{"id":494,"date":"2023-07-03T16:44:07","date_gmt":"2023-07-03T08:44:07","guid":{"rendered":"https:\/\/blog.cirno.fun\/?p=494"},"modified":"2025-03-19T00:33:37","modified_gmt":"2025-03-18T16:33:37","slug":"%e5%8d%95%e5%a4%9a%e5%8f%98%e9%87%8f%e6%a2%af%e5%ba%a6%e4%b8%8b%e9%99%8d%e7%ba%bf%e6%80%a7%e5%9b%9e%e5%bd%92","status":"publish","type":"post","link":"https:\/\/blog.sssn.tech\/?p=494","title":{"rendered":"[Chap1]–\u5355(\u591a)\u53d8\u91cf\u68af\u5ea6\u4e0b\u964d\u7ebf\u6027\u56de\u5f52"},"content":{"rendered":"

\u5728\u672c\u8282\u4e2d\u6211\u4eec\u5e0c\u671b\u901a\u8fc7\u62df\u5408\u4e00\u4e2a\u7ebf\u6027\u51fd\u6570\uff0c\u5bf9\u4e00\u4e2a\u5b9e\u9645\u95ee\u9898\u8fdb\u884c\u7ebf\u6027\u56de\u5f52<\/p>\n

\u5355\u53d8\u91cf\u7ebf\u6027\u56de\u5f52<\/h2>\n

\"file\"<\/p>\n

\u60f3\u8c61\u6211\u4eec\u4f5c\u4e3a\u4e00\u5bb6\u8fde\u9501\u5546\u5e97\u7684CEO\uff0c\u4e0a\u56fe\u662f\u4e00\u4e2a\u6240\u6709\u5e97\u9762\u7684\u6240\u5728\u57ce\u5e02\u4eba\u53e3-\u5229\u6da6\u5206\u90e8\u56fe\uff0c\u6211\u4eec\u5e0c\u671b\u62df\u5408\u4e00\u6761\u76f4\u7ebf\uff0c\u6765\u8861\u91cf\u57ce\u5e02\u4eba\u53e3\u4e0e\u5229\u6da6\u7684\u5173\u7cfb\uff0c\u4ee5\u4fbf\u6765\u51b3\u5b9a\u4e0b\u4e00\u5bb6\u5e97\u9762\u5f00\u5728\u54ea\u91cc<\/p>\n

\u8fd9\u662f\u6211\u4eec\u5e0c\u671b\u62df\u5408\u7684\u76f4\u7ebf\u65b9\u7a0b<\/p>\n

