN\u7b97\u6cd5\u4e2d&#xff0c;k\u662f\u4e00\u4e2a\u53ef\u4ee5\u4eba\u4e3a\u8bbe\u7f6e\u7684\u53c2\u6570&#xff0c;\u6240\u4ee5\u5c31\u662f\u4e00\u4e2a\u8d85\u53c2\u6570\u3002\u7f51\u683c\u641c\u7d22\u80fd\u81ea\u52a8\u7684\u5e2e\u52a9\u6211\u4eec\u627e\u5230\u6700\u597d\u7684\u8d85\u53c2\u6570\u503c\u3002<\/p>\n<p>api<\/p>\n<p>class sklearn.model_selection.GridSearchCV(estimator, param_grid)<\/p>\n<p>\u8bf4\u660e&#xff1a;<br \/>\n\u540c\u65f6\u8fdb\u884c\u4ea4\u53c9\u9a8c\u8bc1(CV)\u3001\u548c\u7f51\u683c\u641c\u7d22(GridSearch)&#xff0c;GridSearchCV\u5b9e\u9645\u4e0a\u4e5f\u662f\u4e00\u4e2a\u4f30\u8ba1\u5668(estimator)&#xff0c;<br \/>\n\u540c\u65f6\u5b83\u6709\u51e0\u4e2a\u91cd\u8981\u5c5e\u6027&#xff1a;<br \/>\n      best_params_  \u6700\u4f73\u53c2\u6570<br \/>\n      best_score_ \u5728\u8bad\u7ec3\u96c6\u4e2d\u7684\u51c6\u786e\u7387<br \/>\n      best_estimator_ \u6700\u4f73\u4f30\u8ba1\u5668<br \/>\n      cv_results_ \u4ea4\u53c9\u9a8c\u8bc1\u8fc7\u7a0b\u63cf\u8ff0<br \/>\n      best_index_\u6700\u4f73k\u5728\u5217\u8868\u4e2d\u7684\u4e0b\u6807<br \/>\n\u53c2\u6570&#xff1a;<br \/>\nestimator&#xff1a; scikit-learn\u4f30\u8ba1\u5668\u5b9e\u4f8b<br \/>\nparam_grid:\u4ee5\u53c2\u6570\u540d\u79f0&#xff08;str&#xff09;\u4f5c\u4e3a\u952e&#xff0c;\u5c06\u53c2\u6570\u8bbe\u7f6e\u5217\u8868\u5c1d\u8bd5\u4f5c\u4e3a\u503c\u7684\u5b57\u5178<br \/>\n\u793a\u4f8b&#xff1a; {&#034;n_neighbors&#034;: [1, 3, 5, 7, 9, 11]}<br \/>\n    cv: \u786e\u5b9a\u4ea4\u53c9\u9a8c\u8bc1\u5207\u5206\u7b56\u7565,\u503c\u4e3a:<br \/>\n        (1)None  \u9ed8\u8ba45\u6298<br \/>\n        (2)integer  \u8bbe\u7f6e\u591a\u5c11\u6298<br \/>\n        \u5982\u679c\u4f30\u8ba1\u5668\u662f\u5206\u7c7b\u5668&#xff0c;\u4f7f\u7528&#034;\u5206\u5c42k-\u6298\u4ea4\u53c9\u9a8c\u8bc1(StratifiedKFold)&#034;\u3002<br \/>\n        \u5728\u6240\u6709\u5176\u4ed6\u60c5\u51b5\u4e0b&#xff0c;\u4f7f\u7528KFold\u3002<\/p>\n<p>\u793a\u4f8b&#xff1a;<\/p>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> GridSearchCV<\/p>\n<p>x<span class=\"token punctuation\">,<\/span>y<span class=\"token operator\">&#061;<\/span>load_iris<span class=\"token punctuation\">(<\/span>return_X_y<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">True<\/span><span class=\"token punctuation\">)<\/span><br \/>\nknn<span class=\"token operator\">&#061;<\/span>KNeighborsClassifier<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nmodel<span class=\"token operator\">&#061;<\/span>GridSearchCV<span class=\"token punctuation\">(<\/span>knn<span class=\"token punctuation\">,<\/span>param_grid<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">{<\/span><span class=\"token string\">&#039;n_neighbors&#039;<\/span><span class=\"token punctuation\">:<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">6<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">7<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">9<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">,<\/span>cv<span class=\"token operator\">&#061;<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>model<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span>y<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">.<\/span>best_score_<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">.<\/span>best_params_<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">.<\/span>best_index_<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">.<\/span>best_estimator_<span class=\"token operator\">&#061;&#061;<\/span>knn<span class=\"token punctuation\">)<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113337-688a03116fc3f.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h2>\u56db\u3001\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b<\/h2>\n<h3>4.1 \u8d1d\u53f6\u65af\u5206\u7c7b\u7406\u8bba<\/h3>\n<p>\u5047\u8bbe\u73b0\u5728\u6211\u4eec\u6709\u4e00\u4e2a\u6570\u636e\u96c6&#xff0c;\u5b83\u7531\u4e24\u7c7b\u6570\u636e\u7ec4\u6210&#xff0c;\u6570\u636e\u5206\u5e03\u5982\u4e0b\u56fe\u6240\u793a&#xff1a; <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113337-688a03119bd69.