{"id":1945,"date":"2024-05-29T13:05:22","date_gmt":"2024-05-29T05:05:22","guid":{"rendered":"https:\/\/17aitech.com\/?p=1945"},"modified":"2024-10-08T15:24:20","modified_gmt":"2024-10-08T07:24:20","slug":"%e3%80%90%e8%af%be%e7%a8%8b%e6%80%bb%e7%bb%93%e3%80%91day3%ef%bc%9a%e6%a6%82%e7%8e%87%e5%92%8c%e8%b4%9d%e5%8f%b6%e6%96%af%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=1945","title":{"rendered":"\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day3\uff1a\u6982\u7387\u548c\u8d1d\u53f6\u65af\u7b97\u6cd5"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 ez-toc-wrap-left-text counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">\u6587\u7ae0\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table 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ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/17aitech.com\/?p=1945\/#One_hot%E7%BC%96%E7%A0%81\" >One hot\u7f16\u7801<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E7%A6%BB%E6%95%A3%E9%87%8F%E8%AE%A1%E7%AE%97%E6%A6%82%E7%8E%87%E7%9A%84%E4%BE%8B%E5%AD%90\" >\u79bb\u6563\u91cf\u8ba1\u7b97\u6982\u7387\u7684\u4f8b\u5b50<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E8%BF%9E%E7%BB%AD%E5%9E%8B%E5%8F%98%E9%87%8F\" >\u8fde\u7eed\u578b\u53d8\u91cf<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E5%AE%9A%E4%B9%89\" >\u5b9a\u4e49<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E6%A6%82%E7%8E%87%E5%AF%86%E5%BA%A6%E5%87%BD%E6%95%B0\" >\u6982\u7387\u5bc6\u5ea6\u51fd\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E9%AB%98%E6%96%AF%E5%88%86%E5%B8%83%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83\" >\u9ad8\u65af\u5206\u5e03(\u6b63\u6001\u5206\u5e03)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E7%90%86%E8%AE%BA%E4%B8%AD%E7%9A%84%E6%A6%82%E7%8E%87%E4%B8%8E%E5%B7%A5%E7%A8%8B%E4%B8%AD%E7%9A%84%E6%A6%82%E7%8E%87\" >\u7406\u8bba\u4e2d\u7684\u6982\u7387\u4e0e\u5de5\u7a0b\u4e2d\u7684\u6982\u7387<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E8%BF%9E%E7%BB%AD%E9%87%8F%E8%AE%A1%E7%AE%97%E6%A6%82%E7%8E%87%E7%9A%84%E4%BE%8B%E5%AD%90\" 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ez-toc-heading-22\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E5%BA%94%E5%AF%B9%E7%AD%96%E7%95%A5\" >\u5e94\u5bf9\u7b56\u7565<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E5%85%AC%E5%BC%8F%E6%8E%A8%E5%AF%BC\" >\u516c\u5f0f\u63a8\u5bfc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95-2\" >\u8ba1\u7b97\u65b9\u6cd5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E4%BB%A3%E7%A0%81%E5%AE%9E%E7%8E%B0%E4%BD%BF%E7%94%A8sklearn\" >\u4ee3\u7801\u5b9e\u73b0(\u4f7f\u7528sklearn)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E4%BB%A3%E7%A0%81%E5%AE%9E%E7%8E%B0%E4%B8%8D%E4%BD%BF%E7%94%A8sklearn\" >\u4ee3\u7801\u5b9e\u73b0(\u4e0d\u4f7f\u7528sklearn)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E5%9F%BA%E6%9C%AC%E7%BB%9F%E8%AE%A1%E9%87%8F\" >\u57fa\u672c\u7edf\u8ba1\u91cf<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E5%9D%87%E5%80%BC%EF%BC%88Mean%EF%BC%89\" >\u5747\u503c\uff08Mean\uff09<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-29\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E6%A0%87%E5%87%86%E5%B7%AE%EF%BC%88Standard_Deviation%EF%BC%89\" >\u6807\u51c6\u5dee\uff08Standard Deviation\uff09<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-30\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E6%96%B9%E5%B7%AE%EF%BC%88Variance%EF%BC%89\" >\u65b9\u5dee\uff08Variance\uff09<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-31\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E5%8D%8F%E6%96%B9%E5%B7%AE%EF%BC%88Covariance%EF%BC%89\" >\u534f\u65b9\u5dee\uff08Covariance\uff09<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-32\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E7%9A%AE%E5%B0%94%E9%80%8A%E7%9B%B8%E5%85%B3%E5%87%BD%E6%95%B0\" >\u76ae\u5c14\u900a\u76f8\u5173\u51fd\u6570<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-33\" href=\"https:\/\/17aitech.com\/?p=1945\/#%E5%86%85%E5%AE%B9%E5%B0%8F%E7%BB%93\" >\u5185\u5bb9\u5c0f\u7ed3<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E5%89%8D%E8%A8%80\"><\/span>\u524d\u8a00<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u672c\u7ae0\u5185\u5bb9\u4e3b\u8981\u662f\u5b66\u4e60\u4e86\u6982\u7387\u76f8\u5173\u7684\u77e5\u8bc6\uff0c\u5305\u62ec\uff1a<code>\u6982\u7387<\/code>\u3001<code>\u79bb\u6563\u578b\u6982\u7387<\/code>\u8ba1\u7b97\u65b9\u6cd5\u3001<code>\u8fde\u7eed\u6027\u6982\u7387<\/code>\u8ba1\u7b97\u65b9\u6cd5\u3001<code>\u6761\u4ef6\u6982\u7387<\/code>\u7b49\u6570\u7406\u7edf\u8ba1\u77e5\u8bc6\uff0c\u540c\u65f6\u7ed3\u5408<code>\u9ad8\u65af\u8d1d\u53f6\u65af<\/code>\u7b97\u6cd5\uff0c\u5bf9\u9e22\u5c3e\u82b1\u8fdb\u884c\u6a21\u578b\u9884\u6d4b\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E6%A6%82%E7%8E%87%E4%B8%8E%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1\"><\/span>\u6982\u7387\u4e0e\u6570\u7406\u7edf\u8ba1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"%E6%A6%82%E7%8E%87\"><\/span>\u6982\u7387<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u6982\u7387\u662f\u63cf\u8ff0\u968f\u673a\u73b0\u8c61\u53d1\u751f\u53ef\u80fd\u6027\u7684\u6570\u5b66\u5de5\u5177\uff0c\u662f\u7528\u6765\u91cf\u5316\u4e0d\u786e\u5b9a\u6027\u7684\u6982\u5ff5\u3002\u6982\u7387\u548c\u6570\u7406\u7edf\u8ba1\u5728\u4eba\u5de5\u667a\u80fd\u4e2d\u7528\u4e8e\u8f85\u52a9\u5efa\u6a21\uff0c\u5176\u5efa\u6a21\u601d\u60f3\u5e7f\u6cdb\u5e94\u7528\u4e8e\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u4e0d\u540c\u6a21\u578b\uff0c\u5982\uff1a\u9ad8\u65af\u8d1d\u53f6\u65af\u3002<\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E6%A6%82%E5%BF%B5\"><\/span>\u6982\u5ff5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u6982\u7387(Probability)\u662f\u63cf\u8ff0\u968f\u673a\u4e8b\u4ef6\u53d1\u751f\u53ef\u80fd\u6027\u7684\u6570\u503c\uff0c\u901a\u5e38\u8868\u793a\u4e3a\u4ecb\u4e8e 