{"id":166,"date":"2020-02-04T20:58:54","date_gmt":"2020-02-04T12:58:54","guid":{"rendered":"https:\/\/kishere.gq\/?p=166"},"modified":"2023-04-25T15:51:52","modified_gmt":"2023-04-25T07:51:52","slug":"%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a03","status":"publish","type":"post","link":"https:\/\/blog.kishere.cn\/?p=166","title":{"rendered":"\u673a\u5668\u5b66\u4e603"},"content":{"rendered":"

\u5b66\u4e60\u7387\u03b1 \u548c \u8c03\u8bd5(Debugging)<\/h2>\n

\u4fdd\u8bc1\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u6b63\u5e38\u5de5\u4f5c
\n\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u7684\u4f5c\u7528\u662f\u627e\u5230\u4e00\u4e2atheta<\/span>\u503c\u6765\u4f7f\u4ee3\u4ef7\u51fd\u6570J(theta)<\/span>\u6700\u5c0f\u5316.<\/p>\n

\u5728\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u6267\u884c\u65f6, \u8bb0\u5f55J(theta)<\/span>\u7684\u503c, \u4ee5\u8fed\u4ee3\u6b21\u6570\u4e3aX\u8f74, J(theta)<\/span>\u7684\u503c\u4e3aY\u8f74\u7ed8\u51fa\u56fe\u50cf. \u5982\u679c\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u6b63\u5e38, \u90a3\u4e48\u6bcf\u6b21\u8fed\u4ee3J(theta)<\/span>\u7684\u503c\u90fd\u4f1a\u4e0b\u964d. \u540c\u65f6\u56fe\u50cf\u4e5f\u53ef\u4ee5\u8ba9\u6211\u4eec\u89c2\u5bdf\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u662f\u5426\u5df2\u7ecf\u6536\u655b.<\/p>\n

\u5982\u679c\u968f\u7740\u8fed\u4ee3\u6b21\u6570\u7684\u589e\u52a0, J(theta)<\/span>\u4e0d\u65ad\u4e0a\u5347, \u6700\u5e38\u89c1\u7684\u539f\u56e0\u662f:alpha<\/span>\u7684\u503c\u592a\u5927, \u5e94\u8be5\u51cf\u5c0falpha<\/span>\u7684\u503c. \u5982\u679cJ(theta)<\/span>\u7684\u503c\u4e0d\u65ad\u9707\u8361, \u4e5f\u5e94\u8be5\u51cf\u5c0falpha<\/span>\u7684\u503c.<\/p>\n

\u4f46\u662f\u5982\u679calpha<\/span>\u592a\u5c0f, \u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u4f1a\u4e0b\u964d\u5f97\u5f88\u6162.<\/p>\n

\u591a\u9879\u5f0f\u56de\u5f52<\/h2>\n

\u5982\u4f55\u5c06\u6a21\u578b\u548c\u6570\u636e\u8fdb\u884c\u62df\u5408?
\n\u591a\u9879\u5f0f\u56de\u5f52: \u7528\u5047\u8bbe\u7684\u4e00\u6b21\u9879\u7279\u5f81\u6765\u4ee3\u66ff\u9ad8\u6b21\u9879\u7279\u5f81.<\/p>\n

\u6b63\u89c4\u65b9\u7a0bNormal eqution<\/h2>\n

\u6b63\u89c4\u65b9\u7a0b\u63d0\u4f9b\u4e86\u4e00\u79cd\u6c42theta<\/span>\u7684\u89e3\u6790\u89e3\u6cd5, \u53ef\u4ee5\u4e00\u6b21\u6027\u6c42\u89e3theta<\/span>\u7684\u6700\u4f18\u89e3.<\/p>\n

