{"id":319,"date":"2016-05-15T03:35:39","date_gmt":"2016-05-15T03:35:39","guid":{"rendered":"http:\/\/blogs.softwareclue.com\/?p=319"},"modified":"2016-05-15T04:46:49","modified_gmt":"2016-05-15T04:46:49","slug":"%e3%80%8a%e5%8f%b0%e5%a4%a7%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e5%9f%ba%e7%9f%b3%e3%80%8blinear-regression","status":"publish","type":"post","link":"http:\/\/blog.softwareclues.com\/zh\/%e3%80%8a%e5%8f%b0%e5%a4%a7%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e5%9f%ba%e7%9f%b3%e3%80%8blinear-regression","title":{"rendered":"\u300a\u53f0\u5927\u673a\u5668\u5b66\u4e60\u57fa\u77f3\u300bLinear Regression"},"content":{"rendered":"<p>By Kubi Code<\/p>\n<p>Source:<a href=\"http:\/\/kubicode.me\/2015\/08\/19\/Machine%20Learning\/Linear-Regression\/\" target=\"_blank\"> http:\/\/kubicode.me\/2015\/08\/19\/Machine%20Learning\/Linear-Regression\/<\/a><\/p>\n<h2 id=\"Linear_Regression\">Linear Regression<\/h2>\n<p>\u73b0\u5728\u76f8\u5bf9\u6bd4\u4e8e\u4e4b\u524d\u7684<a href=\"http:\/\/kubicode.me\/2015\/08\/06\/Machine%20Learning\/Perceptron-Learning-Algorithm\/\" target=\"_blank\" rel=\"external\">Perceptron Learning Algorithm<\/a>\u7b97\u6cd5\uff0c\u5047\u5982\u6211\u4eec\u73b0\u5728\u65f6\u7684\u95ee\u9898\u4e0d\u662f\u89e3\u51b3\u662f\u5426\u53d1\u884c\u7528\u5361\uff0c\u800c\u662f\u8be5\u53d1<strong>\u591a\u5c11\u989d\u5ea6<\/strong>\u7684\u95ee\u9898<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/ed.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/ed.png?resize=300%2C300\" width=\"300 px\" height=\"300 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u4e5f\u5c31\u662f\u8f93\u51fa\u7a7a\u95f4\u5c5e\u4e8e\u4e00\u4e2a\u5b9e\u6570\uff0c\u90a3\u4e48\u5c31\u9700\u8981\u4e00\u4e2a\u56de\u5f52\u7b97\u6cd5\u6765\u89e3\u51b3\u8be5\u95ee\u9898\uff01<br \/>\n<a id=\"more\"><\/a><\/p>\n<p>\u90a3\u4e48\u6211\u4eec\u5176\u5b9e\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u7279\u5f81\u5c5e\u6027\u4e0e\u6743\u91cd\u7684\u52a0\u6743\u6c42\u548c\u6765\u8868\u793a\u9700\u8981\u53d1\u7684\u4fe1\u7528\u989d\u5ea6\u5373\u53ef(\u4e0e<code>PLA<\/code>\u7c7b\u4f3c\uff0c\u4f46\u662f\u6ca1\u6709\u6fc0\u6d3b\u51fd\u6570\uff1a\u4e8c\u503c\u5224\u65ad\u9006\u51fd\u6570)<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/jq.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/jq.png?resize=500%2C300\" width=\"500 px\" height=\"300 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u4e0a\u56fe\u4e2d\u8868\u793a\u7684\u5c31\u662f\u4e3a\u7ebf\u6027\u56de\u5f52(<code>Linear Regression<\/code>)\uff0c\u5176\u4e2d<code>w<sup>T<\/sup>x<\/code>\u5c31\u662f\u8868\u793a\u4e3a\u5168\u90e8\u7684\u5047\u8bbe\u7a7a\u95f4(<code>hypothesis set<\/code>)<\/p>\n<p>\u5982\u679c\u5f53\u524d\u7684\u7279\u5f81\u662f\u4e00\u7ef4\u7684\uff0c\u90a3\u4e48\u8fd9\u91cc\u7684<code>hypothesis set<\/code>\u5c31\u8868\u793a\u4e00\u6761\u7ebf\uff0c\uff08\u56e0\u4e3a\u603b\u4f53\u7684\u7279\u5f81\u5411\u91cf\u91cc\u9762\u8fd8\u6709\u4e00\u4e2a\u5e38\u6570\u503c\uff09<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/2d.