0 \u5230 1 \u4e4b\u95f4\u7684\u5b9e\u6570\u3002\u6982\u7387\u4e3a 0 \u8868\u793a\u4e8b\u4ef6\u4e0d\u53ef\u80fd\u53d1\u751f\uff0c\u6982\u7387\u4e3a 1 \u8868\u793a\u4e8b\u4ef6\u4e00\u5b9a\u53d1\u751f\u3002<\/p>\n<ul>\n<li><code>\u6982\u7387<\/code>\u662f\u4e00\u79cd\u56fa\u6709\u5c5e\u6027\uff0c\u56e0\u4e3a\u6c42\u6982\u7387\u662f\u6bd4\u8f83\u96be\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u5f80\u5f80\u4f7f\u7528<code>\u9891\u7387<\/code><em>(frequency\uff0c\u5728\u5b9e\u9645\u89c2\u6d4b\u6216\u8bd5\u9a8c\u4e2d\uff0c\u67d0\u4e00\u4e8b\u4ef6\u53d1\u751f\u7684\u6b21\u6570\u4e0e\u603b\u8bd5\u9a8c\u6b21\u6570\u4e4b\u6bd4)<\/em>\u6765\u4ee3\u66ff\u3002<\/li>\n<li>\u5f53\u5b9e\u9a8c\u6b21\u6570\u8d8a\u6765\u8d8a\u591a\u65f6\uff0c<font color='red'><strong>\u9891\u7387<\/strong>\u5c31\u8d8b\u8fd1\u4e8e<strong>\u6982\u7387<\/strong><\/font>\u3002\u5728\u5de5\u7a0b\u5b9e\u8df5\u4e2d\uff0c\u6570\u636e\u91cf\u5f88\u5927\u65f6\uff0c\u6982\u7387\u76f4\u63a5\u62ff\u9891\u7387\u6765\u4ee3\u66ff\u5373\u53ef\u3002<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"%E5%9F%BA%E6%9C%AC%E7%89%B9%E6%80%A7\"><\/span>\u57fa\u672c\u7279\u6027<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\n<p>\u975e\u8d1f\u6027\uff1a\u6982\u7387\u503c\u59cb\u7ec8\u662f\u975e\u8d1f\u7684\uff0c\u5373\u6982\u7387\u503c\u4e0d\u4f1a\u4e3a\u8d1f\u6570\uff0c\u5373\uff1a1 &gt;= P(A) &gt;= 0<\/p>\n<\/li>\n<li>\n<p>\u89c4\u8303\u6027\uff1a\u6240\u6709\u53ef\u80fd\u4e8b\u4ef6\u7684\u6982\u7387\u4e4b\u548c\u7b49\u4e8e1\uff0c\u5373\uff1aP(A) + P(B) + P(B) &#8230; = 1<\/p>\n<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95\"><\/span>\u8ba1\u7b97\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"%E7%A6%BB%E6%95%A3%E5%9E%8B%E5%8F%98%E9%87%8F\"><\/span>\u79bb\u6563\u578b\u53d8\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h5><span class=\"ez-toc-section\" id=\"%E6%A6%82%E5%BF%B5-2\"><\/span>\u6982\u5ff5<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>\u79bb\u6563\u578b\u53d8\u91cf\u662f\u6307\u6709\u9650\u7684\u72b6\u6001\u4e2d\u9009\u4e00\u4e2a\u53d8\u91cf\u3002<\/li>\n<li>\u4e3e\u4f8b\uff1a\n<ul>\n<li>\u4f8b\u5982\uff1a\u4ea4\u901a\u706f\u6709\u7ea2\u706f\u3001\u7eff\u706f\u3001\u9ec4\u706f\uff1b<\/li>\n<li>\u4f8b\u5982\uff1a\u6027\u522b\u6709\u7537\u3001\u5973\u3001\u672a\u77e5\uff1b<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u79bb\u6563\u91cf\u4e00\u822c\u9700\u8981\u7f16\u7801\uff0c\u7f16\u7801\u7684\u65b9\u5f0f\u5e38\u89c1\u7684\u6709\u4e0b\u9762\u4e24\u79cd\uff1a<\/p>\n<h5><span class=\"ez-toc-section\" id=\"Zero_index%E7%BC%96%E7%A0%81\"><\/span>Zero index\u7f16\u7801<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>\u7f16\u7801\u662f\u4ece0\u5f00\u59cb\uff0c\u4f8b\u5982\uff1a0, 1, 2, 3, 4,&#8230;, N-1<\/li>\n<li>\u7f16\u7801\u672c\u8eab\u6709\u5927\u5c0f\uff0c\u4f46\u662f\u8fd9\u4e2a\u5927\u5c0f\u5e76\u6ca1\u6709\u6570\u5b66\u5185\u6db5<br \/>\n<blockquote>\n<p>\u4f8b\u5982\uff1a\u7f16\u78011\u548c\u7f16\u78014\uff0c\u5b83\u4eec\u53ea\u662f\u4e00\u4e2a\u7f16\u7801\uff0c\u5b83\u4eec\u662f\u5e73\u7b49\u7684\uff0c\u5e76\u4e0d\u5b58\u5728\u7c7b\u4f3c\u8003\u8bd5\u6210\u7ee9\u7684\u6392\u540d\uff0c\u8fd9\u4e2a\u5c31\u662f\u503c\u6ca1\u6709\u6570\u5b66\u5185\u6db5\u3002<\/p>\n<\/blockquote>\n<\/li>\n<\/ul>\n<h5><span class=\"ez-toc-section\" id=\"One_hot%E7%BC%96%E7%A0%81\"><\/span>One hot\u7f16\u7801<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>\u7f16\u7801\u662f\u5411\u91cf\u7f16\u7801\uff0c\u5176\u5f62\u5f0f\u4e00\u822c\u4e3a\uff1a\n<pre><code class=\"language-bash\">0: [1, 0, 0, 0, 0, ... ]\n1: [0, 1, 0, 0, 0, ... ]\n2: [0, 0, 1, 0, 0, ... ]<\/code><\/pre>\n<p>\u5907\u6ce8\uff1aone hot\u662f\u4e00\u79cd\u91cd\u8981\u7684\u7f16\u7801\uff0c\u5b83\u4ece\u4e00\u5f00\u59cb\u8ba4\u4e3a\u4eba\u4eba\u5e73\u7b49\uff0c\u8fd9\u4e00\u601d\u60f3\u5728\u81ea\u7136\u8bed\u8a00\u5904\u7406\u4e2d\u662f\u6838\u5fc3\u7406\u5ff5\u3002<\/p>\n<\/li>\n<\/ul>\n<h5><span class=\"ez-toc-section\" id=\"%E7%A6%BB%E6%95%A3%E9%87%8F%E8%AE%A1%E7%AE%97%E6%A6%82%E7%8E%87%E7%9A%84%E4%BE%8B%E5%AD%90\"><\/span>\u79bb\u6563\u91cf\u8ba1\u7b97\u6982\u7387\u7684\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>\u5047\u5b9a\u6709\u4e00\u4e2a\u79bb\u6563\u91cf\u505a\u5b9e\u9a8c\u5f97\u5230\u7684\u6570\u636e\u4e3a\uff1a[1, 2, 2, 2, 3, 1, 1]<\/li>\n<li>\u8ba1\u7b97\u65b9\u6cd5\uff1a(\u51fa\u73b0\u4e2a\u6570\/\u603b\u7684\u4e2a\u6570)<\/li>\n<li>\u6982\u7387\uff1a\n<ul>\n<li>\u4e8b\u4ef61\u51fa\u73b0\u7684\u6982\u7387P(1) = 3 \/ 8<\/li>\n<li>\u4e8b\u4ef62\u51fa\u73b0\u7684\u6982\u7387P(2) = 4 \/ 8<\/li>\n<li>\u4e8b\u4ef63\u51fa\u73b0\u7684\u6982\u7387P(3) = 1 \/ 8<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u4ee5\u9e22\u5c3e\u82b1\u4e3a\u4f8b\uff0c\u901a\u8fc7\u4ee3\u7801\u6c42\u5f97\u5404\u4e2a\u7c7b\u522b\u7684\u51fa\u73b0\u6982\u7387\uff0c\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<pre><code class=\"language-python\">from sklearn.datasets import load_iris\n\n# \u52a0\u8f7d\u5f00\u6e90\u5e93\u4e2d\u7684iris\u6570\u636e\u96c6\nX,y = load_iris(return_X_y=True)\n\nP_y0 = (y == 0).mean()\nP_y1 = (y == 1).mean()\nP_y2 = (y == 2).mean()\n\nprint(f&#039;\u7c7b\u522b0\u7684\u9e22\u5c3e\u82b1\u51fa\u73b0\u6982\u7387P(0) = &#039;, P_y0)\nprint(f&#039;\u7c7b\u522b1\u7684\u9e22\u5c3e\u82b1\u51fa\u73b0\u6982\u7387P(1) = &#039;, P_y1)\nprint(f&#039;\u7c7b\u522b2\u7684\u9e22\u5c3e\u82b1\u51fa\u73b0\u6982\u7387P(2) = &#039;, P_y2)<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716952246282.