h(x) = \\theta ^T X = \\theta _0 + \\theta _1 x <\/code><\/pre>\n
h\u4ee3\u8868\u9884\u6d4b(hypothesis)\uff0c\u5f53\u6211\u4eec\u7528<\/p>\n
x^{(i)}, y^{(i)}<\/code><\/pre>\n
\u6765\u8868\u793a\u6570\u636e\u96c6\u4e2d\u7684\u6bcf\u4e2a\u70b9\u65f6\uff0c\u6211\u4eec\u89c4\u5b9a\u635f\u5931\u51fd\u6570<\/p>\n
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
\u5373\u4f30\u8ba1\u6570\u636e\u4e0e\u5b9e\u9645\u6570\u636e\u7684\u5747\u65b9\u5dee\uff0c\u6211\u4eec\u5f53\u524d\u7684\u95ee\u9898\u662f\uff0c\u627e\u5230\u4e24\u4e2a\u03b8\uff0c\u4ee4J(\u03b8)\u6700\u5c0f\uff0c\u5373\u53ef\u62df\u5408\u51fa\u4e00\u6761\u5408\u9002\u7684\u76f4\u7ebf\uff0c\u4f7f\u5f97\u4ed6\u79bb\u6bcf\u4e2a\u70b9\u5e73\u5747\u8ddd\u79bb\u6700\u8fd1<\/p>\n
\u8fd9\u91cc\u76842m\u53ef\u4ee5\u770b\u505a\u662f\u65b9\u4fbf\u540e\u7eed\u8ba1\u7b97\u800c\u591a\u5199\u4e86\u4e00\u4e2a2\uff0c\u56e0\u4e3a\u635f\u5931\u51fd\u6570\u603b\u4f1a\u5bf9\u67d0\u4e2a\u53d8\u91cf\u6c42\u5bfc\uff0c\u800c\u6070\u597d\u53ef\u4ee5\u4e0e\u5e73\u65b9\u9879\u7684\u6c42\u5bfc\u7ed3\u679c\u62b5\u6d88<\/p>\n
\u635f\u5931\u51fd\u6570J\u7684\u81ea\u53d8\u91cf\u662f\u03b8\uff0c\u5728\u672c\u4f8b\u4e2d\u6709\u4e24\u4e2a\uff0c\u6240\u4ee5\u53ef\u4ee5\u60f3\u8c61\u5728\u5982\u4e0b\u7684\u4e00\u4e2a\u51fd\u6570\u4e2d\uff0c\u627e\u5bfb\u5e73\u9762\u7684\u6700\u4f4e\u70b9 \"file\"\u5982\u4f55\u627e\u5bfb\u5462\uff1f\u68af\u5ea6\u4e0b\u964d\u7684\u65b9\u6cd5\u662f\u5bf9\u4e8e\u7b2c\u4e00\u6b21\u8ba1\u7b97\u635f\u5931\uff0c\u6211\u4eec\u53ef\u4ee5\u4efb\u9009\u4e24\u4e2a\u03b8\u503c\uff0c\u6b64\u65f6\u6211\u4eec\u53ef\u4ee5\u627e\u5230\u4e0a\u56fe\u5e73\u9762\u7684\u4e00\u70b9\uff0c\u901a\u8fc7\u8ba1\u7b97\u68af\u5ea6\uff0c\u6765\u8861\u91cf\u4e0b\u4e00\u6b21\u8fed\u4ee3\u7684\u65b9\u5411\uff0c\u7136\u540e\u5411\u8be5\u65b9\u5411\u524d\u8fdb\u4e00\u5c0f\u6b65<\/p>\n
{{\\theta }_{j}}:={{\\theta }_{j}}-\\alpha \\frac{\\partial }{\\partial {{\\theta }_{j}}}J\\left( \\theta \\right)<\/code><\/pre>\n
\u5176\u4e2dalpha\u79f0\u4e3a\u5b66\u4e60\u7387\uff0c\u53ef\u4ee5\u5f71\u54cd\u6bcf\u4e00\u6b65\u7684\u6b65\u957f<\/p>\n
\u4e8b\u5b9e\u4e0a:<\/p>\n
\\frac{\\partial }{\\partial {{\\theta }_{j}}}J\\left( \\theta \\right) =\n\\frac {1}{2m} \\frac{\\partial }{\\partial {{\\theta }_{j}}}\\sum_{i=1}^{m} h_\\theta (x^{(i)})-y^{(i)})^2\n<\/code><\/pre>\n
\u5176\u4e2d<\/p>\n
h_\\theta (x^{(i)})=\\theta_0+\\theta_1x<\/code><\/pre>\n
\u6240\u4ee5<\/p>\n
{{\\theta }_{j}}:={{\\theta }_{j}}-\\frac{\\alpha}{m} \\sum_{i=1}^{m} (h_\\theta (x^{(i)}-y^{(i)})x_j<\/code><\/pre>\n
\"file\"<\/p>\n
