{"id":505,"date":"2023-07-13T19:25:12","date_gmt":"2023-07-13T11:25:12","guid":{"rendered":"https:\/\/blog.cirno.fun\/?p=505"},"modified":"2025-03-19T00:33:06","modified_gmt":"2025-03-18T16:33:06","slug":"chap3-%e9%80%bb%e8%be%91%e5%9b%9e%e5%bd%92","status":"publish","type":"post","link":"https:\/\/blog.sssn.tech\/?p=505","title":{"rendered":"[Chap3]-\u903b\u8f91\u56de\u5f52"},"content":{"rendered":"<p>\u903b\u8f91\u56de\u5f52(logistic regression)\u662f\u5e94\u7528\u5e7f\u6cdb\u7684\u4e00\u79cd<strong>\u5206\u7c7b\u7b97\u6cd5<\/strong><\/p>\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u903b\u8f91\u56de\u5f52\u548c\u201c\u56de\u5f52\u201d\u6ca1\u4ec0\u4e48\u5173\u7cfb\uff0c\u5c3d\u7ba1\u4ed6\u7684\u540d\u5b57\u91cc\u6709\u8fd9\u4e2a\u8bcd<\/p>\n<h2>\u5206\u7c7b\u95ee\u9898<\/h2>\n<p>\u5728\u5206\u7c7b\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u9884\u6d4b\u7684\u76ee\u6807\u4e0d\u518d\u662f\u56de\u5f52\u95ee\u9898\u4e2d\u8fde\u7eed\u7684\u503c\uff0c\u800c\u662f\u79bb\u6563\u7684<\/p>\n<p>\u6bd4\u5982\u5224\u5b9a\u4e00\u4e2a\u90ae\u4ef6\u662f\u5426\u662f\u5783\u573e\u90ae\u4ef6\uff0c\u4e00\u4e2a\u80bf\u7624\u662f\u5426\u4e3a\u6076\u6027\uff0c\u90fd\u662f\u4e8c\u5143\u5206\u7c7b\u95ee\u9898<\/p>\n<p>\u5f53\u7136\u5206\u7c7b\u95ee\u9898\u4e5f\u53ef\u4ee5\u662f\u591a\u5143\u7684\uff0c\u6bd4\u5982MBTI16\u4eba\u683c\u6d4b\u8bd5<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u4ee5\u5224\u5b9a\u80bf\u7624\u662f\u5426\u4e3a\u6076\u6027\u4e3a\u4f8b\uff0c\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u7ec4\u8bad\u7ec3\u96c6\uff0c\u5305\u542b\u80bf\u7624\u7684\u5927\u5c0f\u548c\u662f\u5426\u4e3a\u6076\u6027\u4e24\u4e2a\u4fe1\u606f\uff0c\u663e\u7136\u6211\u4eec\u7684\u9884\u6d4b\u7b97\u6cd5\u5e94\u8be5\u662f\u63a5\u53d7\u4e00\u4e2a\u53d8\u91cf\uff08\u5927\u5c0f\uff09\u8f93\u51fa\u4e00\u4e2a\u53d8\u91cf\uff08\u662f\u5426\u4e3a\u6076\u6027\u7684\uff09<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/07\/image-1689247129331.png\" alt=\"file\" \/><\/p>\n<p>\u6211\u4eec\u5f88\u81ea\u7136\u7684\u53ef\u4ee5\u60f3\u5230\u8fd0\u7528\u4e0a\u8282\u8bf4\u5230\u7684\u7ebf\u6027\u56de\u5f52\u6765\u5c1d\u8bd5\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u5bf9\u4e8e\u82e5\u5e72\u80bf\u7624\uff08\u56fe\u4e2d\u7684\u7ea2\u53c9\uff09\uff0c\u53ef\u4ee5\u62df\u5408\u51fa\u4e00\u6761\u76f4\u7ebf\u6765\u9884\u6d4b\u7ed3\u679c\uff0c\u4f8b\u5982\uff0cy\u5927\u4e8e0.5\u65f6\u5019\u9884\u6d4b1\uff0c\u5426\u5219\u9884\u6d4b0<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/07\/image-1689246814399.png\" alt=\"file\" 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src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/07\/image-1689247274901.png\" alt=\"file\" \/><\/p>\n<p>\u5728\u903b\u8f91\u56de\u5f52\u4e2d\uff0c\u6211\u4eec\u8ba4\u4e3a\u51fd\u6570\u8f93\u51fa(h(x))\u662f<strong>\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u53d8\u91cfx\uff0cx\u7531\u53c2\u6570theta\u5f71\u54cd\uff0c\u8be5\u6837\u672c\u5c5e\u4e8e1\u5206\u7c7b\u7684\u6982\u7387<\/strong>\uff0c\u5373<\/p>\n<pre><code