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716952246282.png\" alt=\"file\" \/><\/a><\/p>\n<blockquote>\n<p>\u8865\u5145\u77e5\u8bc6\u70b9\uff1a<br \/>\n\u4ee5\u4e0a\u8ba1\u7b97\u5f97\u5230\u7684\u662f<code>\u5148\u9a8c\u6982\u7387<\/code>\uff0c\u5148\u9a8c\u6982\u7387\u662f\u6307\u5df2\u7ecf\u5f62\u6210\u65e2\u5b9a\u4e8b\u5b9e\u7684\u6982\u7387\u5206\u5e03\uff0c\u5176\u662f\u4e0e\u751f\u4ff1\u6765\u7684\uff0c\u6539\u53d8\u4e0d\u4e86\u7684\u3002<\/p>\n<\/blockquote>\n<h4><span class=\"ez-toc-section\" id=\"%E8%BF%9E%E7%BB%AD%E5%9E%8B%E5%8F%98%E9%87%8F\"><\/span>\u8fde\u7eed\u578b\u53d8\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h5><span class=\"ez-toc-section\" id=\"%E5%AE%9A%E4%B9%89\"><\/span>\u5b9a\u4e49<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>\n<p>\u8fde\u7eed\u578b\u53d8\u91cf\u662f\u6307\u53ef\u4ee5\u53d6\u65e0\u9650\u4e2a\u6570\u503c\u7684\u53d8\u91cf\uff0c\u5176\u53d6\u503c\u53ef\u4ee5\u5728\u4e00\u4e2a\u533a\u95f4\u5185\u4efb\u610f\u53d6\u503c\u3002<\/p>\n<blockquote>\n<p>\u4f8b\u5982\uff1a<br \/>\n[0\uff0c 1]\uff1a\u4e00\u4e2a\u4ece 0 \u5230 1 \u7684\u8fde\u7eed\u91cf\u4e2d\u95f4\u53ef\u4ee5\u6709\u65e0\u6570\u4e2a\u91c7\u6837\u7ed3\u679c<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<p>\u4e25\u683c\u610f\u4e49\u4e0a\uff1a<\/p>\n<ul>\n<li>\u5bf9\u4e8e\u8fde\u7eed\u91cf\u7684\u67d0\u4e2a\u5355\u70b9(\u4f8b\u5982\uff1a0.6)\uff0c\u8fd9\u4e2a\u70b9\u7684\u6982\u7387\u662f0(\u56e0\u4e3a\u5bbd\u5ea6\u4e3a0\uff0c\u6c42\u79ef\u5206\u4e3a0)<\/li>\n<li>\u8fde\u7eed\u91cf\u7684\u6982\u7387\u662f<code>\u6982\u7387\u5bc6\u5ea6\u51fd\u6570<\/code>\u79ef\u5206\uff0c\u5355\u70b9\u7684\u79ef\u5206\u4e0a\u4e0b\u9650\u662f0<br \/>\n<blockquote>\n<p>\u7406\u8bba\u4e2d\u7684\u5b9a\u4e49\uff0c\u5728\u73b0\u5b9e\u4e2d\u662f\u4e0d\u592a\u53ef\u80fd\u7684\uff0c\u4f8b\u5982\uff1a\u5728\u7269\u7406\u4e2d\u7ecf\u5e38\u63d0\u5230\u5728\u5149\u6ed1\u7684\u5e73\u9762\u4e0a\u6c42\u5f97&#8230;.\uff0c\u5b8c\u5168\u5149\u6ed1\u7684\u5e73\u9762\u5728\u73b0\u5b9e\u4e2d\u662f\u4e0d\u5b58\u5728\u7684\u3002\u6240\u4ee5\uff0c\u5728\u5de5\u7a0b\u4e2d\u8981\u8fdb\u884c\u5316\u7b80\uff0c\u800c\u4eba\u5de5\u667a\u80fd\u662f\u7eaf\u7406\u8bba\u6570\u5b66\u7684\u5de5\u7a0b\u5316\u7b80\u3002<\/p>\n<\/blockquote>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h5><span class=\"ez-toc-section\" id=\"%E6%A6%82%E7%8E%87%E5%AF%86%E5%BA%A6%E5%87%BD%E6%95%B0\"><\/span>\u6982\u7387\u5bc6\u5ea6\u51fd\u6570<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p>\u4e0a\u8ff0\u5bf9\u8fde\u7eed\u91cf\u7684\u6982\u7387\u4ecb\u7ecd\u65f6\uff0c\u63d0\u5230\u4e86\u4e00\u4e2a\u91cd\u8981\u7684\u6982\u5ff5\u4e3a<code>\u6982\u7387\u5bc6\u5ea6\u51fd\u6570<\/code>(PDF, Probability Density Function)<\/p>\n<ul>\n<li>\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u662f\u6982\u7387\u7684\u5bfc\u51fd\u6570(\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u2192\u6c42\u79ef\u5206\u2192\u6982\u7387)<\/li>\n<li>\u6982\u7387\u662f\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u7684\u79ef\u5206(\u6982\u7387\u2192\u6c42\u5fae\u5206\u2192\u6982\u7387\u5bc6\u5ea6\u51fd\u6570)<\/li>\n<li>\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u662f\u6bd4\u8f83\u5e38\u89c1\u7684\uff0c\u5176\u4e2d\u4fbf\u6709\uff1a\u9ad8\u65af\u5206\u5e03<\/li>\n<\/ul>\n<h5><span class=\"ez-toc-section\" id=\"%E9%AB%98%E6%96%AF%E5%88%86%E5%B8%83%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83\"><\/span>\u9ad8\u65af\u5206\u5e03(\u6b63\u6001\u5206\u5e03)<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>\n<p>\u5b9a\u4e49\uff1a\u9ad8\u65af\u5206\u5e03\u662f\u4e00\u79cd\u8fde\u7eed\u578b\u6982\u7387\u5206\u5e03\uff0c\u5176\u66f2\u7ebf\u5448\u949f\u5f62\uff0c\u5bf9\u79f0\u5206\u5e03\u5728\u5747\u503c\u5904\uff0c\u5e76\u7531\u5747\u503c\u548c\u65b9\u5dee\u4e24\u4e2a\u53c2\u6570\u5b8c\u5168\u63cf\u8ff0\u3002<\/p>\n<\/li>\n<li>\n<p>\u9ad8\u65af\u5206\u5e03\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a<\/p>\n<pre><code class=\"language-katex\">f(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma} e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}<\/code><\/pre>\n<p>\u5176\u4e2d\uff0c<code class=\"katex-inline\">\\mu<\/code>\u662f\u5747\u503c\uff0c<code class=\"katex-inline\">\\sigma<\/code>\u662f\u6807\u51c6\u5dee\u3002<\/p>\n<\/li>\n<li>\n<p>Python\u7ed8\u5236\u9ad8\u65af\u5206\u5e03\uff1a<\/p>\n<\/li>\n<\/ul>\n<pre><code class=\"language-python\">import numpy as np\nfrom matplotlib import pyplot as plt\n\ndef gaussian(x, mu, sigma):\n    &quot;&quot;&quot;\n    \u8ba1\u7b97\u9ad8\u65af\u5206\u5e03\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u503c\n\n    \u53c2\u6570\uff1a\n    x: \u968f\u673a\u53d8\u91cf\n    mu: \u5747\u503c\n    sigma: \u6807\u51c6\u5dee\n\n    \u8fd4\u56de\uff1a\n    \u9ad8\u65af\u5206\u5e03\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u503c\n    &quot;&quot;&quot;\n    return 1\/(np.sqrt(2*np.pi)*sigma) * np.exp(-(x - mu)**2 \/ (2*sigma**2))\n\n# \u6d4b\u8bd5\u9ad8\u65af\u5206\u5e03\u51fd\u6570\nx = np.linspace(start=-5, stop=5, num=100)\nmu = 0\nsigma = 1\n\n# \u53ef\u89c6\u5316\u9ad8\u65af\u5206\u5e03\nplt.plot(x, gaussian(x, mu=0, sigma=1), label=&quot;$\\mu=0, \\sigma=1$&quot;)\nplt.plot(x, gaussian(x, mu=1, sigma=1), label=&quot;$\\mu=1, \\sigma=1$&quot;)\nplt.plot(x, gaussian(x, mu=0, sigma=2), label=&quot;$\\mu=0, \\sigma=2$&quot;)\n\nplt.title(&#039;Gaussian Distribution&#039;)\nplt.xlabel(&#039;x&#039;)\nplt.ylabel(&#039;Probability Density Function&#039;)\nplt.grid(True)\nplt.legend()\nplt.show()<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716954511425.