\u5f53\u5f62\u5982\u4e8c\u6b21\u51fd\u6570\u7684J(theta)<\/span>\u4e2d\u7684theta<\/span>\u4e3a\u5b9e\u6570\u65f6,\u6700\u4f4e\u70b9\u7684\u5bfc\u6570=0, \u5229\u7528\u8fd9\u4e2a\u6761\u4ef6\u5c31\u53ef\u4ee5\u6c42\u89e3\u65b9\u7a0b. \u4f46\u662f\u5982\u679ctheta<\/span>\u662f\u4e00\u4e2a\u5411\u91cf, \u90a3\u5c31\u9700\u8981\u5bf9\u5411\u91cf\u4e2d\u7684\u6bcf\u4e00\u4e2a\u7279\u5f81\u503c\u8fdb\u884c\u504f\u5bfc=0\u7684\u65b9\u7a0b\u6c42\u89e3. \u5f97\u5230\u7684\u6bcf\u4e2atheta<\/span>\u7684\u503c\u7ec4\u6210\u7684\u5411\u91cf\u5c31\u662f\u6700\u5c0f\u503c.<\/p>\n

\u6709\u4e00\u4e2am=4\u7684\u8bad\u7ec3\u6837\u672c:<\/p>\n

\"\"<\/p>\n

\u5728\u7b2c\u4e00\u5217\u524d\u8865\u5145\u4e00\u5217x_0=1<\/span>, \u5c06x\u53d8\u6210\u4e00\u4e2am*n+1\u7684\u77e9\u9635. \u540c\u65f6\u5c06y\u4e5f\u53d8\u4e3a\u4e00\u4e2am\u7ef4\u5411\u91cf. \u5728\u6709m\u4e2a\u8bad\u7ec3\u6837\u672c(x^1,y^1),dots,(x^m,y^m)<\/span> , n\u4e2a\u7279\u5f81\u503c: x^i = {begin{bmatrix} x_0^i\\x_1^i\\ vdots x_n^i end{bmatrix}}<\/span>\u7684\u60c5\u51b5\u4e0b. \u53ef\u4ee5\u5f97\u5230\u4f7f\u5f97\u4ee3\u4ef7\u51fd\u6570\u6700\u5c0f\u5316\u7684theta<\/span>\u4e3a :<\/p>\n

theta=(X^TX)^{-1}X^Ty<\/span><\/p>\n

\u4f7f\u7528\u6b63\u89c4\u65b9\u7a0b\u4e0d\u9700\u8981\u9009\u62e9\u5b66\u4e60\u7387alpha<\/span>, \u4e0d\u9700\u8981\u8fdb\u884c\u8fed\u4ee3. \u4f46\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u5bf9\u4e8e\u5927\u6570\u636e\u91cf\u4ecd\u80fd\u4fdd\u6301\u6b63\u5e38\u5de5\u4f5c. \u800c\u6b63\u89c4\u65b9\u7a0b\u9700\u8981\u8ba1\u7b97(X^TX)^{-1}<\/span>, \u5728\u6570\u636e\u91cf\u8f83\u5927\u65f6\u8ba1\u7b97\u6bd4\u8f83\u7f13\u6162.<\/p>\n

\u5982\u679c(X^TX)<\/span>\u662f\u4e00\u4e2a\u4e0d\u53ef\u9006\u7684\u5947\u5f02\u77e9\u9635. \u4e00\u822c\u6765\u8bf4, (X^TX)<\/span>\u4e0d\u53ef\u9006\u7684\u539f\u56e0\u662f\u6709\u591a\u4f59\u7684\u7279\u5f81\u503c(\u6bd4\u5982\u6709\u4e24\u4e2a\u7279\u5f81\u503c\u7ebf\u6027\u76f8\u5173)\u6216\u8005\u7279\u5f81\u503c\u8fc7\u591a. \u5728Octave\u4e2d, \u4f7f\u7528pinv\u53ef\u4ee5\u5f97\u5230\u4f2a\u9006. \u8fd9\u6837\u77e9\u9635\u662f\u4e00\u5b9a\u80fd\u6c42\u51fa\u9006\u7684(\u4f7f\u7528inv\u6c42\u51fa\u7684\u662f\u771f\u5b9e\u7684\u9006).<\/p>\n","protected":false},"excerpt":{"rendered":"