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/2d.png?resize=300%2C300\" width=\"300 px\" height=\"300 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u5982\u679c\u5f53\u524d\u7684\u7279\u5f81\u662f\u4e8c\u7ef4\u7684\uff0c\u90a3\u4e48\u8fd9\u91cc\u7684<code>hypothesis set<\/code>\u5c31\u4e00\u4e2a\u5e73\u9762<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/3d.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/3d.png?resize=300%2C300\" width=\"300 px\" height=\"300 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u5f53\u7136\u7279\u5f81\u66f4\u52a0\u591a\u5f97\u8bdd\uff0c\u6700\u7ec8<code>hypothesis set<\/code>\u8868\u793a\u4e00\u4e2a\u8d85\u5e73\u9762<br \/>\n\u5176\u4e2d\u56fe\u4e0a\u7ea2\u8272\u7684\u90e8\u5206\u53eb\u505a\u8bef\u5dee\uff08\u89c6\u9891\u91cc\u9762\u53eb\u505a<strong>\u4f59\u6570<\/strong>\uff09\uff0c\u90a3\u4e48\u56de\u5f52\u5206\u6790\u7684\u76ee\u6807\u5c31\u662f\u5c06\u6240\u6709\u7684\u8bef\u5dee\u964d\u5230\u6700\u5c0f\u8d8a\u597d<br \/>\n\u8fd9\u91cc\u4f7f\u7528\u5e73\u65b9\u8bef\u5dee\u6765\u8861\u91cf\u6574\u4f53\u7684\u8bef\u5dee<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/se.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/se.png?resize=300%2C100\" width=\"300 px\" height=\"100 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u90a3\u4e48\u4ece\u673a\u5668\u5b66\u4e60\u7684\u89d2\u5ea6\u6765\u8bf4\uff0c\u8fd9\u91cc\u7684\u8bef\u5dee\u5c31\u53ef\u4ee5\u770b\u505a(\u4e0b\u9762\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u5c31\u5f88\u719f\u6089\u4e86)<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/jse.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/jse.png?resize=300%2C100\" width=\"300 px\" height=\"100 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u76f8\u5e94\u7684<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/jse2.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/jse2.png?resize=300%2C100\" width=\"300 px\" height=\"100 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u8868\u793a\u8fd9\u4e2a\u5206\u7c7b\u5668\u5728\u672a\u6765\u672a\u8bad\u7ec3\u6570\u636e\u96c6\u4e2d\u4ea7\u751f\u7684\u8bef\u5dee\u662f\u591a\u5c11<br \/>\n\u90a3\u4e48\u73b0\u5728\u7684\u7ebf\u6027\u56de\u5f52\u7684\u95ee\u9898\u5c31\u662f\u8f6c\u4e3a\u5c06<code>E<sub>in<\/sub>(w)<\/code>\u4f18\u5316\u5230\u6700\u5c0f\u3002<\/p>\n<h2 id=\"Ein(w)\u6700\u5c0f\u5316\">Ein(w)\u6700\u5c0f\u5316<\/h2>\n<p>\u73b0\u5c06\u4e0a\u9762\u5c0f\u8282\u7684\u4e2d\u7684<code>E<sub>in<\/sub><\/code>\u8f6c\u4e3a\u77e9\u9635\u7684\u8fd0\u7b97<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/mt.