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716954511425.png\" alt=\"file\" \/><\/a><\/p>\n<h5><span class=\"ez-toc-section\" id=\"%E7%90%86%E8%AE%BA%E4%B8%AD%E7%9A%84%E6%A6%82%E7%8E%87%E4%B8%8E%E5%B7%A5%E7%A8%8B%E4%B8%AD%E7%9A%84%E6%A6%82%E7%8E%87\"><\/span>\u7406\u8bba\u4e2d\u7684\u6982\u7387\u4e0e\u5de5\u7a0b\u4e2d\u7684\u6982\u7387<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p>\u5982\u679c\u8981\u6c42\u4e00\u4e2a\u9ad8\u65af\u5206\u5e03\u51fd\u6570\u4e0a\u67d0\u4e00\u70b9\u7684\u6982\u7387\uff0c\u5176\u65b9\u6cd5\u4e3a\u6c42\u66f2\u7ebf\u7684\u79ef\u5206\uff1a<br \/>\n<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716955011374.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716955011374.png\" alt=\"file\" \/><\/a><\/p>\n<blockquote>\n<p>\u5982\u679c\u6309\u7167\u7406\u8bba\u7684\u65b9\u6cd5\u662f\u6c42\u4e0d\u4e86\u6982\u7387\u7684(\u56e0\u4e3a\u7406\u8bba\u4e2d\u4efb\u610f\u4e00\u70b9\u7684\u5bbd\u5ea6\u4e3a0\uff0c\u8fdb\u800c\u6982\u7387\u4e5f\u4e3a0)\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u8fdb\u884c\u5de5\u7a0b\u5316\u7b80\u3002<\/p>\n<\/blockquote>\n<p><strong>\u6838\u5fc3\u601d\u60f3<\/strong>\uff1a\u5e38\u89c4\u60c5\u51b5\u4e0b\uff0c\u6a21\u578b\u4e2d\u5bf9\u6982\u7387\u7684\u4f7f\u7528\uff0c<\/p>\n<ul>\n<li><font color='red'>\u91cd\u5728\u6bd4\u8f83\u6982\u7387\u7684\u5927\u5c0f<\/font>\uff0c\u800c\u4e0d\u662f\u8ba1\u7b97\u6982\u7387\u7684\u5177\u4f53\u6570\u503c\u662f\u591a\u5c11<\/li>\n<li>\u6c42\u8fde\u7eed\u91cf\u7684\u6982\u7387\u65f6\uff0c\u5f80\u5f80\u4f7f\u7528\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u7684\u503c\u6765\u4ee3\u66ff\u6982\u7387\u7684\u503c(\u539f\u56e0\uff1a\u6c42\u5f97\u662f\u76f8\u5bf9\u5927\u5c0f\uff0c\u800c\u4e0d\u662f\u7edd\u5bf9\u5927\u5c0f)<\/li>\n<\/ul>\n<h5><span class=\"ez-toc-section\" id=\"%E8%BF%9E%E7%BB%AD%E9%87%8F%E8%AE%A1%E7%AE%97%E6%A6%82%E7%8E%87%E7%9A%84%E4%BE%8B%E5%AD%90\"><\/span>\u8fde\u7eed\u91cf\u8ba1\u7b97\u6982\u7387\u7684\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>\u5047\u5b9a\u6709\u4e00\u4e2a\u8fde\u7eed\u91cf\u91c7\u6837\u6570\u636e\uff1a[1, 2, 2, 2, 3, 1, 1]<\/li>\n<li>\u8ba1\u7b97\u65b9\u6cd5\uff1a\n<ol>\n<li>\u8ba1\u7b97\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u6765\u4ee3\u66ff<\/li>\n<li>\u7531\u4e8e\u4e0a\u8ff0\u91c7\u6837\u6570\u636e\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u4e0d\u53ef\u77e5\uff0c\u6240\u4ee5\u8fdb\u4e00\u6b65\u5de5\u7a0b\u5316\u7b80<\/li>\n<li>\u7531\u4e8e\u81ea\u7136\u754c\u666e\u904d\u90fd\u662f\u9ad8\u65af\u5206\u5e03\uff0c\u6240\u4ee5\u5047\u5b9a\u5176\u662f\u9ad8\u65af\u5206\u5e03\u5373\u53ef<\/li>\n<\/ol>\n<\/li>\n<li>\u6c42\u6982\u7387\u7684\u4ee3\u7801\uff1a<\/li>\n<\/ul>\n<pre><code class=\"language-python\">import numpy as np\n\ndef gaussian(x, mu, sigma):\n    &quot;&quot;&quot;\n    \u8ba1\u7b97\u9ad8\u65af\u5206\u5e03\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u503c\n\n    \u53c2\u6570\uff1a\n    x: \u968f\u673a\u53d8\u91cf\n    mu: \u5747\u503c\n    sigma: \u6807\u51c6\u5dee\n\n    \u8fd4\u56de\uff1a\n    \u9ad8\u65af\u5206\u5e03\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u503c\n    &quot;&quot;&quot;\n    return 1\/(np.sqrt(2*np.pi)*sigma) * np.exp(-(x - mu)**2 \/ (2*sigma**2))\n\n# \u91c7\u6837\u6570\u636e\nlogitis = np.array([1, 2, 2, 2, 2, 3, 1, 1])\n\n# mu\u5373\u4e3a\u91c7\u6837\u6570\u636e\u7684\u5747\u503c\nmu = logitis.mean()\n\n# sigma\u5373\u4e3a\u91c7\u6837\u6570\u636e\u7684\u6807\u51c6\u5dee\nsigma = logitis.std()\n\n# \u6c42P(1)\u7684\u6982\u7387\nP1 = gaussian(x=1, mu=mu, sigma=sigma)\n# \u6c42P(2)\u7684\u6982\u7387\nP2 = gaussian(x=2, mu=mu, sigma=sigma)\n# \u6c42P(3)\u7684\u6982\u7387\nP3 = gaussian(x=3, mu=mu, sigma=sigma)\n\nprint(f&#039;P(1)\u7684\u6982\u7387\u4e3a\uff1a&#039;,P1)\nprint(f&#039;P(2)\u7684\u6982\u7387\u4e3a\uff1a&#039;,P2)\nprint(f&#039;P(3)\u7684\u6982\u7387\u4e3a\uff1a&#039;,P3)<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716956246739.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716956246739.png\" alt=\"file\" \/><\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E6%9D%A1%E4%BB%B6%E6%A6%82%E7%8E%87\"><\/span>\u6761\u4ef6\u6982\u7387<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"%E5%AE%9A%E4%B9%89-2\"><\/span>\u5b9a\u4e49<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u6761\u4ef6\u6982\u7387\u662f\u6307\u5728\u7ed9\u5b9a\u53e6\u4e00\u4e2a\u4e8b\u4ef6\u53d1\u751f\u7684\u524d\u63d0\u4e0b\uff0c\u67d0\u4e00\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u3002<\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E8%A1%A8%E7%A4%BA%E6%96%B9%E6%B3%95\"><\/span>\u8868\u793a\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u7ed9\u5b9a\u4e8b\u4ef6 B \u53d1\u751f\u7684\u6761\u4ef6\u4e0b\uff0c\u4e8b\u4ef6 A \u53d1\u751f\u7684\u6982\u7387\u79f0\u4e3a\u4e8b\u4ef6 A \u5728\u4e8b\u4ef6 B \u6761\u4ef6\u4e0b\u7684\u6761\u4ef6\u6982\u7387\uff0c\u8bb0\u4f5c<code class=\"katex-inline\">P(A|B)<\/code><\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E4%B8%80%E4%B8%AA%E4%BE%8B%E5%AD%90\"><\/span>\u4e00\u4e2a\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\u6751\u91cc\u9009\u6751\u957f\uff0c\u5019\u9009\u4eba\u6709:<br \/>\n<blockquote>\n<ul>\n<li>\u674e\uff1a1, 2,  3;<\/li>\n<li>\u738b\uff1a1, 2\uff1b<\/li>\n<li>\u5218\uff1a1<\/li>\n<\/ul>\n<\/blockquote>\n<\/li>\n<\/ul>\n<p>P(\u674e1)\u5f53\u9009\u7684\u6982\u7387\uff1a<\/p>\n<ul>\n<li>\u6ca1\u6709\u6697\u7bb1\u64cd\u4f5c\u4e0b\uff0c\u674e1\u5f53\u9009\u7684\u6982\u7387\u662f1\/6\uff1b<\/li>\n<li>\u5982\u6709\u6697\u7bb1\u64cd\u4f5c(\u59d3\u674e\u7684\u5f53\u9009)\uff0c\u674e1\u5f53\u9009\u6982\u7387\u4f4e1\/3\u3002<br \/>\n\u4ee5\u4e0a\u95ee\u9898\u662f\u5178\u578b\u7684\u6761\u4ef6\u6982\u7387\u3002<\/p>\n<blockquote>\n<p>\u6837\u672c\u91cd\u7ec4\uff1a\u4e0a\u4f8b\u4e2d\uff0c\u5df2\u77e5\u59d3\u674e\u7684\u5f53\u9009\u65f6\uff0c\u8fdb\u884c\u4e86\u91cd\u65b0\u5212\u5206\u6837\u672c\u7a7a\u95f4\u3002<\/p>\n<\/blockquote>\n<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"%E5%BA%94%E5%AF%B9%E7%AD%96%E7%95%A5\"><\/span>\u5e94\u5bf9\u7b56\u7565<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u6839\u636e\u6761\u4ef6\uff0c\u91cd\u65b0\u5212\u5206\u6837\u672c\u7a7a\u95f4\uff0c\u5c06\u4e0d\u6ee1\u8db3\u6761\u4ef6\u7684\u5e72\u6389\uff0c\u7136\u540e\u518d\u8ba1\u7b97\u6982\u7387\u3002<\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E5%85%AC%E5%BC%8F%E6%8E%A8%E5%AF%BC\"><\/span>\u516c\u5f0f\u63a8\u5bfc<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><center>\u7531\u516c\u5f0f\u53ef\u5f97<\/center><\/p>\n<p><code class=\"katex-inline\">P(A|B) = P(AB) \/ P(B)<\/code><br \/>\n<code class=\"katex-inline\">P(B|A) = P(AB) \/ P(A)<\/code><\/p>\n<p><center>\u8fdb\u4e00\u6b65\u5316\u7b80<\/center><br \/>\n<center>\u2193<\/center><\/p>\n<p><code class=\"katex-inline\">P(A|B) * P(B)= P(AB)<\/code><br \/>\n<code class=\"katex-inline\">P(B|A) * P(A)= P(AB)<\/code><\/p>\n<p><center>\u7531\u4e8e\u5de6\u53f3\u4e24\u8fb9\u76f8\u7b49\uff0c\u8fdb\u4e00\u6b65\u8f6c\u6362<\/center><br \/>\n<center>\u2193<\/center><\/p>\n<p><code class=\"katex-inline\">P(A|B) = P(B|A) * P(A) \/ P(B)<\/code><\/p>\n<blockquote>\n<p>\u4ee5\u4e0a\u63a8\u5bfc\u7ed3\u679c\u5373\u4e3aP(A|B)\u4e3aB\u7684\u6761\u4ef6\u4e0bA\u53d1\u751f\u7684\u6982\u7387\u8ba1\u7b97\u65b9\u6cd5<\/p>\n<\/blockquote>\n<p><center>\u5c06\u5b57\u6bcd\u8fdb\u884c\u66ff\u6362\uff08A\u2192y\uff0cB\u2192x\uff09<\/center><br \/>\n<center>\u2193<\/center><\/p>\n<p><code class=\"katex-inline\">P(y|X) = P(X|y) P(y) \/ P(X)<\/code><\/p>\n<p><center>\u8fdb\u4e00\u6b65\u5b57\u6bcd\u66ff\u6362\uff08y\u66ff\u6362\u4e3ay0\uff09<\/center><br \/>\n<center>\u2193<\/center><\/p>\n<p><code class=\"katex-inline\">P(y0|X) = P(X|y0) P(y0) \/ P(X)<\/code><\/p>\n<ul>\n<li>X\uff1a\u4e00\u4e2a\u8f93\u5165\u6837\u672c\u7684\u7279\u5f81\uff0c\u5305\u62ec[x1, x2, x3 \u2026]<\/li>\n<li>y0\uff1a\u7b2c0\u7c7b<\/li>\n<li>\u542b\u4e49\uff0c\u5728\u8f93\u5165\u6837\u672cX\u7684\u60c5\u51b5\u4e0b\uff0c\u7b2c0\u7c7b\u7684\u6982\u7387<\/li>\n<\/ul>\n<p><center>\u540c\u7406\u53ef\u5f97<\/center><br \/>\n<center>\u2193<\/center><\/p>\n<p><code class=\"katex-inline\">P(y1|X) = P(X|y1) P(y1) \/ P(X)<\/code><br \/>\n<code class=\"katex-inline\">P(y2|X) = P(X|y2) P(y2) \/ P(X)<\/code><\/p>\n<p>\u5728N\u5206\u7c7b\u95ee\u9898\u4e0a\uff0c\u901a\u8fc7\u8ba1\u7b97\u8f93\u5165\u6837\u672c\u6761\u4ef6\u4e0b\u4e0d\u540c\u7c7b\u522b(y0,y1,y2..yn)\u7684\u6982\u7387\uff0c\u7136\u540e\u9009\u62e9\u6982\u7387\u6700\u5927\u7684\u90a3\u4e2a\u6982\u7387\u4f5c\u4e3a\u8f93\u51fa\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5373\u4e3a\u8d1d\u53f6\u65af\u7b97\u6cd5\uff0c\u4e5f\u53eb\u9ad8\u65af\u8d1d\u53f6\u65af\u7b97\u6cd5\u3002<\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95-2\"><\/span>\u8ba1\u7b97\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><center>\u63a5\u7740\u4e0a\u9762\u7684\u63a8\u5bfc\u516c\u5f0f\u8fdb\u884c\u8ba1\u7b97<\/center><\/p>\n<p><code class=\"katex-inline\">P(y0|X) = P(X|y0) P(y0) \/ P(X)<\/code><br \/>\n<code class=\"katex-inline\">P(y1|X) = P(X|y1) P(y1) \/ P(X)<\/code><br \/>\n<code class=\"katex-inline\">P(y2|X) = P(X|y2) P(y2) \/ P(X)<\/code><\/p>\n<p><center>\u7531\u4e8e\u4e0a\u4fa7\u516c\u5f0f\u53f3\u4fa7\u7edf\u4e00\u90fd\u6709P(X)\uff0c\u6240\u4ee5\u57fa\u4e8e\u975e\u8d1f\u6027\u539f\u7406\uff0c\u53ef\u4ee5\u5c06\u4e0a\u8ff0\u516c\u5f0f\u7b80\u5316\u4e3a<\/center><br \/>\n<center>\u2193<\/center><\/p>\n<p><code class=\"katex-inline\">P(y0|X) = P(X|y0) P(y0)<\/code><br \/>\n<code class=\"katex-inline\">P(y1|X) = P(X|y1) P(y1)<\/code><br \/>\n<code class=\"katex-inline\">P(y2|X) = P(X|y2) P(y2)<\/code><\/p>\n<p>\u7b80\u5316\u540e\u7684\u516c\u5f0f\u4e2d:<\/p>\n<ul>\n<li>P(y0)\u3001P(y1)\u3001P(y2)\u7684\u6982\u7387\u6c42\u89e3\u65b9\u6cd5\u5bb9\u6613\u6c42\u5f97(\u56e0\u4e3a\u662f\u79bb\u6563\u91cf\uff0c\u6240\u4ee5\u4f7f\u7528\u51fa\u73b0\u6b21\u6570\/\u603b\u6b21\u6570\u5c31\u53ef\u6c42\u5f97)\u3002<\/li>\n<li>P(X|y0)\u7684\u6982\u7387\u6c42\u89e3\u65b9\u6cd5\uff1a\n<ul>\n<li>\u5c06\u7c7b\u522b\u4e3a1\u548c2\u7684\u6837\u672c\u8e22\u51fa\u53bb\uff0c\u7136\u540e\u6c42\u5728\u7c7b\u522b0\u7684\u60c5\u51b5\u4e0b&gt; X\u7279\u5f81\u7684\u6982\u7387\u3002<\/li>\n<li>\u7531\u4e8eX\u662f\u4e00\u5806\u7279\u5f81\uff0c\u6240\u4ee5P(X|y0)\u4ee3\u8868\u5728\u7c7b\u522b0\u7684\u6761\u4ef6&gt; \u4e0b\uff0cx1\u3001x2\u3001x3\u8fd9\u4e9b\u72ec\u7acb\u7279\u5f81\u540c\u65f6\u53d1\u751f\u7684\u6982\u7387<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><center>\u56e0\u6b64\uff0c\u516c\u5f0f\u8fdb\u4e00\u6b65\u8f6c\u6362\u4e3a<\/center><br \/>\n<center>\u2193<\/center><\/p>\n<p><code class=\"katex-inline\">P(y0|X) = P(x1,x2,x3..