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u6211\u4eec\u73b0\u5728\u7528p1(x,y)\u8868\u793a\u6570\u636e\u70b9(x,y)\u5c5e\u4e8e\u7c7b\u522b1(\u56fe\u4e2d\u7ea2\u8272\u5706\u70b9\u8868\u793a\u7684\u7c7b\u522b)\u7684\u6982\u7387&#xff0c;\u7528p2(x,y)\u8868\u793a\u6570\u636e\u70b9(x,y)\u5c5e\u4e8e\u7c7b\u522b2(\u56fe\u4e2d\u84dd\u8272\u4e09\u89d2\u5f62\u8868\u793a\u7684\u7c7b\u522b)\u7684\u6982\u7387&#xff0c;\u90a3\u4e48\u5bf9\u4e8e\u4e00\u4e2a\u65b0\u6570\u636e\u70b9(x,y)&#xff0c;\u53ef\u4ee5\u7528\u4e0b\u9762\u7684\u89c4\u5219\u6765\u5224\u65ad\u5b83\u7684\u7c7b\u522b&#xff1a;<\/p>\n<ul>\n<li>\u5982\u679cp1(x,y)&gt;p2(x,y)&#xff0c;\u90a3\u4e48\u7c7b\u522b\u4e3a1<\/li>\n<li>\u5982\u679cp1(x,y)&lt;p2(x,y)&#xff0c;\u90a3\u4e48\u7c7b\u522b\u4e3a2<\/li>\n<\/ul>\n<p>\u4e5f\u5c31\u662f\u8bf4&#xff0c;\u6211\u4eec\u4f1a\u9009\u62e9\u9ad8\u6982\u7387\u5bf9\u5e94\u7684\u7c7b\u522b\u3002\u8fd9\u5c31\u662f\u8d1d\u53f6\u65af\u51b3\u7b56\u7406\u8bba\u7684\u6838\u5fc3\u601d\u60f3&#xff0c;\u5373\u9009\u62e9\u5177\u6709\u6700\u9ad8\u6982\u7387\u7684\u51b3\u7b56\u3002\u5df2\u7ecf\u4e86\u89e3\u4e86\u8d1d\u53f6\u65af\u51b3\u7b56\u7406\u8bba\u7684\u6838\u5fc3\u601d\u60f3&#xff0c;\u90a3\u4e48\u63a5\u4e0b\u6765&#xff0c;\u5c31\u662f\u5b66\u4e60\u5982\u4f55\u8ba1\u7b97p1\u548cp2\u6982\u7387\u3002<\/p>\n<h3>4.2 \u6761\u4ef6\u6982\u7387<\/h3>\n<p>\u5728\u5b66\u4e60\u8ba1\u7b97p1 \u548cp2\u6982\u7387\u4e4b\u524d&#xff0c;\u6211\u4eec\u9700\u8981\u4e86\u89e3\u4ec0\u4e48\u662f\u6761\u4ef6\u6982\u7387(Conditional probability)&#xff0c;\u5c31\u662f\u6307\u5728\u4e8b\u4ef6B\u53d1\u751f\u7684\u60c5\u51b5\u4e0b&#xff0c;\u4e8b\u4ef6A\u53d1\u751f\u7684\u6982\u7387&#xff0c;\u7528P(A|B)\u6765\u8868\u793a\u3002 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113338-688a0312bed3c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u6839\u636e\u6587\u6c0f\u56fe&#xff0c;\u53ef\u4ee5\u5f88\u6e05\u695a\u5730\u770b\u5230\u5728\u4e8b\u4ef6B\u53d1\u751f\u7684\u60c5\u51b5\u4e0b&#xff0c;\u4e8b\u4ef6A\u53d1\u751f\u7684\u6982\u7387\u5c31\u662fP(A\u2229B)\u9664\u4ee5P(B)&#xff0c;\u5373<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        A<\/p>\n<p>        \u2223<\/p>\n<p>        B<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          A<\/p>\n<p>          \u2229<\/p>\n<p>          B<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          B<\/p>\n<p>          )<\/p>\n<p>       P(A \\\\mid B) &#061; \\\\frac{P(A \\\\cap B)}{P(B)}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.53em;vertical-align: -0.52em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.01em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.485em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">A<\/span><span class=\"mbin mtight\">\u2229<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.52em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u56e0\u6b64&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        A<\/p>\n<p>        \u2229<\/p>\n<p>        B<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        A<\/p>\n<p>        \u2223<\/p>\n<p>        B<\/p>\n<p>        )<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        B<\/p>\n<p>        )<\/p>\n<p>       P(A \\\\cap B) &#061; P(A \\\\mid B)P(B)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2229<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c; \u540c\u7406\u53ef\u5f97&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        A<\/p>\n<p>        \u2229<\/p>\n<p>        B<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        B<\/p>\n<p>        \u2223<\/p>\n<p>        A<\/p>\n<p>        )<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        A<\/p>\n<p>        )<\/p>\n<p>       P(A \\\\cap B) &#061; P(B \\\\mid A)P(A)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2229<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;<\/p>\n<p>\u5373<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        A<\/p>\n<p>        \u2223<\/p>\n<p>        B<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          B<\/p>\n<p>          \u2223<\/p>\n<p>          A<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          A<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          B<\/p>\n<p>          )<\/p>\n<p>       P(A \\\\mid B) &#061; \\\\frac{P(B \\\\mid A)P(A)}{P(B)}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.53em;vertical-align: -0.52em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.01em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.485em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mrel