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/mt.png?resize=500%2C400\" width=\"500 px\" height=\"400 px\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<ol>\n<li>\u5411\u91cf\u5185\u79ef\u53ef\u4ea4\u6362\uff0c\u5c06<code>w<sup>T<\/sup>x<\/code>\u8f6c\u4e3a<code>x<sup>T<\/sup>w<\/code><\/li>\n<li>\u5c06\u8fde\u52a0\u8f6c\u4e3a\u5411\u91cf\u5f62\u5f0f\u7684\u957f\u5ea6\uff08\u5e94\u8be5\u662f\u4e8c\u8303\u6570\uff09<\/li>\n<li>\u5c06<code>w<\/code>\u5355\u72ec\u63d0\u51fa\u6765\uff08\u76f8\u5f53\u4e8e\u9694\u79bb\u51fa\u4e86\u4e00\u4e2a\u7279\u5f81\u5c5e\u6027\u5411\u91cf\u7684\u77e9\u9635\uff09<\/li>\n<li>\u6700\u7ec8\u4f7f\u7528\u7f29\u5199\u6765\u8fdb\u884c\u6574\u7406<\/li>\n<\/ol>\n<p>\u5230\u4e86\u8fd9\u4e00\u6b65\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0<code>E<sub>in<\/sub>(w)<\/code>\u53ea\u4e0e<code>w<\/code>\u6709\u5173\uff0c\u90a3\u4e48\u4ed6\u4eec\u7684\u5173\u7cfb\u56fe\u662f<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/wq.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/wq.png?resize=300%2C300\" width=\"300 px\" height=\"300 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u53ef\u4ee5\u53d1\u73b0<code>E<sub>in<\/sub>(w)<\/code>\u662f\u8fde\u7eed\u53ef\u5bfc\uff0c\u8fd8\u6709\u5b83\u662f\u51f8\u7684<br \/>\n\u90a3\u4e48\u7528<code>E<sub>in<\/sub>(w)<\/code>\u5bf9<code>w<\/code>\u6c42\u504f\u5bfc\u5373\u53ef\u6c42\u5bfc\u6700\u4f18\u503c(\u68af\u5ea6\u4e3a0\u7684\u4f4d\u7f6e)<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/td.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/td.png?resize=400%2C300\" width=\"400 px\" height=\"300 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u8fd9\u6837\u73b0\u5728\u95ee\u9898\u53c8\u8f6c\u4e3a\u4e86 \u6c42<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/task.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/task.png?resize=300%2C100\" width=\"300 px\" height=\"100 px\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<p>\u9996\u5148\u5c06<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/ei.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/ei.png?resize=400%2C100\" width=\"400 px\" height=\"100 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u73b0\u5728\u5bf9\u5176\u6c42\u504f\u5bfc<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/pd.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/pd.png?resize=300%2C100\" width=\"300 px\" height=\"100 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u5b8c\u4e86\u4e4b\u540e\u518d\u5c06<code>A,b<\/code>\u66ff\u6362\u56de\u53bb<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/qw.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/qw.png?resize=300%2C100\" width=\"300 px\" height=\"100 px\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<p>\u8fdb\u4e00\u6b65\u5c06\u95ee\u9898\u8f6c\u6362\u4e3a<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/task2.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/task2.png?resize=400%2C100\" width=\"400 px\" height=\"100 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u5f0f\u5b50\u4e2d<code>X<sup>T<\/sup>X<\/code>\u548c<code>X<sup>T<\/sup>y<\/code>\u90fd\u662f\u5df2\u77e5\u7684\uff0c\u552f\u4e00\u4e0d\u77e5\u9053\u7684\u5c31\u662f<code>w<\/code>\uff0c\u8fd9\u6837\u5c31\u53d8\u4e3a\u4e86\u4e00\u4e2a\u4e00\u6b21\u7684\u65b9\u7a0b\u5f0f<\/p>\n<ol>\n<li>\u5047\u5982\u6709<code>(X<sup>T<\/sup>X)<sup>-1<\/sup><\/code>\u53cd\u77e9\u9635\u7684\u5b58\u5728\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u76f4\u63a5\u5f97\u5230\u89e3\u4e86,\u5e76\u4e14\u662f\u552f\u4e00\u7684<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/s1.