|y0) P(y0)<\/code><br \/>\n<code class=\"katex-inline\">P(y1|X) = P(x1,x2,x3..|y1) P(y1)<\/code><br \/>\n<code class=\"katex-inline\">P(y2|X) = P(x1,x2,x3..|y2) P(y2)<\/code><\/p>\n<p><center>\u7531\u4e8e\u662f\u72ec\u7acb\u7279\u5f81\uff0c\u6240\u4ee5\u53ef\u4ee5\u5355\u72ec\u8ba1\u7b97\u4e4b\u540e\u518d\u8fdb\u884c\u4e58\u79ef\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u5c06\u4e0a\u8ff0\u8ba1\u7b97\u516c\u5f0f\u62c6\u5f00\u4e3a\uff1a<\/center><br \/>\n<center>\u2193<\/center><\/p>\n<p><code class=\"katex-inline\">P(y0|X) = P(x1|y0)P(x2|y0)P(x3|y0)...P(xn|y0) P(y0)<\/code><br \/>\n<code class=\"katex-inline\">P(y1|X) = P(x1|y1)P(x2|y1)P(x3|y1)...P(xn|y1) P(y1)<\/code><br \/>\n<code class=\"katex-inline\">P(y2|X) = P(x1|y2)P(x2|y2)P(x3|y2) ...P(xn|y2)P(y2)<\/code><\/p>\n<p>\u4e0a\u8ff0\u516c\u5f0f\u4e2d\uff0cP(x1|y0)\u3001P(x2|y0)&#8230;\u5373\u53ef\u4f7f\u7528\u9ad8\u65af\u6a21\u62df\u6c42\u5f97\u6982\u7387\u3002<\/p>\n<blockquote>\n<p>\u9ad8\u65af\u8d1d\u53f6\u65af\u53ea\u80fd\u8fdb\u884c\u5206\u7c7b\uff0c\u5176\u867d\u7136\u6548\u679c\u5dee\u4e00\u4e9b(\u56e0\u4e3a\u8ba4\u4e3a\u90fd\u5c5e\u4e8e\u9ad8\u65af\u5206\u5e03)\uff0c\u4f46\u662f\u8ba1\u7b97\u901f\u5ea6\u975e\u5e38\u5feb\u3002<br \/>\n\u5728\u8ba1\u7b97\u673a\u65e9\u671f\u65f6\u4ee3\uff0c\u5728\u8fdb\u884c\u5206\u7c7b\u65f6\u4f7f\u7528\u7684\u662f\u9ad8\u65af\u8d1d\u53f6\u65af\uff0c\u5f53\u65f6\u8fd8\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002<\/p>\n<\/blockquote>\n<h4><span class=\"ez-toc-section\" id=\"%E4%BB%A3%E7%A0%81%E5%AE%9E%E7%8E%B0%E4%BD%BF%E7%94%A8sklearn\"><\/span>\u4ee3\u7801\u5b9e\u73b0(\u4f7f\u7528sklearn)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<pre><code class=\"language-python\">from sklearn.datasets import load_iris\nfrom sklearn.model_selection import train_test_split\n\n# \u52a0\u8f7d\u5f00\u6e90\u5e93\u4e2d\u7684iris\u6570\u636e\u96c6\nX,y = load_iris(return_X_y=True)\n\n# \u5207\u5206\u6570\u636e\u96c6\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, \n                                                    shuffle=True, \n                                                    random_state=0) \n\n# \u5f15\u5165\u9ad8\u65af\u8d1d\u53f6\u65af\u6a21\u578b\nfrom sklearn.naive_bayes import GaussianNB\n\n# 1,\u6784\u5efa\u6a21\u578b\ngnb = GaussianNB()\n\n# 2,\u8bad\u7ec3\u6a21\u578b\ngnb.fit(X=X_train, y=y_train)\n\n# 3, \u9884\u6d4b\uff0c\u5c06\u7ed3\u679c\u4fdd\u5b58\u5230y_pred\ny_pred = gnb.predict(X=X_test)\n\nacc = (y_pred == y_test).mean()\n\nacc<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716963011848.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716963011848.png\" alt=\"\" \/><\/a><\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E4%BB%A3%E7%A0%81%E5%AE%9E%E7%8E%B0%E4%B8%8D%E4%BD%BF%E7%94%A8sklearn\"><\/span>\u4ee3\u7801\u5b9e\u73b0(\u4e0d\u4f7f\u7528sklearn)<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<pre><code class=\"language-python\">import numpy as np\n\nclass MyGaussianNB(object):\n    def fit(self, X, y):\n        self.X = X\n        self.y = y\n\n        #\u6839\u636e\u8bad\u7ec3\u6570\u636e\u96c6 y \u4e2d\u7684\u7c7b\u522b\u6807\u7b7e\uff0c\u627e\u51fa\u6240\u6709\u4e0d\u91cd\u590d\u7684\u7c7b\u522b\uff0c\u5e76\u5c06\u5176\u5b58\u50a8\u5728 self.classes\n        self.classes = np.unique(y)   \n        self.parameters = []\n\n        # \u8ba1\u7b97\u6bcf\u4e2a\u7c7b\u522b\u7684\u5747\u503c\u548c\u6807\u51c6\u5dee\n        # \u5bf9 y \u4e2d\u7c7b\u522b\u8fdb\u884c\u904d\u5386\uff0c\u5c06\u7d22\u5f15\u548c\u5bf9\u5e94\u7684\u5143\u7d20\u503c\u5206\u522b\u8d4b\u7ed9\u53d8\u91cf i \u548c c\n        for i, c in enumerate(self.classes):\n            # \u53d6\u5bf9\u5e94 y \u7c7b\u522b\u4e2d\u7684 X\n            X_c = X[y == c]\n            self.parameters.append([])\n\n            # \u904d\u5386 X \u7684\u6bcf\u4e00\u5217\u6570\u636e,\u5c06\u8ba1\u7b97\u7684\u5747\u503c\u548c\u6807\u51c6\u5dee\u4fdd\u5b58\u5230parameters\u4e2d\n            for col in X_c.T:\n                parameters = {&quot;mean&quot;: col.mean(), &quot;std&quot;: col.std()}\n                self.parameters[i].append(parameters)\n\n    def _calculate_likelihood(self, mean, std, x):\n        # \u8ba1\u7b97\u9ad8\u65af\u5206\u5e03\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u503c\n        return (1 \/ (np.sqrt(2 * np.pi) * std)) * np.exp(-((x - mean) ** 2 \/ (2 * std ** 2)))\n\n    def _calculate_prior(self, c):\n        # \u8ba1\u7b97\u5148\u9a8c\u6982\u7387\n        return np.mean(self.y == c)\n\n    def predict(self, X):\n        preds = []\n\n        # \u904d\u5386 X \u5143\u7d20\n        for x in X:\n            posteriors = []\n\n            # \u4f9d\u6b21\u904d\u5386 y \u7c7b\u522b\n            for i, c in enumerate(self.classes):\n                likelihood = 1\n                # \u4f7f\u7528\u4e4b\u524d\u5df2\u7ecf\u8ba1\u7b97\u597d\u7684\u5747\u503c\u548c\u65b9\u5dee\uff0c\u4ee3\u5165\u5230\u9ad8\u65af\u5bc6\u5ea6\u51fd\u6570\u4e2d\u8ba1\u7b97\u6982\u7387\u503c\n                for j, param in enumerate(self.parameters[i]):\n                    likelihood *= self._calculate_likelihood(param[&quot;mean&quot;], param[&quot;std&quot;], x[j])\n\n                # \u8ba1\u7b97P(y0)\u3001P(y1)\u3001P(y2)\u7b49\u5148\u9a8c\u6982\u7387\n                prior = self._calculate_prior(c)\n\n                # \u8ba1\u7b97P(x1|y0)P(x2|y0)P(x3|y0)...P(xn|y0) P(y0)\u7684\u4e58\u79ef\n                posterior = prior * likelihood\n                # \u8ba1\u7b97\u7ed3\u679c\u6dfb\u52a0\u5230posteriors\u5217\u8868\u4e2d\uff0c\u7528\u4e8e\u540e\u7eed\u6c42\u6700\u5927\u503c\n                