class=\"language-katex\">h_{\\theta}(x) = P(y = 1|x; \\theta)<\/code><\/pre>\n<p>\u672c\u4f8b\u4e2d\u662f\u80bf\u7624\u662f\u6076\u6027\u7684\u6982\u7387<\/p>\n<h2>\u51b3\u7b56\u8fb9\u754c<\/h2>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/07\/image-1689247643284.png\" alt=\"file\" \/><\/p>\n<p>\u5047\u8bbe\u6211\u4eec\u73b0\u5728\u5728\u8fdb\u884c\u4e00\u4e2a\u53cc\u53d8\u91cf\u7684\u4e8c\u5143\u903b\u8f91\u56de\u5f52\uff0c\u56fe\u4e2d\u7ed9\u51fa\u4e86\u4e24\u79cd\u7c7b\u522b\u7684\u6570\u636e\u548c\u9884\u6d4b\u51fd\u6570\uff0c\u6211\u4eec\u6682\u65f6\u4e0d\u8c08theta\u5411\u91cf\u7684\u66f4\u65b0\u65b9\u5f0f\uff0c\u5047\u8bbe\u4ed6\u5df2\u7ecf\u66f4\u65b0\u597d\u4e86\uff0c\u5373:\uff08-3\uff0c 1\uff0c 1\uff09<\/p>\n<p>\u6b64\u65f6\u5f53x1+x2&gt;3\u65f6\uff0c\u6a21\u578b\u4f1a\u9884\u6d4b1\uff0c\u5426\u5219\u9884\u6d4b0\uff0c\u8fd9\u91cc\u7684x1+x2=3\u76f4\u7ebf\u5c31\u53eb\u505a\u51b3\u7b56\u8fb9\u754c(Decision Boundary)<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/07\/image-1689247975836.png\" alt=\"file\" \/><\/p>\n<p>\u51b3\u7b56\u8fb9\u754c\u53ef\u4ee5\u975e\u5e38\u590d\u6742\uff0c\u8fd9\u53d6\u51b3\u4e8e\u53c2\u6570\u5217\u8868\u957f\u5ea6\uff08\u53d8\u91cf\u7684\u5e42\u6b21\uff09\uff0c\u6bd4\u5982\u4e0a\u56fe\u4e2d\u663e\u7136\u53ea\u652f\u6301\u76f4\u7ebf\u8fb9\u754c\uff0c\u5f53\u6211\u4eec\u5ef6\u957f\u53c2\u6570\u5217\u8868\u81f3x1x2\u5e73\u65b9\u65f6\uff0c\u53ef\u4ee5\u652f\u6301\u66f2\u7ebf\u8fb9\u754c<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/07\/image-1689248086699.png\" alt=\"file\" \/><\/p>\n<h2>\u4ee3\u4ef7\u51fd\u6570\u4e0e\u68af\u5ea6\u4e0b\u964d<\/h2>\n<p>\u6211\u4eec\u5982\u4f55\u6765\u8861\u91cf\u4e00\u6b21\u62df\u5408\u7684\u6548\u679c\uff1f\u5982\u679c\u4f7f\u7528\u4e0a\u8282\u7684\u5747\u65b9\u5dee\u635f\u5931\u51fd\u6570:<\/p>\n<pre><code class=\"language-katex\">J\\left( \\theta  \\right)=\\frac{1}{2m}\\sum\\limits_{i=1}^{m}{{{\\left( {{h}_{\\theta }}\\left( {{x}^{(i)}} \\right)-{{y}^{(i)}} \\right)}^{2}}}<\/code><\/pre>\n<p>\u4f1a\u51fa\u73b0\u95ee\u9898\uff0c\u56e0\u4e3ah(x)\u4e0d\u518d\u8bd5\u7ebf\u6027\u7684\uff0c\u4ed6\u7684\u89e3\u6790\u5f0f\u975e\u5e38\u590d\u6742\uff0c\u540c\u6837\u7684\uff0c\u4ed6\u7684\u5747\u65b9\u5dee\u635f\u5931\u51fd\u6570\u4e5f\u4e0d\u662f\u51f8\u51fd\u6570<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/07\/image-1689254113597.png\" alt=\"file\" \/><\/p>\n<p>\u5f88\u591a\u5c40\u90e8\u6700\u5c0f\u503c\u4f1a\u5f71\u54cd\u68af\u5ea6\u4e0b\u964d\u7684\u7ed3\u679c<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u903b\u8f91\u56de\u5f52\u7ecf\u5e38\u7528\u5230\u4ee5\u4e0b\u635f\u5931\u51fd\u6570:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/07\/image-1689254187533.png\" alt=\"file\" \/><\/p>\n<p>\u89c2\u5bdf\u56fe\u50cf\u53ef\u4ee5\u53d1\u73b0\uff0c\u5f53y=1\u65f6\uff0c\u9884\u6d4b\u503c\u79bb1\u8d8a\u8fdc\uff0c\u4ee3\u4ef7\u8d8a\u8d8b\u8fd1\u65e0\u7a77\uff0cy=0\u65f6\u4ea6\u7136\u3002\u800c\u5f53\u9884\u6d4b\u6b63\u786e\u65f6\uff0c\u4ee3\u4ef7\u4e3a0<\/p>\n<p>\u4e8b\u5b9e\u4e0a\u4e0a\u8ff0\u51fd\u6570\u53ef\u4ee5\u5199\u6210\