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/s1.png?resize=250%2C250\" width=\"250 px\" height=\"250 px\" data-recalc-dims=\"1\" \/><\/a><\/li>\n<li>\u4f46\u662f\u5982\u679c<code>(X<sup>T<\/sup>X)<sup>-1<\/sup><\/code>\u53cd\u77e9\u9635\u4e0d\u5b58\u5728\uff0c\u90a3\u4e48\u5f97\u5230\u7684\u89e3\u53ef\u80fd\u5c31\u4e0d\u552f\u4e00\u4e86<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/s2.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/s2.png?resize=250%2C250\" width=\"250 px\" height=\"250 px\" data-recalc-dims=\"1\" \/><\/a><\/li>\n<\/ol>\n<p>\u6240\u4ee5\u8fd9\u91cc\u7684\u6838\u5fc3\u5c31\u662f\u8ba1\u7b97\u865a\u5047\u7684\u53cd\u77e9\u9635(<code>pseudo-inverse<\/code>),\u542c\u6797\u8001\u5e08\u8bf4\u8fd9\u4e2a\u7684\u8ba1\u7b97\u5f88\u591a\u5de5\u5177\u90fd\u662f\u7531\u73b0\u6210\u7684^_^<\/p>\n<blockquote><p>\u521a\u521a\u6c42<code>E<sub>in<\/sub>(w)<\/code>\u6700\u5c0f\u5316\u7684\u8fc7\u7a0b\u4e2d\u770b\u4f3c\u76f4\u63a5\u7528\u516c\u5f0f\u4ee3\u66ff\u53ef\u5230\uff0c\u4f46\u662f\u5176\u4e2d\u7684<code>pseudo-inverse<\/code>\u8ba1\u7b97\u8d77\u6765\u9ebb\u70e6\uff0c\u6700\u7ec8\u5728\u8ba1\u7b97\u7684\u65f6\u5019\u8fd8\u662f\u9700\u8981\u8fed\u4ee3\uff0c\u7136\u540e\u4f1a\u89e6\u53d1<code>E<sub>in<\/sub>(w)<\/code>\u548c<code>E<sub>out<\/sub>(w)<\/code>\u7684\u53d8\u5316\uff0c\u662f\u4e00\u4e2a\u6df1\u5ea6\u9690\u542b\u7684\u5b66\u4e60\u8fc7\u7a0b(\u8fd9\u79cd\u662f\u53eb\u505a<code>Analytic Solution<\/code>)\u3002<\/p><\/blockquote>\n<h2 id=\"Learning_happened\">Learning happened<\/h2>\n<p>\u90a3\u4e48\u8be5\u5982\u679c\u4fdd\u8bc1<code>E<sub>out<\/sub><\/code>\u53ef\u4ee5\u662f\u5c0f\u7684\u5462\uff1f<br \/>\n\u6211\u4eec\u5148\u6765\u770b\u4e00\u4e0b<code>E<sub>in<\/sub><\/code>\u7684\u5e73\u5747<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/eip.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/eip.png?resize=500%2C100\" width=\"500 px\" height=\"100 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u5176\u4e2d<code>nosie level<\/code>\u8868\u793a\u6837\u672c\u4e2d\u566a\u58f0\u7684\u4e00\u4e2a\u60c5\u51b5\uff0c<code>d+1<\/code>\u8868\u793a\u6a21\u578b\u7684\u81ea\u7531\u5ea6\uff0c<code>N<\/code>\u8868\u793a\u6837\u672c\u7684\u5bb9\u91cf<br \/>\n\u5176\u4e2d\u5355\u72ec\u8868\u793a<code>E<sub>in<\/sub>(w)<\/code>\u7684\u8bdd\u4e3a<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/eipt.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/eipt.png?resize=500%2C200\" width=\"500 px\" height=\"200 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u8fd9\u6837\u5c31\u5f62\u6210\u4e86\u4e24\u9879<code>1-XX<sup>+<\/sup><\/code>\u548c<code>y<\/code>\uff0c\u4e5f\u5c31\u662f\u76f8\u5f53\u4e8e\u5c06\u8f93\u5165\u559d\u8f93\u51fa\u8fdb\u884c\u4e86\u4e00\u4e2a\u5206\u79bb,\u5176\u4e2d<code>XX<sup>+<\/sup><\/code>\u53eb\u505a<code>hat matrix<\/code><br \/>\n\u5173\u4e8e\u8fd9\u4e2a<code>hat matrix<\/code>,\u5b83\u7684\u610f\u4e49\u662f\u8fd9\u6837\u7eb8\u7684<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/hm.