“`” \u53c2\u8003\u56de\u7b54\uff1a<\/p>\n
GBDT \u5168\u79f0\u4e3a Gradient Boosting Decision Tree\u3002\u987e\u540d\u601d\u4e49,\u5b83\u662f\u4e00\u79cd\u57fa\u4e8e\u51b3\u7b56\u6811(decision tree)\u5b9e\u73b0\u7684\u5206\u7c7b\u56de\u5f52\u7b97\u6cd5\u3002<\/p>\n
Gradient Descent: method of steepest descent<\/p>\n
\u68af\u5ea6\u4e0b\u964d\u4f5c\u4e3a\u6c42\u89e3\u786e\u5b9a\u53ef\u5fae\u65b9\u7a0b\u7684\u5e38\u7528\u65b9\u6cd5\u800c\u88ab\u4eba\u6240\u719f\u77e5\u3002\u5b83\u662f\u4e00\u79cd\u8fed\u4ee3\u6c42\u89e3\u8fc7\u7a0b,\u5177\u4f53\u5c31\u662f\u4f7f\u89e3\u6cbf\u7740\u5f53\u524d\u89e3\u6240\u5bf9\u5e94\u68af\u5ea6\u7684\u53cd\u65b9\u5411\u8fed\u4ee3\u3002\u8fd9\u4e2a\u65b9\u5411\u4e5f\u53eb\u505a\u6700\u901f\u4e0b\u964d\u65b9\u5411\u3002\u5177\u4f53\u63a8\u5bfc\u8fc7\u7a0b\u5982\u4e0b\u3002\u5047\u5b9a\u5f53\u524d\u5df2\u7ecf\u8fed\u4ee3\u5230\u7b2c k \u8f6e\u7ed3\u675f,\u90a3\u4e48\u7b2c k+1 \u8f6e\u7684\u7ed3\u679c\u600e\u4e48\u5f97\u5230\u5462?\u6211\u4eec\u5bf9\u51fd\u6570 f \u505a\u5982\u4e0b\u4e00\u9636\u6cf0\u52d2\u5c55\u5f00\uff1a<\/p>\n
<\/p>\n
\u4e3a\u4e86\u4f7f\u5f97\u7b2ck+1 \u8f6e\u7684\u51fd\u6570\u503c\u6bd4\u7b2c k \u8f6e\u7684\u5c0f,\u5373\u5982\u4e0b\u4e0d\u7b49\u5f0f\u6210\u7acb\u3002<\/p>\n
<\/p>\n
\u5219\u53ea\u9700\u4f7f:<\/p>\n
<\/p>\n
\u6309\u7167\u8fd9\u6837\u4e00\u76f4\u8fed\u4ee3\u4e0b\u53bb,\u76f4\u5230 ∇f(xk)=0, xk+1=xk \uff0c\u51fd\u6570\u6536\u655b,\u8fed\u4ee3\u505c\u6b62\u3002\u7531\u4e8e\u5728\u505a\u6cf0\u52d2\u5c55\u5f00\u65f6,\u8981\u6c42xk+1−xk \u8db3\u591f\u5c0f\u3002\u56e0\u6b64,\u9700\u8981γ\u6bd4\u8f83\u5c0f\u624d\u884c,\u4e00\u822c\u8bbe\u7f6e\u4e3a 0~1 \u7684\u5c0f\u6570\u3002<\/p>\n
\u987a\u5e26\u63d0\u4e00\u4e0b,Gradient Descent \u662f\u4e00\u79cd\u4e00\u9636\u4f18\u5316\u65b9\u6cd5,\u4e3a\u4ec0\u4e48\u8fd9\u4e48\u8bf4\u5462?