\u4e0a\u56fe\u8bf4\u660e\u4e86\u4e00\u4e2a\u95ee\u9898\uff0c\u5728\u635f\u5931\u51fd\u6570\u6bd4\u8f83\u590d\u6742\u65f6\uff0c\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u53ea\u80fd\u627e\u5230\u4e00\u4e9b\u5c40\u90e8\u7684\u6700\u5c0f\u503c\uff0c\u4e0d\u80fd\u4fdd\u8bc1\u4e00\u6b21\u8d70\u5230\u5168\u5c40\u7684\u6700\u5c0f\u503c<\/p>\n
\u5728\u672c\u4f8b\u4e2d\uff0c\u635f\u5931\u51fd\u6570\u5f88\u7b80\u5355\uff0c\u6700\u5c0f\u503c\u662f\u552f\u4e00\u7684\uff0c\u6240\u4ee5\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u5fc5\u53ef\u4ee5\u4e00\u6b21\u627e\u5230\u6700\u4f18\u7684\u03b8<\/p>\n
\u591a\u53d8\u91cf\u7ebf\u6027\u56de\u5f52<\/h2>\n
\u60f3\u8c61\u4e00\u4e2a\u95ee\u9898\uff0c\u5728\u521a\u521a\u7684\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u5f97\u77e5\u7684\u4fe1\u606f\u4e0d\u5355\u5355\u53ea\u6709\u57ce\u5e02\u4eba\u53e3\u4e0e\u5229\u6da6\uff0c\u8fd8\u6709\u8bf8\u591a\u5f71\u54cd\u56e0\u7d20\uff0c\u6bd4\u5982\u8425\u4e1a\u65f6\u95f4\uff0c\u5458\u5de5\u7d20\u8d28\uff0c…\u5047\u8bbe\u6211\u4eec\u5df2\u7ecf\u53ef\u4ee5\u5f88\u597d\u7684\u7528\u6570\u503c\u6765\u8861\u91cf\u8fd9\u4e9b\u56e0\u7d20\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba4\u4e3a\u5229\u6da6\u662f\u8fd9\u4e9b\u56e0\u7d20\u5171\u540c\u4f5c\u7528\u7684\u7ed3\u679c<\/p>\n
{{h}_{\\theta }}\\left( x \\right)={{\\theta }^{T}}X={{\\theta }_{0}}{{x}_{0}}+{{\\theta }_{1}}{{x}_{1}}+{{\\theta }_{2}}{{x}_{2}}+...+{{\\theta }_{n}}{{x}_{n}}<\/code><\/pre>\n
\u5f53\u7136\uff0c\u6211\u4eec\u8fd8\u662f\u5047\u8bbe\u6bcf\u4e2a\u56e0\u7d20\u5bf9\u5229\u6da6\u7684\u7ed3\u679c\u90fd\u662f\u7ebf\u6027\uff08\u4e00\u6b21\uff09\u7684<\/p>\n
\u6b64\u65f6\u7528\u77e9\u9635\uff08\u5411\u91cf\uff09\u7684\u89d2\u5ea6\u6765\u8ba8\u8bba\u8fd9\u4e2a\u95ee\u9898\u4f1a\u65b9\u4fbf\u7684\u591a<\/p>\n
\"file\"<\/p>\n
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\u6b64\u65f6\u7684\u635f\u5931\u51fd\u6570\u4e0e\u8fed\u4ee3\u65b9\u6cd5\u4e0d\u53d8<\/p>\n","protected":false},"excerpt":{"rendered":"
\u5728\u672c\u8282\u4e2d\u6211\u4eec\u5e0c\u671b\u901a\u8fc7\u62df\u5408\u4e00\u4e2a\u7ebf\u6027\u51fd\u6570\uff0c\u5bf9\u4e00\u4e2a\u5b9e\u9645\u95ee\u9898\u8fdb\u884c\u7ebf\u6027\u56de\u5f52 \u5355\u53d8\u91cf\u7ebf\u6027\u56de\u5f52 […]<\/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-494","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\/494","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=494"}],"version-history":[{"count":5,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/494\/revisions"}],"predecessor-version":[{"id":837,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/494\/revisions\/837"}],"wp:attachment":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=494"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=494"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}