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/hm.png?resize=500%2C400\" width=\"500 px\" height=\"400 px\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<ol>\n<li>\u7ea2\u8272\u533a\u5757\u8868\u793a\u5411\u91cf<code>X<\/code>\u7684\u4e00\u4e2a\u6269\u6563\uff0c\u800c<code>y^<\/code>\u5c31\u662f\u843d\u5728\u8fd9\u4e2a\u7a7a\u95f4\u4e0a<\/li>\n<li>\u76ee\u6807\u5c31\u662f\u6c42<code>y-y^<\/code>\u7684\u6700\u5c0f\u5316\uff0c\u4e5f\u5c31\u662f\u56fe\u79cd\u7684\u7eff\u8272\u90a3\u6761\u7ebf\uff08<code>y^<\/code>\uff09\u5411\u4e0b\u6295\u5f71\u7684\u7ebf<\/li>\n<li><code>H<\/code>\u5c31\u662f\u8868\u793a\u8fd9\u4e2a\u7a7a\u95f4\u4e0a<code>y<\/code>\u5230<code>y^<\/code>\u7684\u4e00\u4e2a\u6295\u5f71<\/li>\n<li><code>I-H<\/code>\u5c31\u662f\u8868\u793a\u8bef\u5dee\u90e8\u5206<code>y-y^<\/code><\/li>\n<\/ol>\n<p>\u76f8\u5e94\u7684\u4f1a\u6709<code>trace(I-H)=N-(d+1)<\/code><\/p>\n<p>\u597d\uff0c\u73b0\u5728\u518d\u6765\u770b<code>E<sub>in<\/sub><\/code>\u7684\u5e73\u5747\u5230\u5e95\u662f\u4ec0\u4e48\u610f\u601d<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/eips.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/eips.png?resize=500%2C400\" width=\"500 px\" height=\"400 px\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<ol>\n<li>\u5176\u4e2d\u5982\u679c<code>f(x)<\/code>\u4e3a\u76ee\u6807\u51fd\u6570\uff0c\u90a3\u4e48\u76ee\u6807\u503c<code>y<\/code>\u5c31\u76f8\u5f53\u4e8e\u5728<code>f(x)<\/code>\u4e0a\u6dfb\u52a0\u566a\u58f0<\/li>\n<li>\u7136\u540e\u8fd9\u4e2a\u566a\u58f0\u901a\u8fc7<code>I-H<\/code>\u5c31\u53ef\u4ee5\u8f6c\u4e3a<code>y-y^<\/code><\/li>\n<\/ol>\n<p>\u73b0\u5728\u5bf9\u566a\u58f0\u4f5c\u8bc4\u4ef7\u7684\u8bdd\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u5f97\u5230<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/eint2.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/eint2.png?resize=500%2C60\" width=\"500 px\" height=\"60 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u6b64\u65f6<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/eint3.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/eint3.png?resize=500%2C60\" width=\"500 px\" height=\"60 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u8fd9\u4e24\u4e2a\u5f0f\u5b50\u54f2\u5b66\u4e0a\u7684\u610f\u601d\u662f<code>E<sub>in<\/sub><\/code>\u7684\u5e73\u5747\u662f\u53ef\u4ee5\u770b\u5230\u7684\uff0c\u6240\u4ee5\u5f53\u5b58\u5728\u566a\u58f0\u7684\u65f6\u5019\u770b\u5230\u7684\u7ebf\u4f1a\u504f\u5411\u4e8e\u566a\u58f0\u65b9\u5411\uff0c\u800c\u5728<code>E<sub>out<\/sub><\/code>\u7684\u5e73\u5747\u662f\u672a\u77e5\u7684\uff0c\u6bd4\u6700\u597d\u7684\u90a3\u4e2a\u7ebf\u8fd8\u8981\u5411\u53f3\u8fb9\u504f\u4e00\u70b9\uff08\u6ca1\u542c\u61c2-_-\uff09<\/p>\n<p>\u4ed6\u4eec\u4fe9\u4f1a\u5f62\u6210\u5982\u4e0b\u7684\u5173\u7cfb\u7ebf<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/einout.