mtight\">\u2223<\/span><span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">A<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.52em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span> &#xff0c;\u8fd9\u5c31\u662f\u6761\u4ef6\u6982\u7387\u7684\u8ba1\u7b97\u516c\u5f0f\u3002<\/p>\n<h3>4.3 \u5168\u6982\u7387\u516c\u5f0f<\/h3>\n<p>\u9664\u4e86\u6761\u4ef6\u6982\u7387\u4ee5\u5916&#xff0c;\u5728\u8ba1\u7b97p1\u548cp2\u7684\u65f6\u5019&#xff0c;\u8fd8\u8981\u7528\u5230\u5168\u6982\u7387\u516c\u5f0f&#xff0c;\u56e0\u6b64&#xff0c;\u8fd9\u91cc\u7ee7\u7eed\u63a8\u5bfc\u5168\u6982\u7387\u516c\u5f0f\u3002<\/p>\n<p>\u5047\u5b9a\u6837\u672c\u7a7a\u95f4S&#xff0c;\u662f\u4e24\u4e2a\u4e8b\u4ef6A\u4e0eA\u2019\u7684\u548c\u3002 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113339-688a0313c96a7.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u4e0a\u56fe\u4e2d&#xff0c;\u7ea2\u8272\u90e8\u5206\u662f\u4e8b\u4ef6A&#xff0c;\u7eff\u8272\u90e8\u5206\u662f\u4e8b\u4ef6A\u2019&#xff0c;\u5b83\u4eec\u5171\u540c\u6784\u6210\u4e86\u6837\u672c\u7a7a\u95f4S\u3002<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b&#xff0c;\u4e8b\u4ef6B\u53ef\u4ee5\u5212\u5206\u6210\u4e24\u4e2a\u90e8\u5206\u3002 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113340-688a03147c5f4.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u5373&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        B<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        B<\/p>\n<p>        \u2229<\/p>\n<p>        A<\/p>\n<p>        )<\/p>\n<p>        &#043;<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        B<\/p>\n<p>        \u2229<\/p>\n<p>         A<\/p>\n<p>         \u2032<\/p>\n<p>        )<\/p>\n<p>       P(B) &#061; P(B \\\\cap A) &#043; P(B \\\\cap A&#039;)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2229<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2229<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0019em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5728\u4e0a\u9762\u7684\u63a8\u5bfc\u5f53\u4e2d&#xff0c;\u6211\u4eec\u5df2\u77e5<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        B<\/p>\n<p>        \u2229<\/p>\n<p>        A<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        B<\/p>\n<p>        \u2223<\/p>\n<p>        A<\/p>\n<p>        )<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        A<\/p>\n<p>        )<\/p>\n<p>       P(B \\\\cap A) &#061; P(B|A)P(A)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2229<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6240\u4ee5&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        B<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        B<\/p>\n<p>        \u2223<\/p>\n<p>        A<\/p>\n<p>        )<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        A<\/p>\n<p>        )<\/p>\n<p>        &#043;<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        B<\/p>\n<p>        \u2223<\/p>\n<p>         A<\/p>\n<p>         \u2032<\/p>\n<p>        )<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>         A<\/p>\n<p>         \u2032<\/p>\n<p>        )<\/p>\n<p>       P(B) &#061; P(B|A)P(A) &#043; P(B|A&#039;)P(A&#039;)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0019em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7519em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u5c31\u662f\u5168\u6982\u7387\u516c\u5f0f\u3002\u5b83\u7684\u542b\u4e49\u662f&#xff0c;\u5982\u679cA\u548cA\u2019\u6784\u6210\u6837\u672c\u7a7a\u95f4\u7684\u4e00\u4e2a\u5212\u5206&#xff0c;\u90a3\u4e48\u4e8b\u4ef6B\u7684\u6982\u7387&#xff0c;\u5c31\u7b49\u4e8eA\u548cA\u2019\u7684\u6982\u7387\u5206\u522b\u4e58\u4ee5B\u5bf9\u8fd9\u4e24\u4e2a\u4e8b\u4ef6\u7684\u6761\u4ef6\u6982\u7387\u4e4b\u548c\u3002<\/p>\n<p>\u5c06\u8fd9\u4e2a\u516c\u5f0f\u4ee3\u5165\u4e0a\u4e00\u8282\u7684\u6761\u4ef6\u6982\u7387\u516c\u5f0f&#xff0c;\u5c31\u5f97\u5230\u4e86\u6761\u4ef6\u6982\u7387\u7684\u53e6\u4e00\u79cd\u5199\u6cd5&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         (<\/p>\n<p>         A<\/p>\n<p>         \u2223<\/p>\n<p>         B<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>           B<\/p>\n<p>           \u2223<\/p>\n<p>           A<\/p>\n<p>           )<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>           A<\/p>\n<p>           )<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>           B<\/p>\n<p>           \u2223<\/p>\n<p>           