posteriors.append(posterior)\n\n            # \u6839\u636eposteriors\u4e2d\u7684\u6700\u5927\u503c\u7684\u7d22\u5f15\uff0c\u5728\u7c7b\u522b\u5217\u8868 self.classes \u4e2d\u627e\u5230\u5bf9\u5e94\u7684\u7c7b\u522b\uff0c\n            # \u5e76\u5c06\u5176\u6dfb\u52a0\u5230\u9884\u6d4b\u7ed3\u679c\u5217\u8868 preds \u4e2d\n            preds.append(self.classes[np.argmax(posteriors)])\n\n        return preds\n<\/code><\/pre>\n<p>\u8c03\u7528\u6a21\u578b<\/p>\n<pre><code class=\"language-python\"># 1,\u6784\u5efa\u6a21\u578b\nmygnb = MyGaussianNB()\n\n# 2,\u8bad\u7ec3\u6a21\u578b\nmygnb.fit(X=X_train, y=y_train)\n\n# 3, \u9884\u6d4b\uff0c\u5c06\u7ed3\u679c\u4fdd\u5b58\u5230y_pred\ny_pred = mygnb.predict(X=X_test)\n\nacc = (y_pred == y_test).mean()\n\nacc<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716964450764.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716964450764.png\" alt=\"file\" \/><\/a><br \/>\n\u8ba1\u7b97\u7ed3\u679c\u4e5f\u4e3a1.0\uff0cmyGaussianNB\u4e0esklearn\u7684GaussianNB\u8ba1\u7b97\u7ed3\u679c\u4e00\u81f4\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E5%9F%BA%E6%9C%AC%E7%BB%9F%E8%AE%A1%E9%87%8F\"><\/span>\u57fa\u672c\u7edf\u8ba1\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"%E5%9D%87%E5%80%BC%EF%BC%88Mean%EF%BC%89\"><\/span><strong>\u5747\u503c\uff08Mean\uff09<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u5747\u503c\u662f\u4e00\u7ec4\u6570\u636e\u4e2d\u6240\u6709\u6570\u636e\u503c\u7684\u603b\u548c\u9664\u4ee5\u6570\u636e\u503c\u7684\u4e2a\u6570\u3002<br \/>\n<strong>\u4f5c\u7528<\/strong>\uff1a\u8868\u793a\u4e00\u7ec4\u6570\u636e\u7684\u5e73\u5747\u503c\u3002<\/p>\n<p><strong>\u8ba1\u7b97\u65b9\u6cd5<\/strong>\uff1a\u5747\u503c <code class=\"katex-inline\">\\mu = \\frac{\\sum_{i=1}^{n} x_i}{n}<\/code>\uff0c\u5176\u4e2d <code class=\"katex-inline\">x_i<\/code> \u662f\u6570\u636e\u96c6\u4e2d\u7684\u6bcf\u4e2a\u6570\u636e\u503c\uff0c<code class=\"katex-inline\">n<\/code> \u662f\u6570\u636e\u503c\u7684\u4e2a\u6570\u3002<\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E6%A0%87%E5%87%86%E5%B7%AE%EF%BC%88Standard_Deviation%EF%BC%89\"><\/span><strong>\u6807\u51c6\u5dee\uff08Standard Deviation\uff09<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u6807\u51c6\u5dee\u662f\u65b9\u5dee\u7684\u5e73\u65b9\u6839\uff0c\u7528\u4e8e\u8861\u91cf\u6570\u636e\u503c\u7684\u79bb\u6563\u7a0b\u5ea6\u3002<br \/>\n<strong>\u4f5c\u7528<\/strong>\uff1a\u8868\u793a\u6570\u636e\u7684\u79bb\u6563\u7a0b\u5ea6\u3002<\/p>\n<p><strong>\u8ba1\u7b97\u65b9\u6cd5<\/strong>\uff1a\u6807\u51c6\u5dee <code class=\"katex-inline\">\\sigma = \\sqrt{\\frac{\\sum_{i=1}^{n} (x_i - \\mu)^2}{n}}<\/code>\uff0c\u5176\u4e2d <code class=\"katex-inline\">x_i<\/code> \u662f\u6570\u636e\u96c6\u4e2d\u7684\u6bcf\u4e2a\u6570\u636e\u503c\uff0c<code class=\"katex-inline\">\\mu<\/code> \u662f\u5747\u503c\uff0c<code class=\"katex-inline\">n<\/code> \u662f\u6570\u636e\u503c\u7684\u4e2a\u6570\u3002<\/p>\n<blockquote>\n<ul>\n<li>1\uff0c\u6c42\u5747\u503c<\/li>\n<li>2\uff0c\u6c42\u6bcf\u4e2a\u6570\u8ddf\u5747\u503c\u7684\u5dee<\/li>\n<li>3\uff0c\u628a\u5dee\u53d6\u5e73\u65b9<\/li>\n<li>4\uff0c\u518d\u628a\u5e73\u65b9\u7684\u7ed3\u679c\u53d6\u5747\u503c<\/li>\n<li>5\uff0c\u518d\u628a\u7ed3\u679c\u53d6\u5e73\u65b9\u6839<\/li>\n<\/ul>\n<\/blockquote>\n<h4><span class=\"ez-toc-section\" id=\"%E6%96%B9%E5%B7%AE%EF%BC%88Variance%EF%BC%89\"><\/span><strong>\u65b9\u5dee\uff08Variance\uff09<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u65b9\u5dee\u662f\u6bcf\u4e2a\u6570\u636e\u503c\u4e0e\u5747\u503c\u4e4b\u5dee\u7684\u5e73\u65b9\u7684\u5e73\u5747\u503c\u3002<br \/>\n<strong>\u4f5c\u7528<\/strong>\uff1a\u8868\u793a\u6570\u636e\u4e0e\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u7a0b\u5ea6\u3002\uff08\u5982\u679c\u6bd4\u8f83\u79bb\u6563\u7684\u8bdd\uff0c\u65b9\u5dee\u8d8a\u5927\uff1b\u5982\u679c\u6bd4\u8f83\u96c6\u4e2d\u7684\u8bdd\uff0c\u65b9\u5dee\u8d8a\u5c0f\uff09<\/p>\n<p><strong>\u8ba1\u7b97\u65b9\u6cd5<\/strong>\uff1a\u65b9\u5dee <code class=\"katex-inline\">\\sigma^2 = \\frac{\\sum_{i=1}^{n} (x_i - \\mu)^2}{n}<\/code>\uff0c\u5176\u4e2d <code class=\"katex-inline\">x_i<\/code> \u662f\u6570\u636e\u96c6\u4e2d\u7684\u6bcf\u4e2a\u6570\u636e\u503c\uff0c<code class=\"katex-inline\">\\mu<\/code> \u662f\u5747\u503c\uff0c<code class=\"katex-inline\">n<\/code> \u662f\u6570\u636e\u503c\u7684\u4e2a\u6570\u3002<\/p>\n<p>\u793a\u4f8b\u4ee3\u7801\uff1a<\/p>\n<pre><code class=\"language-python\">import numpy as np\n\n# \u793a\u4f8b\u6570\u636e\u96c6\ndata = np.array([1, 2, 3, 4, 5])\n\n# \u8ba1\u7b97\u5747\u503c\nmean = np.mean(data)\n# \u8ba1\u7b97\u6807\u51c6\u5dee\nstd = np.std(data)\n# \u8ba1\u7b97\u65b9\u5dee\nvariance = np.var(data)\n\nprint(&quot;\u5747\u503c:&quot;, mean)\nprint(&quot;\u6807\u51c6\u5dee:&quot;, std)\nprint(&quot;\u65b9\u5dee:&quot;, variance)<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716965434335.