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/einout.png?resize=300%2C300\" width=\"300 px\" height=\"300 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u5b83\u63cf\u8ff0\u7684\u662f\u5f53\u524d\u7684\u6837\u672c\u91cf\u4e0e\u5e73\u5747\u7684<code>E<sub>in<\/sub><\/code>\u548c<code>E<sub>out<\/sub><\/code>\u7684\u5173\u7cfb,\u968f\u7740\u6837\u672c\u91cf<code>N<\/code>\u7684\u589e\u957f\uff0c\u6700\u7ec8\u4f1a\u8d8b\u5411\u4e8e<code>nosie level<\/code><\/p>\n<p>\u90a3\u4e48\u5c31\u53ef\u4ee5\u5f97\u5230<br \/>\n<a class=\"fancybox\" title=\"\" href=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/vvv.png\" rel=\"article0\"><img decoding=\"async\" src=\"https:\/\/i0.wp.com\/kubicode.me\/img\/Linear-Regression\/vvv.png?resize=300%2C200\" width=\"300 px\" height=\"200 px\" data-recalc-dims=\"1\" \/><\/a><br \/>\n\u8bf4\u660e<code>N<\/code>\u8db3\u591f\u5927\uff0c\u7136\u540e\u4ed6\u7684<code>noise level<\/code>\u591f\u5c0f\u65f6\uff0c\u8bf4\u660e\u4e86<code>Learning happened<\/code><\/p>\n<h2 id=\"\u603b\u7ed3\">\u603b\u7ed3<\/h2>\n<ol>\n<li>\u7ebf\u6027\u56de\u5f52\u6700\u7ec8\u6c42\u51fa\u7684\u662f\u4e00\u4e2a\u52a0\u6743\u6c42\u548c\u7684\u503c.<\/li>\n<\/ol>\n<ul>\n<li>\u7ebf\u6027\u56de\u5f52\u7684<code>E<sub>in<\/sub><\/code>\u7684\u91c7\u7528\u7684\u662f\u6700\u5c0f\u5e73\u65b9\u8bef\u5dee.<\/li>\n<li>\u5728\u8ba1\u7b97<code>E<sub>in<\/sub><\/code>\u7684\u6700\u5c0f\u5316\u65f6\uff0c\u53ef\u4ee5\u5c06\u95ee\u9898\u8f6c\u4e3a\u77e9\u9635\u4e4b\u540e\u5c31\u9006\u77e9\u9635\u76f8\u5173\u5373\u53ef.<\/li>\n<li>\u901a\u8fc7<code>E<sub>in<\/sub><\/code>\u5e73\u5747\u7684\u8ba1\u7b97,\u8bf4\u660e\u4e86<code>Learning happened<\/code>.<\/li>\n<li>\u5176\u5b9e\u7ebf\u6027\u56de\u5f52\u53bb\u5750\u5206\u7c7b\u95ee\u9898\u4e5f\u662f\u53ef\u4ee5\u7684^_^\uff0c\u7b2c9\u8bfe\u7b2c4\u4e2a\u5c0f\u89c6\u9891.<\/li>\n<\/ul>\n<h2 id=\"\u53c2\u8003\">\u53c2\u8003<\/h2>\n<ul>\n<li>\u300a\u53f0\u6e7e\u56fd\u7acb\u5927\u5b66-\u673a\u5668\u5b66\u4e60\u57fa\u77f3\u300b\u7b2c\u4e5d\u8bb2<\/li>\n<\/ul>\n<p>\u914d\u56fe\u5747\u6765\u81ea\u300a\u53f0\u6e7e\u56fd\u7acb\u5927\u5b66-\u673a\u5668\u5b66\u4e60\u57fa\u77f3\u300b<\/p>\n","protected":false},"excerpt":{"rendered":"<p>By Kubi Code Source: http:\/\/kubicode.me\/2015\/08\/19\/Mach &hellip; <a href=\"http:\/\/blog.softwareclues.com\/zh\/%e3%80%8a%e5%8f%b0%e5%a4%a7%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e5%9f%ba%e7%9f%b3%e3%80%8blinear-regression\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u201c\u300a\u53f0\u5927\u673a\u5668\u5b66\u4e60\u57fa\u77f3\u300bLinear Regression\u201d<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[3],"tags":[57,73,56],"translation":{"provider":"WPGlobus","version":"2.12.2","language":"zh","enabled_languages":["en","zh"],"languages":{"en":{"title":true,"content":true,"excerpt":false},"zh":{"title":false,"content":false,"excerpt":false}}},"jetpack_publicize_connections":[],"yoast_head":"<!-- This site is optimized 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