\u5b66\u4e60\u7387\u03b1 \u548c \u8c03\u8bd5(Debugging) \u4fdd\u8bc1\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u6b63\u5e38\u5de5\u4f5c \u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u7684\u4f5c\u7528\u662f\u627e\u5230\u4e00\u4e2atheta\u503c\u6765\u4f7f\u4ee3\u4ef7\u51fd\u6570J(theta)\u6700\u5c0f\u5316. \u5728\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u6267\u884c\u65f6, \u8bb0\u5f55J(theta)\u7684\u503c, \u4ee5\u8fed\u4ee3\u6b21\u6570\u4e3aX\u8f74, J(theta)\u7684\u503c\u4e3aY\u8f74\u7ed8\u51fa\u56fe\u50cf. \u5982\u679c\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u6b63\u5e38, \u90a3\u4e48\u6bcf\u6b21\u8fed\u4ee3J(theta)\u7684\u503c\u90fd\u4f1a\u4e0b\u964d. \u540c\u65f6\u56fe\u50cf\u4e5f\u53ef\u4ee5\u8ba9\u6211\u4eec\u89c2\u5bdf\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u662f\u5426\u5df2\u7ecf\u6536\u655b. \u5982\u679c\u968f\u7740\u8fed\u4ee3\u6b21\u6570\u7684\u589e\u52a0, J(theta)\u4e0d\u65ad\u4e0a\u5347, \u6700\u5e38\u89c1\u7684\u539f\u56e0\u662f:alpha\u7684\u503c\u592a\u5927, \u5e94\u8be5\u51cf\u5c0falpha\u7684\u503c. \u5982\u679cJ(theta)\u7684\u503c\u4e0d\u65ad\u9707\u8361, \u4e5f\u5e94\u8be5\u51cf\u5c0falpha\u7684\u503c. \u4f46\u662f\u5982\u679calpha\u592a\u5c0f, \u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u4f1a\u4e0b\u964d\u5f97\u5f88\u6162. \u591a\u9879\u5f0f\u56de\u5f52 \u5982\u4f55\u5c06\u6a21\u578b\u548c\u6570\u636e\u8fdb\u884c\u62df\u5408? \u591a\u9879\u5f0f\u56de\u5f52: \u7528\u5047\u8bbe\u7684\u4e00\u6b21\u9879\u7279\u5f81\u6765\u4ee3\u66ff\u9ad8\u6b21\u9879\u7279\u5f81. \u6b63\u89c4\u65b9\u7a0bNormal eqution \u6b63\u89c4\u65b9\u7a0b\u63d0\u4f9b\u4e86\u4e00\u79cd\u6c42theta\u7684\u89e3\u6790\u89e3\u6cd5, \u53ef\u4ee5\u4e00\u6b21\u6027\u6c42\u89e3theta\u7684\u6700\u4f18\u89e3. \u5f53\u5f62\u5982\u4e8c\u6b21\u51fd\u6570\u7684J(theta)\u4e2d\u7684theta\u4e3a\u5b9e\u6570\u65f6,\u6700\u4f4e\u70b9\u7684\u5bfc\u6570=0, \u5229\u7528\u8fd9\u4e2a\u6761\u4ef6\u5c31\u53ef\u4ee5\u6c42\u89e3\u65b9\u7a0b. \u4f46\u662f\u5982\u679ctheta\u662f\u4e00\u4e2a\u5411\u91cf, \u90a3\u5c31\u9700\u8981\u5bf9\u5411\u91cf\u4e2d\u7684\u6bcf\u4e00\u4e2a\u7279\u5f81\u503c\u8fdb\u884c\u504f\u5bfc=0\u7684\u65b9\u7a0b\u6c42\u89e3. \u5f97\u5230\u7684\u6bcf\u4e2atheta\u7684\u503c\u7ec4\u6210\u7684\u5411\u91cf\u5c31\u662f\u6700\u5c0f\u503c. \u6709\u4e00\u4e2am=4\u7684\u8bad\u7ec3\u6837\u672c: \u5728\u7b2c\u4e00\u5217\u524d\u8865\u5145\u4e00\u5217x_0=1, \u5c06x\u53d8\u6210\u4e00\u4e2am*n+1\u7684\u77e9\u9635. \u540c\u65f6\u5c06y\u4e5f\u53d8\u4e3a\u4e00\u4e2am\u7ef4\u5411\u91cf. \u5728\u6709m\u4e2a\u8bad\u7ec3\u6837\u672c(x^1,y^1),dots,(x^m,y^m) , n\u4e2a\u7279\u5f81\u503c: x^i = {begin{bmatrix} x_0^i\\x_1^i\\ vdots x_n^i end{bmatrix}}\u7684\u60c5\u51b5\u4e0b. \u53ef\u4ee5\u5f97\u5230\u4f7f\u5f97\u4ee3\u4ef7\u51fd\u6570\u6700\u5c0f\u5316\u7684theta\u4e3a : theta=(X^TX)^{-1}X^Ty \u4f7f\u7528\u6b63\u89c4\u65b9\u7a0b\u4e0d\u9700\u8981\u9009\u62e9\u5b66\u4e60\u7387alpha, \u4e0d\u9700\u8981\u8fdb\u884c\u8fed\u4ee3. \u4f46\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u5bf9\u4e8e\u5927\u6570\u636e\u91cf\u4ecd\u80fd\u4fdd\u6301\u6b63\u5e38\u5de5\u4f5c. \u800c\u6b63\u89c4\u65b9\u7a0b\u9700\u8981\u8ba1\u7b97(X^TX)^{-1}, \u5728\u6570\u636e\u91cf\u8f83\u5927\u65f6\u8ba1\u7b97\u6bd4\u8f83\u7f13\u6162. \u5982\u679c(X^TX)\u662f\u4e00\u4e2a\u4e0d\u53ef\u9006\u7684\u5947\u5f02\u77e9\u9635. \u4e00\u822c\u6765\u8bf4, (X^TX)\u4e0d\u53ef\u9006\u7684\u539f\u56e0\u662f\u6709\u591a\u4f59\u7684\u7279\u5f81\u503c(\u6bd4\u5982\u6709\u4e24\u4e2a\u7279\u5f81\u503c\u7ebf\u6027\u76f8\u5173)\u6216\u8005\u7279\u5f81\u503c\u8fc7\u591a. \u5728Octave\u4e2d, \u4f7f\u7528pinv\u53ef\u4ee5\u5f97\u5230\u4f2a\u9006. \u8fd9\u6837\u77e9\u9635\u662f\u4e00\u5b9a\u80fd\u6c42\u51fa\u9006\u7684(\u4f7f\u7528inv\u6c42\u51fa\u7684\u662f\u771f\u5b9e\u7684\u9006).<\/p>\n","protected":false},"author":1,"featured_media":94,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[8],"tags":[],"_links":{"self":[{"href":"https:\/\/blog.kishere.cn\/index.php?rest_route=\/wp\/v2\/posts\/166"}],"collection":[{"href":"https:\/\/blog.kishere.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.kishere.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.kishere.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.kishere.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=166"}],"version-history":[{"count":12,"href":"https:\/\/blog.kishere.cn\/index.php?rest_route=\/wp\/v2\/posts\/166\/revisions"}],"predecessor-version":[{"id":295,"href":"https:\/\/blog.kishere.cn\/index.php?rest_route=\/wp\/v2\/posts\/166\/revisions\/295"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.kishere.cn\/index.php?rest_route=\/wp\/v2\/media\/94"}],"wp:attachment":[{"href":"https:\/\/blog.kishere.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=166"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.kishere.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=166"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.kishere.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}