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716965434335.png\" alt=\"file\" \/><\/a><\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E5%8D%8F%E6%96%B9%E5%B7%AE%EF%BC%88Covariance%EF%BC%89\"><\/span><strong>\u534f\u65b9\u5dee\uff08Covariance\uff09<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u534f\u65b9\u5dee\u8861\u91cf\u4e24\u4e2a\u53d8\u91cf\u4e00\u8d77\u53d8\u5316\u7684\u7a0b\u5ea6\u3002<br \/>\n<strong>\u4f5c\u7528<\/strong>\uff1a\u8003\u5bdf\u4e24\u5217\u6570\u636e\u7684\u53d8\u5316\u8d8b\u52bf\u662f\u5426\u76f8\u540c<\/p>\n<p><strong>\u8ba1\u7b97\u65b9\u6cd5<\/strong>\uff1a\u534f\u65b9\u5dee <code class=\"katex-inline\">\\text{Cov}(X, Y) = \\frac{\\sum_{i=1}^{n} (X_i - \\mu_X)(Y_i - \\mu_Y)}{n}<\/code>\uff0c\u5176\u4e2d <code class=\"katex-inline\">X_i<\/code> \u548c <code class=\"katex-inline\">Y_i<\/code> \u5206\u522b\u662f\u4e24\u4e2a\u53d8\u91cf\u4e2d\u7684\u6bcf\u4e2a\u6570\u636e\u503c\uff0c<code class=\"katex-inline\">\\mu_X<\/code> \u548c <code class=\"katex-inline\">\\mu_Y<\/code> \u5206\u522b\u662f\u4e24\u4e2a\u53d8\u91cf\u7684\u5747\u503c\uff0c<code class=\"katex-inline\">n<\/code> \u662f\u6570\u636e\u503c\u7684\u4e2a\u6570\u3002<\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E7%9A%AE%E5%B0%94%E9%80%8A%E7%9B%B8%E5%85%B3%E5%87%BD%E6%95%B0\"><\/span>\u76ae\u5c14\u900a\u76f8\u5173\u51fd\u6570<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\u628a\u534f\u65b9\u5dee\u5f52\u4e00\u5316<\/li>\n<li>\u8303\u56f4[-1, 1]<\/li>\n<li>-1\uff1a\u4e25\u683c\u8d1f\u76f8\u5173<\/li>\n<li>\u00a01\uff1a\u4e25\u683c\u6b63\u76f8\u5173<\/li>\n<li>\u00a00\uff1a\u4e0d\u76f8\u5173<\/li>\n<\/ul>\n<pre><code class=\"language-python\">X = np.array([1, 3, 5, 7, 9])\nY = np.array([2, 4, 6, 8, 10])\nZ = Y[::-1]\n\ncovariance_x_y = ((X - X.mean()) * (Y - Y.mean())).mean()\ncovariance_x_z = ((X - X.mean()) * (Z - Z.mean())).mean()\n\n# \u8ba1\u7b97\u6807\u51c6\u5dee\nstd_X = X.std()\nstd_Y = Y.std()\nstd_Z = Z.std()\n\n# \u8ba1\u7b97\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\npearson_corr_x_y = covariance_x_y \/ (std_X * std_Y)\npearson_corr_x_z = covariance_x_z \/ (std_X * std_Z)\n\nprint(&quot;X\u548cY\u5f52\u4e00\u5316\u7ed3\u679c\u4e3a\uff1a&quot;, pearson_corr_x_y)\nprint(&quot;X\u548cZ\u5f52\u4e00\u5316\u7ed3\u679c\u4e3a\uff1a&quot;, pearson_corr_x_z)<\/code><\/pre>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716966213090.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/05\/image-1716966213090.png\" alt=\"file\" \/><\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E5%86%85%E5%AE%B9%E5%B0%8F%E7%BB%93\"><\/span>\u5185\u5bb9\u5c0f\u7ed3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\u6982\u7387\u548c\u6570\u7406\u7edf\u8ba1\u662f\u4e00\u79cd\u5efa\u6a21\u601d\u60f3\uff0c\u5176\u4e2d\u4f7f\u7528\u8f83\u591a\u7684\u9ad8\u65af\u8d1d\u53f6\u65af\u7b97\u6cd5\u5c31\u662f\u8fd9\u4e00\u601d\u60f3\u7684\u5b9e\u8df5\u3002<\/li>\n<li>\u6982\u7387\u662f\u4e00\u79cd\u56fa\u6709\u5c5e\u6027\uff0c\u5176\u6709\u975e\u8d1f\u6027\u548c\u89c4\u8303\u6027\u4e24\u4e2a\u7279\u6027<\/li>\n<li>\u6982\u7387\u8ba1\u7b97\u65f6\u5206\u79bb\u6563\u578b\u53d8\u91cf\u548c\u8fde\u7eed\u76f8\u53d8\u91cf\u4e24\u79cd\n<ul>\n<li>\u79bb\u6563\u578b\u53d8\u91cf\u6982\u7387\u8ba1\u7b97\u4f7f\u7528\u51fa\u73b0\u6b21\u6570\/ \u603b\u7684\u6b21\u6570\u5373\u53ef<\/li>\n<li>\u8fde\u7eed\u578b\u53d8\u91cf\u6982\u7387\u8ba1\u7b97\u65b9\u6cd5\u8f83\u4e3a\u590d\u6742\uff0c\u9700\u8981\u8fdb\u884c\u5de5\u7a0b\u5316\u7b80+\u5047\u5b9a\u4e3a\u9ad8\u65af\u5206\u5e03\u6765\u8fdb\u884c\u8ba1\u7b97<\/li>\n<li>\u5e38\u89c4\u60c5\u51b5\u4e0b\uff0c\u7531\u4e8e\u6211\u4eec\u91cd\u5728\u6bd4\u8f83\u6982\u7387\u5927\u5c0f\uff0c\u800c\u4e0d\u662f\u8ba1\u7b97\u5177\u4f53\u6570\u503c\uff0c\u6240\u4ee5\u4f7f\u7528\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u7684\u503c\u6765\u4ee3\u66ff\u6982\u7387\u7684\u503c<\/li>\n<\/ul>\n<\/li>\n<li>\u6761\u4ef6\u6982\u7387\u4e5f\u662f\u4e00\u79cd\u6982\u7387<\/li>\n<li>\u6761\u4ef6\u6982\u7387\u7684\u8ba1\u7b97\u65b9\u6cd5\u5927\u81f4\u601d\u60f3\u662f\u5c06\u5728X\u8f93\u5165\u6837\u672c\u7684\u60c5\u51b5\u4e0b\uff0c\u8ba1\u7b97\u5bf9\u5e94\u7c7b\u7684\u6982\u7387\uff0c\u6700\u540e\u6c42\u5f97\u6982\u7387\u6700\u5927\u7684\u4f5c\u4e3a\u8f93\u51fa\u3002\u8fd9\u4e00\u65b9\u6cd5\u4e5f\u53eb\u9ad8\u65af\u8d1d\u53f6\u65af\u65b9\u6cd5\u3002<\/li>\n<li>\u9ad8\u65af\u8d1d\u53f6\u65af\u53ea\u80fd\u8fdb\u884c\u5206\u7c7b\uff0c\u5176\u6548\u679c\u867d\u7136\u5dee\u4e00\u4e9b(\u56e0\u4e3a\u8ba4\u4e3a\u90fd\u5c5e\u4e8e\u9ad8\u65af\u5206\u5e03)\uff0c\u4f46\u662f\u8ba1\u7b97\u901f\u5ea6\u975e\u5e38\u5feb\u3002\u5728\u8ba1\u7b97\u673a\u65e9\u671f\u53d1\u5c55\u65f6\u671f\uff0cNLP\u7b49\u81ea\u7136\u8bed\u8a00\u5904\u7406\u65f6\u5e38\u7528\u9ad8\u65af\u8d1d\u53f6\u65af\u3002<\/li>\n<\/ul>\n<p align=\"center\">\u6b22\u8fce\u5173\u6ce8\u516c\u4f17\u53f7\u4ee5\u83b7\u5f97\u6700\u65b0\u7684\u6587\u7ae0\u548c\u65b0\u95fb<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/09\/\u626b\u7801_\u641c\u7d22\u8054\u5408\u4f20\u64ad\u6837\u5f0f-\u767d\u8272\u7248.bmp\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/09\/\u626b\u7801_\u641c\u7d22\u8054\u5408\u4f20\u64ad\u6837\u5f0f-\u767d\u8272\u7248.bmp\" alt=\"\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u524d\u8a00 \u672c\u7ae0\u5185\u5bb9\u4e3b\u8981\u662f\u5b66\u4e60\u4e86\u6982\u7387\u76f8\u5173\u7684\u77e5\u8bc6 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1959,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"aside","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[28],"tags":[63,55],"class_list":["post-1945","post","type-post","status-publish","format-aside","has-post-thumbnail","hentry","category-blog","tag-63","tag-55","post_format-post-format-aside"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u3010\u8bfe\u7a0b\u603b\u7ed3\u3011Day3\uff1a\u6982\u7387\u548c\u8d1d\u53f6\u65af\u7b97\u6cd5 - \u4e00\u8d77AI\u6280\u672f<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/17aitech.com\/?p=1945\" \/>\n<script type=\"application\/ld+json\" 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