\u56e0\u4e3a\u5b83\u5728\u8fed\u4ee3\u8fc7\u7a0b\u4e2d\u4e0d\u9700\u8981\u4e8c\u9636\u53ca\u4ee5\u4e0a\u7684\u4fe1\u606f\u3002\u5982\u679c\u6211\u4eec\u5728\u6cf0\u52d2\u5c55\u5f00\u65f6,\u4e0d\u662f\u4e00\u9636\u5c55\u5f00,\u800c\u662f\u4e8c\u9636\u5c55\u5f00\u3002\u90a3\u5bf9\u5e94\u7684\u65b9\u6cd5\u5c31\u662f\u53e6\u4e00\u4e2a\u88ab\u5927\u5bb6\u6240\u719f\u77e5\u7684\u53ef\u5fae\u65b9\u7a0b\u6c42\u89e3\u65b9\u6cd5:Newton Method,\u5173\u4e8e\u725b\u987f\u6cd5\u7684\u8be6\u7ec6\u5185\u5bb9,\u6211\u4eec\u4f1a\u5728\u540e\u7eed\u6587\u7ae0\u4ecb\u7ecd\u3002<\/p>\n
Boosting: Gradient Descent in functional space<\/p>\n
Boosting\u4e00\u822c\u4f5c\u4e3a\u4e00\u79cd\u6a21\u578b\u7ec4\u5408\u65b9\u5f0f\u5b58\u5728,\u8fd9\u4e5f\u662f\u5b83\u5728 GBDT \u4e2d\u7684\u4f5c\u7528\u3002\u90a3Boosting \u4e0e gradient descent \u6709\u4ec0\u4e48\u5173\u7cfb\u5462?\u4e0a\u4e00\u8282\u6211\u4eec\u8bf4\u5230 gradient descent \u662f\u4e00\u79cd\u786e\u5b9a\u53ef\u5fae\u65b9\u7a0b\u7684\u6c42\u89e3\u65b9\u6cd5\u3002\u8fd9\u91cc\u7684\u53ef\u5fae\u6709\u4e00\u4e2a\u8981\u6c42,\u5c31\u662f\u8bf4\u4e0a\u6587\u4e2d\u7684\u635f\u5931\u51fd\u6570 f \u9488\u5bf9\u6a21\u578b x \u76f4\u63a5\u53ef\u5fae\u3002\u56e0\u6b64\u6a21\u578bx\u53ef\u4ee5\u6839\u636e\u68af\u5ea6\u8fed\u4ee3\u76f4\u63a5\u6c42\u89e3\u3002\u800c\u8fd9\u79cd\u635f\u5931\u51fd\u6570\u9488\u5bf9\u6a21\u578b\u76f4\u63a5\u53ef\u5fae\u662f\u4e00\u4e2a\u5f88\u5f3a\u7684\u5047\u8bbe,\u4e0d\u662f\u6240\u6709\u7684\u6a21\u578b\u90fd\u6ee1\u8db3,\u6bd4\u5982\u8bf4\u51b3\u7b56\u6811\u6a21\u578b\u3002\u73b0\u5728\u6211\u4eec\u56de\u5230\u7b2c\u4e00\u8282,\u5c06f(x)\u5199\u7684\u66f4\u5177\u4f53\u4e00\u70b9\uff1a<\/p>\n
f(x)=l(h(x,D),Y)<\/p>\n
\u5176\u4e2dD \u4e3a\u6570\u636e\u7279\u5f81;Y \u4e3a\u6570\u636e label;h \u4e3a\u6a21\u578b\u51fd\u6570,\u89e3\u51b3\u7531 D->Y \u7684\u6620\u5c04,x\u4e3a\u6a21\u578b\u51fd\u6570\u53c2\u6570,\u5373\u901a\u5e38\u6211\u4eec\u8bf4\u7684\u6a21\u578b;l \u4e3a\u76ee\u6807\u51fd\u6570\u6216\u635f\u5931\u51fd\u6570\u3002<\/p>\n
\u4ee5\u903b\u8f91\u56de\u5f52\u4e3a\u4f8b, x\u4e3a\u6743\u91cd\u5411\u91cf, h\u6a21\u578b\u51fd\u6570\u5c55\u5f00\u4e3a:<\/p>\n
<\/p>\n
\u76ee\u6807\u51fd\u6570l\u5c55\u5f00\u4e3a:<\/p>\n
<\/p>\n