u5982\u4e0b\u6bd4\u8f83\u7d27\u51d1\u7684\u5f62\u5f0f<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/07\/image-1689254329146.png\" alt=\"file\" \/><\/p>\n<p>\u8fd9\u4e2a\u635f\u5931\u51fd\u6570\u662f\u51f8\u7684\uff0c\u5373\u6ca1\u6709\u5c40\u90e8\u6700\u5c0f\u503c\uff0c\u975e\u5e38\u9002\u5408\u68af\u5ea6\u4e0b\u964d<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/07\/image-1689254412382.png\" alt=\"file\" \/><\/p>\n<p>\u5176\u4e2dJ(theta)\u6c42\u5bfc\u7684\u8fc7\u7a0b\u653e\u5728\u535a\u5ba2\u6700\u540e<\/p>\n<p>\u53ef\u4ee5\u53d1\u73b0\u53c2\u6570\u8fed\u4ee3\u65b9\u7a0b\u548c\u5747\u65b9\u5dee\u8fed\u4ee3\u65b9\u5f0f\u5b8c\u5168\u4e00\u6837\uff0c\u8fd9\u662f\u5426\u8bf4\u660e\u903b\u8f91\u56de\u5f52\u548c\u7ebf\u6027\u56de\u5f52\u5728\u68af\u5ea6\u4e0b\u964d\u65b9\u9762\u6ca1\u6709\u533a\u522b\u5462\uff1f\u7b54\u6848\u662f\u5426\u5b9a\u7684\uff0c\u867d\u7136\u8fed\u4ee3\u8868\u8fbe\u5f0f\u76f8\u540c\uff0c\u4f46\u662fh(x)\u7684\u8868\u8fbe\u5f0f\u4e0d\u540c\uff0c\u4e8b\u5b9e\u4e0a\uff0c\u903b\u8f91\u56de\u5f52\u7684h(x)\u6bd4\u7ebf\u6027\u56de\u5f52\u591a\u4e86\u4e00\u5c42sigmoid\u51fd\u6570<\/p>\n<h2>\u591a\u5206\u7c7b<\/h2>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/07\/image-1689254644155.png\" alt=\"file\" \/><\/p>\n<p>\u5982\u679c\u95ee\u9898\u53d8\u6210\u4e86\u591a\u4e2a\u7c7b\u522b\u5206\u7c7b\uff0c\u6211\u4eec\u4ecd\u53ef\u4ee5\u7528\u4e0a\u8ff0\u65b9\u6cd5\u6765\u89e3\u51b3\u2014\u2014\u5373\uff0c\u7528\u201c\u4e00\u5bf9\u4f59\u201d\u65b9\u6cd5<\/p>\n<p>\u5bf9\u4e8e\u6bcf\u4e2a\u5206\u7c7b\uff0c\u6211\u4eec\u90fd\u751f\u6210\u4e00\u4e2a\u5206\u7c7b\u5668\uff0c\u6765\u5224\u5b9a\u201c\u662f\u5426\u4e3a\u8be5\u5206\u7c7b\u201d\u95ee\u9898\uff0c\u56fe\u4e2d\u7684\u4e09\u79cd\u7c7b\u522b\uff0c\u5c31\u9700\u8981\u4e09\u4e2a\u4e0d\u540c\u7684\u5206\u7c7b\u5668<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/07\/image-1689254794674.png\" alt=\"file\" \/><\/p>\n<p>\u5728\u9884\u6d4b\u65f6\uff0c\u6211\u4eec\u4f1a\u4f9d\u6b21\u8fd0\u884c\u4e09\u4e2a\u5206\u7c7b\u5668\uff0c\u7136\u540e\u9009\u51fa\u53ef\u80fd\u6027\u6700\u5927\u7684\u4e00\u4e2a\u7ed3\u679c\u4f5c\u4e3a\u6700\u7ec8\u7ed3\u679c<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u903b\u8f91\u56de\u5f52(logistic regression)\u662f\u5e94\u7528\u5e7f\u6cdb\u7684\u4e00\u79cd\u5206\u7c7b\u7b97\u6cd5 \u9700\u8981 [&#8230;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,18],"tags":[],"class_list":["post-505","post","type-post","status-publish","format-standard","hentry","category-11","category-18"],"_links":{"self":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/505","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=505"}],"version-history":[{"count":2,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/505\/revisions"}],"predecessor-version":[{"id":835,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/505\/revisions\/835"}],"wp:attachment":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=505"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=505"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}