A<\/p>\n<p>           )<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>           A<\/p>\n<p>           )<\/p>\n<p>           &#043;<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>           B<\/p>\n<p>           \u2223<\/p>\n<p>            A<\/p>\n<p>            \u2032<\/p>\n<p>           )<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>            A<\/p>\n<p>            \u2032<\/p>\n<p>           )<\/p>\n<p>        P(A|B)&#061;\\\\frac{P(B|A)P(A)}{P(B|A)P(A)&#043;P(B|A&#039;)P(A&#039;)}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6779em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6779em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>4.4 \u8d1d\u53f6\u65af\u63a8\u65ad<\/h3>\n<p>\u5bf9\u6761\u4ef6\u6982\u7387\u516c\u5f0f\u8fdb\u884c\u53d8\u5f62&#xff0c;\u53ef\u4ee5\u5f97\u5230\u5982\u4e0b\u5f62\u5f0f: <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         (<\/p>\n<p>         A<\/p>\n<p>         \u2223<\/p>\n<p>         B<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>         P<\/p>\n<p>         (<\/p>\n<p>         A<\/p>\n<p>         )<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>           B<\/p>\n<p>           \u2223<\/p>\n<p>           A<\/p>\n<p>           )<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>           B<\/p>\n<p>           )<\/p>\n<p>        P(A \\\\mid B) &#061; P(A)\\\\frac{P(B \\\\mid A)}{P(B)}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em;vertical-align: -0.936em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6211\u4eec\u628aP(A)\u79f0\u4e3a&#034;\u5148\u9a8c\u6982\u7387&#034;&#xff08;Prior probability&#xff09;&#xff0c;\u5373\u5728B\u4e8b\u4ef6\u53d1\u751f\u4e4b\u524d&#xff0c;\u6211\u4eec\u5bf9A\u4e8b\u4ef6\u6982\u7387\u7684\u4e00\u4e2a\u5224\u65ad\u3002<\/p>\n<p>P(A|B)\u79f0\u4e3a&#034;\u540e\u9a8c\u6982\u7387&#034;&#xff08;Posterior probability&#xff09;&#xff0c;\u5373\u5728B\u4e8b\u4ef6\u53d1\u751f\u4e4b\u540e&#xff0c;\u6211\u4eec\u5bf9A\u4e8b\u4ef6\u6982\u7387\u7684\u91cd\u65b0\u8bc4\u4f30\u3002<\/p>\n<p>P(B|A)\/P(B)\u79f0\u4e3a&#034;\u53ef\u80fd\u6027\u51fd\u6570&#034;&#xff08;Likelyhood&#xff09;&#xff0c;\u8fd9\u662f\u4e00\u4e2a\u8c03\u6574\u56e0\u5b50&#xff0c;\u4f7f\u5f97\u9884\u4f30\u6982\u7387\u66f4\u63a5\u8fd1\u771f\u5b9e\u6982\u7387\u3002<\/p>\n<p>\u6240\u4ee5&#xff0c;\u6761\u4ef6\u6982\u7387\u53ef\u4ee5\u7406\u89e3\u6210\u5f0f\u5b50&#xff1a;\u540e\u9a8c\u6982\u7387&#xff1d;\u5148\u9a8c\u6982\u7387&#xff58;\u8c03\u6574\u56e0\u5b50<\/p>\n<p>\u8fd9\u5c31\u662f\u8d1d\u53f6\u65af\u63a8\u65ad\u7684\u542b\u4e49\u3002\u6211\u4eec\u5148\u9884\u4f30\u4e00\u4e2a&#034;\u5148\u9a8c\u6982\u7387&#034;&#xff0c;\u7136\u540e\u52a0\u5165\u5b9e\u9a8c\u7ed3\u679c&#xff0c;\u770b\u8fd9\u4e2a\u5b9e\u9a8c\u5230\u5e95\u662f\u589e\u5f3a\u8fd8\u662f\u524a\u5f31\u4e86&#034;\u5148\u9a8c\u6982\u7387&#034;&#xff0c;\u7531\u6b64\u5f97\u5230\u66f4\u63a5\u8fd1\u4e8b\u5b9e\u7684&#034;\u540e\u9a8c\u6982\u7387&#034;\u3002<\/p>\n<h3>4.5 \u6734\u7d20\u8d1d\u53f6\u65af\u63a8\u65ad<\/h3>\n<p>\u7406\u89e3\u4e86\u8d1d\u53f6\u65af\u63a8\u65ad&#xff0c;\u90a3\u4e48\u8ba9\u6211\u4eec\u7ee7\u7eed\u770b\u770b\u6734\u7d20\u8d1d\u53f6\u65af\u3002\u8d1d\u53f6\u65af\u548c\u6734\u7d20\u8d1d\u53f6\u65af\u7684\u6982\u5ff5\u662f\u4e0d\u540c\u7684&#xff0c;\u533a\u522b\u5c31\u5728\u4e8e\u201c\u6734\u7d20\u201d\u4e8c\u5b57&#xff0c;\u6734\u7d20\u8d1d\u53f6\u65af\u5bf9\u6761\u4ef6\u6982\u7387\u5206\u5e03\u505a\u4e86\u6761\u4ef6\u72ec\u7acb\u6027\u7684\u5047\u8bbe\u3002 \u6bd4\u5982\u4e0b\u9762\u7684\u516c\u5f0f&#xff0c;\u5047\u8bbe\u6709n\u4e2a\u7279\u5f81&#xff1a;<\/p>\n<p>\u6839\u636e\u8d1d\u53f6\u65af\u5b9a\u7406&#xff0c;\u540e\u9a8c\u6982\u7387 P(a|X) \u53ef\u4ee5\u8868\u793a\u4e3a&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         P<\/p>\n<p>         (<\/p>\n<p>         a<\/p>\n<p>         \u2223<\/p>\n<p>         X<\/p>\n<p>         )<\/p>\n<p>         &#061;<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>           X<\/p>\n<p>           \u2223<\/p>\n<p>           a<\/p>\n<p>           )<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>           a<\/p>\n<p>           )<\/p>\n<p>           P<\/p>\n<p>           (<\/p>\n<p>           X<\/p>\n<p>           )<\/p>\n<p>        P(a|X) &#061; \\\\frac{P(X|a)P(a)}{P(X)}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d&#xff1a;<\/p>\n<ul>\n<li>P(X|a) \u662f\u7ed9\u5b9a\u7c7b\u522b ( a ) \u4e0b\u89c2\u6d4b\u5230\u7279\u5f81\u5411\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         X<\/p>\n<p>         &#061;<\/p>\n<p>         (<\/p>\n<p>          x<\/p>\n<p>          1<\/p>\n<p>         ,<\/p>\n<p>          x<\/p>\n<p>          2<\/p>\n<p>         ,<\/p>\n<p>         .