\u6211\u4eec\u53d1\u73b0\u51fd\u65701\u5bf9h\u53ef\u5fae,\u540c\u65f6h\u5bf9x\u53ef\u5fae,\u56e0\u6b64l\u5bf9x\u53ef\u5fae\u3002\u56e0\u6b64,\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7 gradient descent\u7684\u65b9\u5f0f\u5bf9x\u8fdb\u884c\u76f4\u63a5\u6c42\u89e3,\u800c\u4e0d\u7528\u5c06h\u4fdd\u5b58\u4e0b\u6765\u3002\u7136\u800c,\u5982\u679cl\u5bf9h\u53ef\u5fae,\u4f46h\u5bf9x\u4e0d\u53ef\u5fae\u5462?\u6211\u4eec\u4ecd\u6309\u7167\u7b2c\u4e00\u8282\u7684\u65b9\u6cd5\u5148\u5bf9l\u8fdb\u884c\u6cf0\u52d2\u5c55\u5f00,\u53ea\u4e0d\u8fc7\u4e0d\u662f\u9488\u5bf9x,\u800c\u662f\u5bf9 h\u3002\u4e3a\u4e86\u7b80\u5355\u8d77\u89c1,\u6211\u4eec\u7701\u7565D,Y\u3002<\/p>\n
<\/p>\n
\u5176\u4e2d:<\/p>\n
<\/p>\n
\u6309\u7167\u7b2c\u4e00\u8282\u7684\u903b\u8f91,\u6211\u4eec\u4e0d\u96be\u5f97\u51fa\u5982\u4e0b\u8fed\u4ee3\u516c\u5f0f:<\/p>\n
<\/p>\n
\u4f46\u522b\u5fd8\u4e86,\u6211\u4eec\u7684\u76ee\u7684\u4e0d\u662f\u6c42 h,\u800c\u662f x\u3002\u7531\u4e8e h \u5bf9 x \u4e0d\u53ef\u5fae,\u6240\u4ee5 x \u5fc5\u987b\u6839\u636e\u6570\u636e\u91cd\u65b0\u5b66\u4e60\u5f97\u5230\u3002\u800c\u6b64\u65f6\u6211\u4eec\u91cd\u65b0\u5b66\u4e60 x \u7684\u76ee\u6807\u5df2\u7ecf\u4e0d\u662f\u6e90\u76ee\u6807 Y,\u800c\u662f\u539f\u635f\u5931\u51fd\u6570 l \u5728\u5f53\u524d H \u5904\u7684\u68af\u5ea6,\u5373:<\/p>\n
<\/p>\n
\u8fd9\u4e2a\u91cd\u65b0\u5b66\u4e60x\u7684\u8fc7\u7a0b\u6b63\u662f\u6bcf\u4e2abase weak learner\u6240\u505a\u7684\u4e8b\u60c5\u3002\u800c\u8fd9\u79cd\u901a\u8fc7weak learner \u62df\u5408\u6bcf\u4e00\u6b65\u8fed\u4ee3\u540e\u7684\u68af\u5ea6,\u8fdb\u800c\u5b9e\u73b0weak learner\u7ec4\u5408\u7684\u65b9\u5f0f,\u5c31\u662fBoosting\u3002\u53c8\u7531\u4e8e\u6211\u4eec\u5728\u6c42\u5bfc\u8fc7\u7a0b\u4e2d,\u635f\u5931\u51fd\u6570l\u6ca1\u6cd5\u5bf9\u6a21\u578bx\u76f4\u63a5\u6c42\u5bfc,\u800c\u53ea\u80fd\u5bf9\u6a21\u578b\u51fd\u6570h\u6c42\u5bfc\u3002\u56e0\u6b64 Boosting\u53c8\u6709\u4e00\u4e2a\u522b\u540d:“\u51fd\u6570\u7a7a\u95f4\u68af\u5ea6\u4e0b\u964d“\u3002<\/p>\n