<\/p>\n<p>         .<\/p>\n<p>         .<\/p>\n<p>         ,<\/p>\n<p>          x<\/p>\n<p>          n<\/p>\n<p>         )<\/p>\n<p>        X&#061;(x_1, x_2, &#8230;, x_n)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">&#8230;<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u7684\u6982\u7387&#xff1b;<\/li>\n<li>P(a) \u662f\u7c7b\u522b a \u7684\u5148\u9a8c\u6982\u7387&#xff1b;<\/li>\n<li>P(X) \u662f\u89c2\u6d4b\u5230\u7279\u5f81\u5411\u91cf X \u7684\u8fb9\u7f18\u6982\u7387&#xff0c;\u901a\u5e38\u4f5c\u4e3a\u5f52\u4e00\u5316\u5e38\u6570\u5904\u7406\u3002<\/li>\n<\/ul>\n<p>\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b\u5668\u7684\u5173\u952e\u5047\u8bbe\u662f\u7279\u5f81\u4e4b\u95f4\u7684\u6761\u4ef6\u72ec\u7acb\u6027&#xff0c;\u5373\u7ed9\u5b9a\u7c7b\u522b a &#xff0c;\u7279\u5f81 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         i<\/p>\n<p>       x_i<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         x<\/p>\n<p>         j<\/p>\n<p>       x_j<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7167em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> (\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        i<\/p>\n<p>        \u2260<\/p>\n<p>        j<\/p>\n<p>       i \\\\neq j<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">&#061;<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.854em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span> \u76f8\u4e92\u72ec\u7acb\u3002)<\/p>\n<p>\u56e0\u6b64&#xff0c;\u6211\u4eec\u53ef\u4ee5\u5c06\u8054\u5408\u6982\u7387 P(X|a) \u5206\u89e3\u4e3a\u5404\u4e2a\u7279\u5f81\u7684\u6982\u7387\u4e58\u79ef&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        X<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         1<\/p>\n<p>        ,<\/p>\n<p>         x<\/p>\n<p>         2<\/p>\n<p>        ,<\/p>\n<p>        .<\/p>\n<p>        .<\/p>\n<p>        .<\/p>\n<p>        ,<\/p>\n<p>         x<\/p>\n<p>         n<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         1<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         2<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>        .<\/p>\n<p>        .<\/p>\n<p>        .<\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>         x<\/p>\n<p>         n<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        )<\/p>\n<p>       P(X|a) &#061; P(x_1, x_2, &#8230;, x_n|a) &#061; P(x_1|a)P(x_2|a)&#8230;P(x_n|a)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">&#8230;<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">&#8230;<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5c06\u8fd9\u4e2a\u6761\u4ef6\u72ec\u7acb\u6027\u5047\u8bbe\u5e94\u7528\u4e8e\u8d1d\u53f6\u65af\u516c\u5f0f&#xff0c;\u6211\u4eec\u5f97\u5230&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        (<\/p>\n<p>        a<\/p>\n<p>        \u2223<\/p>\n<p>        X<\/p>\n<p>        )<\/p>\n<p>        &#061;<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           1<\/p>\n<p>          \u2223<\/p>\n<p>          a<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           2<\/p>\n<p>          \u2223<\/p>\n<p>          a<\/p>\n<p>          )<\/p>\n<p>          .<\/p>\n<p>          .<\/p>\n<p>          .<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>           x<\/p>\n<p>           n<\/p>\n<p>          \u2223<\/p>\n<p>          a<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          a<\/p>\n<p>          )<\/p>\n<p>          P<\/p>\n<p>          (<\/p>\n<p>          X<\/p>\n<p>          )<\/p>\n<p>       P(a|X) &#061; \\\\frac{P(x_1|a)P(x_2|a)&#8230;P(x_n|a)P(a)}{P(X)}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.53em;vertical-align: -0.52em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.01em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.485em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2223<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3173em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2223<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord mtight\">&#8230;<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1645em\"><span class=\"\" style=\"top: -2.357em;margin-left: 0em;margin-right: 0.0714em\"><span class=\"pstrut\" style=\"height: 2.5em\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\">\u2223<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.52em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u6837&#xff0c;\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b\u5668\u5c31\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u6bcf\u79cd\u53ef\u80fd\u7c7b\u522b\u7684\u6761\u4ef6\u6982\u7387\u548c\u5148\u9a8c\u6982\u7387&#xff0c;\u7136\u540e\u9009\u62e9\u5177\u6709\u6700\u9ad8\u6982\u7387\u7684\u7c7b\u522b\u4f5c\u4e3a\u9884\u6d4b\u7ed3\u679c\u3002<\/p>\n<p>\u8fd9\u91cc\u7ed9\u51fa\u4e00\u4e2a\u4f8b\u5b50&#xff1a;<\/p>\n<table>\n<tr>\u7eb9\u7406\u8272\u6cfd\u9f14\u58f0\u7c7b\u522b<\/tr>\n<tbody>\n<tr>\n<td>1<\/td>\n<td>\u6e05\u6670<\/td>\n<td>\u6e05\u7eff<\/td>\n<td>\u6e05\u8106<\/td>\n<td>\u597d\u74dc<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>\u6a21\u7cca<\/td>\n<td>\u4e4c\u9ed1<\/td>\n<td>\u6d4a\u54cd<\/td>\n<td>\u574f\u74dc<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>\u6a21\u7cca<\/td>\n<td>\u6e05\u7eff<\/td>\n<td>\u6d4a\u54cd<\/td>\n<td>\u574f\u74dc<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>\u6e05\u6670<\/td>\n<td>\u4e4c\u9ed1<\/td>\n<td>\u6c89\u95f7<\/td>\n<td>\u597d\u74dc<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>\u6e05\u6670<\/td>\n<td>\u6e05\u7eff<\/td>\n<td>\u6d4a\u54cd<\/td>\n<td>\u597d\u74dc<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>\u6a21\u7cca<\/td>\n<td>\u4e4c\u9ed1<\/td>\n<td>\u6c89\u95f7<\/td>\n<td>\u574f\u74dc<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>\u6e05\u6670<\/td>\n<td>\u4e4c\u9ed1<\/td>\n<td>\u6e05\u8106<\/td>\n<td>\u597d\u74dc<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>\u6a21\u7cca<\/td>\n<td>\u6e05\u7eff<\/td>\n<td>\u6c89\u95f7<\/td>\n<td>\u597d\u74dc<\/td>\n<\/tr>\n<tr>\n<td>9<\/td>\n<td>\u6e05\u6670<\/td>\n<td>\u4e4c\u9ed1<\/td>\n<td>\u6d4a\u54cd<\/td>\n<td>\u574f\u74dc<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>\u6a21\u7cca<\/td>\n<td>\u6e05\u7eff<\/td>\n<td>\u6e05\u8106<\/td>\n<td>\u597d\u74dc<\/td>\n<\/tr>\n<tr>\n<td>11<\/td>\n<td>\u6e05\u6670<\/td>\n<td>\u6e05\u7eff<\/td>\n<td>\u6c89\u95f7<\/td>\n<td>&#xff1f;<\/td>\n<\/tr>\n<tr>\n<td>12<\/td>\n<td>\u6a21\u7cca<\/td>\n<td>\u4e4c\u9ed1<\/td>\n<td>\u6d4a\u54cd<\/td>\n<td>?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u793a\u4f8b&#xff1a;<br \/>\np(a|X) &#061; p(X|a)* p(a)\/p(X)  #\u8d1d\u53f6\u65af\u516c\u5f0f<br \/>\np(X|a) &#061; p(x1,x2,x3&#8230;xn|a) &#061; p(x1|a)*p(x2|a)*p(x3|a)&#8230;p(xn|a)<br \/>\np(X) &#061; p(x1,x2,x3&#8230;xn) &#061; p(x1)*p(x2)*p(x3)&#8230;p(xn)<br \/>\np(a|X) &#061; p(x1|a)*p(x2|a)*p(x3|a)&#8230;p(xn|a) * p(a) \/ p(x1)*p(x2)*p(x3)&#8230;p(xn)  #\u6734\u7d20\u8d1d\u53f6\u65af\u516c\u5f0f<\/p>\n<p>P(\u597d\u74dc)&#061;(\u597d\u74dc\u6570\u91cf)\/\u6240\u6709\u74dc<br \/>\nP(\u574f\u74dc)&#061;(\u574f\u74dc\u6570\u91cf)\/\u6240\u6709\u74dc<br \/>\np&#xff08;\u7eb9\u7406\u6e05\u6670&#xff09;&#061;(\u7eb9\u7406\u6e05\u6670\u6570\u91cf)\/\u6240\u6709\u74dc<br \/>\np&#xff08;\u7eb9\u7406\u6e05\u6670|\u597d\u74dc&#xff09;&#061; \u597d\u74dc\u4e2d\u7eb9\u7406\u6e05\u6670\u6570\u91cf\/\u597d\u74dc\u6570\u91cf<br \/>\np&#xff08;\u7eb9\u7406\u6e05\u6670|\u574f\u74dc)&#061; \u574f\u74dc\u4e2d\u7eb9\u7406\u6e05\u6670\u6570\u91cf\/\u574f\u74dc\u6570\u91cf<\/p>\n<p>p(\u597d\u74dc|\u7eb9\u7406\u6e05\u6670&#xff0c;\u8272\u6cfd\u6e05\u7eff&#xff0c;\u9f13\u58f0\u6c89\u95f7)<br \/>\n&#061;\u3010p(\u597d\u74dc)\u3011*\u3010p(\u7eb9\u7406\u6e05\u6670&#xff0c;\u8272\u6cfd\u6e05\u7eff&#xff0c;\u9f13\u58f0\u6c89\u95f7|\u597d\u74dc)\u3011\/\u3010p(\u7eb9\u7406\u6e05\u6670&#xff0c;\u8272\u6cfd\u6e05\u7eff&#xff0c;\u9f13\u58f0\u6c89\u95f7)\u3011<br \/>\n&#061;\u3010p(\u597d\u74dc)\u3011*\u3010p&#xff08;\u7eb9\u7406\u6e05\u6670|\u597d\u74dc&#xff09;*p&#xff08;\u8272\u6cfd\u6e05\u7eff|\u597d\u74dc&#xff09;*p&#xff08;\u9f13\u58f0\u6c89\u95f7|\u597d\u74dc)\u3011\/\u3010p&#xff08;\u7eb9\u7406\u6e05\u6670&#xff09;*p&#xff08;\u8272\u6cfd\u6e05\u7eff&#xff09;*p&#xff08;\u9f13\u58f0\u6c89\u95f7)\u3011<\/p>\n<p>p(\u574f\u74dc|\u7eb9\u7406\u6e05\u6670&#xff0c;\u8272\u6cfd\u6e05\u7eff&#xff0c;\u9f13\u58f0\u6c89\u95f7)<br \/>\n&#061;\u3010p(\u574f\u74dc)*p&#xff08;\u7eb9\u7406\u6e05\u6670|\u574f\u74dc&#xff09;*p&#xff08;\u8272\u6cfd\u6e05\u7eff|\u574f\u74dc&#xff09;*p&#xff08;\u9f13\u58f0\u6c89\u95f7|\u574f\u74dc)\u3011\/\u3010p&#xff08;\u7eb9\u7406\u6e05\u6670&#xff09;*p&#xff08;\u8272\u6cfd\u6e05\u7eff&#xff09;*p&#xff08;\u9f13\u58f0\u6c89\u95f7)\u3011<\/p>\n<p>\u4ece\u516c\u5f0f\u4e2d\u5224\u65ad&#034;p(\u597d\u74dc|\u7eb9\u7406\u6e05\u6670&#xff0c;\u8272\u6cfd\u6e05\u7eff&#xff0c;\u9f13\u58f0\u6c89\u95f7)&#034;\u548c&#034;p(\u574f\u74dc|\u7eb9\u7406\u6e05\u6670&#xff0c;\u8272\u6cfd\u6e05\u7eff&#xff0c;\u9f13\u58f0\u6c89\u95f7)&#034;\u65f6&#xff0c;\u56e0\u4e3a\u5b83\u4eec\u7684\u5206\u6bcd<br \/>\n\u503c\u662f\u76f8\u540c\u7684&#xff0c;[\u503c\u90fd\u662fp&#xff08;\u7eb9\u7406\u6e05\u6670&#xff09;*p&#xff08;\u8272\u6cfd\u6e05\u7eff&#xff09;*p&#xff08;\u9f13\u58f0\u6c89\u95f7)]&#xff0c;\u6240\u4ee5\u53ea\u8981\u8ba1\u7b97\u5b83\u4eec\u7684\u5206\u5b50\u5c31\u53ef\u4ee5\u5224\u65ad\u662f&#034;\u597d\u74dc&#034;\u8fd8\u662f&#034;\u574f\u74dc&#034;\u4e4b\u95f4\u8c01\u5927\u8c01\u5c0f\u4e86&#xff0c;\u6240\u4ee5\u6ca1\u6709\u5fc5\u8981\u8ba1\u7b97\u5206\u6bcd<br \/>\np(\u597d\u74dc) &#061; 6\/10<br \/>\np(\u574f\u74dc)&#061;4\/10<br \/>\np&#xff08;\u7eb9\u7406\u6e05\u6670|\u597d\u74dc&#xff09; &#061; 4\/6<br \/>\np&#xff08;\u8272\u6cfd\u6e05\u7eff|\u597d\u74dc&#xff09; &#061; 4\/6<br \/>\np&#xff08;\u9f13\u58f0\u6c89\u95f7|\u597d\u74dc&#xff09; &#061; 2\/6<br \/>\np&#xff08;\u7eb9\u7406\u6e05\u6670|\u574f\u74dc&#xff09; &#061; 1\/4<br \/>\np&#xff08;\u8272\u6cfd\u6e05\u7eff|\u574f\u74dc&#xff09; &#061; 1\/4<br \/>\np&#xff08;\u9f13\u58f0\u6c89\u95f7|\u574f\u74dc&#xff09; &#061; 1\/4<br \/>\n\u628a\u4ee5\u4e0a\u8ba1\u7b97\u4ee3\u5165\u516c\u5f0f\u7684\u5206\u5b50<br \/>\np(\u597d\u74dc)*p&#xff08;\u7eb9\u7406\u6e05\u6670|\u597d\u74dc&#xff09;*p&#xff08;\u8272\u6cfd\u6e05\u7eff|\u597d\u74dc&#xff09;*p&#xff08;\u9f13\u58f0\u6c89\u95f7|\u597d\u74dc) &#061; 4\/45<br \/>\np(\u574f\u74dc)*p&#xff08;\u7eb9\u7406\u6e05\u6670|\u574f\u74dc&#xff09;*p&#xff08;\u8272\u6cfd\u6e05\u7eff|\u574f\u74dc&#xff09;*p&#xff08;\u9f13\u58f0\u6c89\u95f7|\u574f\u74dc) &#061; 1\/160<br \/>\n\u6240\u4ee5<br \/>\np(\u597d\u74dc|\u7eb9\u7406\u6e05\u6670&#xff0c;\u8272\u6cfd\u6e05\u7eff&#xff0c;\u9f13\u58f0\u6c89\u95f7) &gt;  p(\u574f\u74dc|\u7eb9\u7406\u6e05\u6670&#xff0c;\u8272\u6cfd\u6e05\u7eff&#xff0c;\u9f13\u58f0\u6c89\u95f7)&#xff0c;<br \/>\n\u6240\u4ee5\u628a(\u7eb9\u7406\u6e05\u6670&#xff0c;\u8272\u6cfd\u6e05\u7eff&#xff0c;\u9f13\u58f0\u6c89\u95f7)\u7684\u6837\u672c\u5f52\u7c7b\u4e3a\u597d\u74dc<\/p>\n<h3>4.6 \u62c9\u666e\u62c9\u65af\u5e73\u6ed1\u7cfb\u6570<\/h3>\n<p>\u67d0\u4e9b\u4e8b\u4ef6\u6216\u7279\u5f81\u53ef\u80fd\u4ece\u672a\u51fa\u73b0\u8fc7&#xff0c;\u8fd9\u4f1a\u5bfc\u81f4\u5b83\u4eec\u7684\u6982\u7387\u88ab\u4f30\u8ba1\u4e3a\u96f6\u3002\u7136\u800c&#xff0c;\u5728\u5b9e\u9645\u5e94\u7528\u4e2d&#xff0c;\u5373\u4f7f\u67d0\u4e2a\u4e8b\u4ef6\u6216\u7279\u5f81\u6ca1\u6709\u51fa\u73b0\u5728\u8bad\u7ec3\u96c6\u4e2d&#xff0c;\u4e5f\u4e0d\u80fd\u5b8c\u5168\u6392\u9664\u5b83\u5728\u672a\u6765\u6837\u672c\u4e2d\u51fa\u73b0\u7684\u53ef\u80fd\u6027\u3002\u62c9\u666e\u62c9\u65af\u5e73\u6ed1\u6280\u672f\u53ef\u4ee5\u907f\u514d\u8fd9\u79cd\u201c\u96f6\u6982\u7387\u9677\u9631\u201d<\/p>\n<p>\u516c\u5f0f\u4e3a: <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113341-688a03156c2f9.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u4e00\u822c\u03b1\u53d6\u503c1&#xff0c;m\u7684\u503c\u4e3a\u603b\u7279\u5f81\u6570\u91cf<\/p>\n<p>\u901a\u8fc7\u8fd9\u79cd\u65b9\u6cd5&#xff0c;\u5373\u4f7f\u67d0\u4e2a\u7279\u5f81\u5728\u8bad\u7ec3\u96c6\u4e2d\u4ece\u672a\u51fa\u73b0\u8fc7&#xff0c;\u5b83\u7684\u6982\u7387\u4e5f\u4e0d\u4f1a\u88ab\u4f30\u8ba1\u4e3a\u96f6&#xff0c;\u800c\u662f\u4f1a\u88ab\u8d4b\u4e88\u4e00\u4e2a\u5f88\u5c0f\u4f46\u975e\u96f6\u7684\u503c&#xff0c;\u4ece\u800c\u907f\u514d\u4e86\u6a21\u578b\u5728\u9762\u5bf9\u65b0\u6570\u636e\u65f6\u53ef\u80fd\u51fa\u73b0\u7684\u8fc7\u62df\u5408\u6216\u9884\u6d4b\u9519\u8bef\u3002<\/p>\n<p>\u6bd4\u5982\u8ba1\u7b97\u5224\u65ad\u65b0\u74dc(\u7eb9\u7406\u6e05\u6670&#xff0c;\u8272\u6cfd\u6de1\u767d&#xff0c;\u9f13\u58f0\u6c89\u95f7)\u662f\u597d\u548c\u574f\u65f6,\u56e0\u4e3a\u5728\u6837\u672c\u4e2d\u8272\u6cfd\u6de1\u767d\u6ca1\u6709\u51fa\u73b0,\u5bfc\u81f4\u51fa\u73b00\u503c,\u4f1a\u5f71\u54cd\u8ba1\u7b97\u7ed3\u679c,\u8981\u91c7\u7528\u62c9\u666e\u62c9\u65af\u5e73\u6ed1\u7cfb\u6570\u3002<\/p>\n<p>p(\u597d\u74dc|\u7eb9\u7406\u6e05\u6670&#xff0c;\u8272\u6cfd\u6de1\u767d&#xff0c;\u9f13\u58f0\u6c89\u95f7)<br \/>\n&#061;\u3010p(\u597d\u74dc)\u3011*\u3010p&#xff08;\u7eb9\u7406\u6e05\u6670|\u597d\u74dc&#xff09;*p&#xff08;\u8272\u6cfd\u6de1\u767d|\u597d\u74dc&#xff09;*p&#xff08;\u9f13\u58f0\u6c89\u95f7|\u597d\u74dc)\u3011\/\u3010p&#xff08;\u7eb9\u7406\u6e05\u6670&#xff09;*p&#xff08;\u8272\u6cfd\u6de1\u767d&#xff09;*p&#xff08;\u9f13\u58f0\u6c89\u95f7)\u3011<br \/>\np(\u574f\u74dc|\u7eb9\u7406\u6e05\u6670&#xff0c;\u8272\u6cfd\u6de1\u767d&#xff0c;\u9f13\u58f0\u6c89\u95f7)<br \/>\n&#061;\u3010p(\u574f\u74dc)\u3011*\u3010p&#xff08;\u7eb9\u7406\u6e05\u6670|\u574f\u74dc&#xff09;*p&#xff08;\u8272\u6cfd\u6de1\u767d|\u574f\u74dc&#xff09;*p&#xff08;\u9f13\u58f0\u6c89\u95f7|\u574f\u74dc)\u3011\/\u3010p&#xff08;\u7eb9\u7406\u6e05\u6670&#xff09;*p&#xff08;\u8272\u6cfd\u6de1\u767d&#xff09;*p&#xff08;\u9f13\u58f0\u6c89\u95f7)\u3011<br \/>\np&#xff08;\u7eb9\u7406\u6e05\u6670|\u597d\u74dc&#xff09;&#061; (4&#043;1)\/(6&#043;3)  # &#043;1\u662f\u56e0\u4e3a\u9632\u6b62\u96f6\u6982\u7387 &#043;3\u662f\u56e0\u4e3a\u67093\u4e2a\u7279\u5f81(\u7eb9\u7406,\u8272\u6cfd,\u9f13\u58f0)<br \/>\np&#xff08;\u8272\u6cfd\u6de1\u767d|\u597d\u74dc&#xff09;&#061; (0&#043;1)\/(6&#043;3)<br \/>\np&#xff08;\u9f13\u58f0\u6c89\u95f7|\u597d\u74dc) &#061; (2&#043;1)\/(6&#043;3)<br \/>\np&#xff08;\u7eb9\u7406\u6e05\u6670|\u574f\u74dc&#xff09;&#061; (1&#043;1)\/(4&#043;3)<br \/>\np&#xff08;\u8272\u6cfd\u6de1\u767d|\u574f\u74dc&#xff09;&#061; (0&#043;1)\/(4&#043;3)<br \/>\np&#xff08;\u9f13\u58f0\u6c89\u95f7|\u574f\u74dc) &#061; (1&#043;1)\/(4&#043;3)  <\/p>\n<h3>4.7 api\u4e0e\u793a\u4f8b<\/h3>\n<p><span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>datasets <span class=\"token keyword\">import<\/span> load_wine<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>model_selection <span class=\"token keyword\">import<\/span> train_test_split<br \/>\n<span class=\"token keyword\">from<\/span> sklearn<span class=\"token punctuation\">.<\/span>naive_bayes <span class=\"token keyword\">import<\/span> MultinomialNB<\/p>\n<p>wine<span class=\"token operator\">&#061;<\/span>load_wine<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nx<span class=\"token operator\">&#061;<\/span>wine<span class=\"token punctuation\">.<\/span>data<br \/>\ny<span class=\"token operator\">&#061;<\/span>wine<span class=\"token punctuation\">.<\/span>target<br \/>\nx_train<span class=\"token punctuation\">,<\/span>x_test<span class=\"token punctuation\">,<\/span>y_train<span class=\"token punctuation\">,<\/span>y_test<span class=\"token operator\">&#061;<\/span>train_test_split<span class=\"token punctuation\">(<\/span>wine<span class=\"token punctuation\">.<\/span>data<span class=\"token punctuation\">,<\/span>wine<span class=\"token punctuation\">.<\/span>target<span class=\"token punctuation\">,<\/span>test_size<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0.2<\/span><span class=\"token punctuation\">,<\/span>random_state<span class=\"token operator\">&#061;<\/span><span class=\"token number\">22<\/span><span class=\"token punctuation\">)<\/span><br \/>\nmodel<span class=\"token operator\">&#061;<\/span>MultinomialNB<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\nmodel<span class=\"token punctuation\">.<\/span>fit<span class=\"token punctuation\">(<\/span>x_train<span class=\"token punctuation\">,<\/span>y_train<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">.<\/span>score<span class=\"token punctuation\">(<\/span>x_test<span class=\"token punctuation\">,<\/span>y_test<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token comment\"># \u65b0\u6570\u636e\u9884\u6d4b<\/span><br \/>\ndata_new<span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">[<\/span>i <span class=\"token keyword\">for<\/span> i <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">13<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><br \/>\n<span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>model<span class=\"token punctuation\">.<\/span>predict<span class=\"token punctuation\">(<\/span>data_new<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/07\/20250730113341-688a03159f595.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<hr 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