\u6b64\u5916,\u4f60\u53ef\u80fd\u4f1a\u542c\u8fc7boosting\u7684\u53ef\u52a0\u6027(additive)\u3002\u8fd9\u91cc\u987a\u4fbf\u63d0\u4e00\u53e5,\u53ef\u52a0\u6027\u6307\u7684\u662f h \u7684\u53ef\u52a0,\u800c\u4e0d\u662fx\u7684\u53ef\u52a0\u3002\u6bd4\u5982x\u662f\u51b3\u7b56\u6811,\u90a3\u4e24\u68f5\u51b3\u7b56\u6811\u672c\u8eab\u600e\u4e48\u52a0\u5728\u4e00\u8d77\u5462?\u4f60\u9876\u591a\u628a\u4ed6\u4eec\u5e76\u6392\u653e\u5728\u4e00\u8d77\u3002\u53ef\u52a0\u7684\u53ea\u662f\u6837\u672c\u6839\u636e\u51b3\u7b56\u6811\u6a21\u578b\u5f97\u5230\u7684\u9884\u6d4b\u503c h(x,D)\u7f62\u4e86\u3002<\/p>\n
Decision Tree: the based weak learner<\/p>\n
Boosting \u7684\u672c\u8d28\u5c31\u662f\u4f7f\u7528\u6bcf\u4e2aweak learner\u6765\u62df\u5408\u622a\u6b62\u5230\u5f53\u524d\u7684\u68af\u5ea6\u3002\u5219\u8fd9\u91cc\u7684D,\u8fd8\u662f\u539f\u6765\u6570\u636e\u4e2d\u7684D,\u800cY\u5df2\u7ecf\u4e0d\u662f\u539f\u6765\u7684Y\u4e86\u3002\u800cGBDT \u4e2d\u7684\u8fd9\u4e2aweak learner \u5c31\u662f\u4e00\u68f5\u5206\u7c7b\u56de\u5f52\u6811(CART)\u3002\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u51b3\u7b56\u6811\u76f4\u63a5\u62df\u5408\u68af\u5ea6:∇l(H(xt))\u3002\u6b64\u65f6\u6211\u4eec\u8981\u6c42\u7684x\u5c31\u53d8\u6210\u4e86\u8fd9\u6837\u4e00\u68f5\u6709k\u4e2a\u53f6\u5b50\u8282\u70b9\u7684\u3001\u4f7f\u5f97\u5982\u4e0b\u76ee\u6807\u51fd\u6570\u6700\u5c0f\u5316\u7684\u51b3\u7b56\u6811:<\/p>\n
<\/p>\n
\u5176\u4e2dT\u4e3a\u76ee\u6807∇l(H(xt)),W\u4e3a\u6bcf\u4e2a\u53f6\u5b50\u8282\u70b9\u7684\u6743\u91cd,L\u4e3a\u53f6\u5b50\u8282\u70b9\u96c6\u5408\u3002\u5bb9\u6613\u6c42\u5f97\u6bcf\u4e2a\u53f6\u5b50\u8282\u70b9\u7684\u6743\u91cd\u4e3a\u5f52\u5c5e\u5230\u5f53\u524d\u53f6\u5b50\u8282\u70b9\u7684\u6837\u672c\u5747\u503c\u3002\u5373 :<\/p>\n
<\/p>\n
\u6bcf\u4e2a\u6837\u672c\u7684\u9884\u6d4b\u503c\u5373\u4e3a\u5176\u6240\u5f52\u5c5e\u7684\u53f6\u5b50\u8282\u70b9\u7684\u6743\u91cd,\u5373h(xt+1)<\/p>\n
\"```\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"“`” \u53c2\u8003\u56de\u7b54\uff1a GBDT \u5168\u79f0\u4e3a Gradient Boosting Decisi […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[101],"tags":[],"class_list":["post-45021","post","type-post","status-publish","format-standard","hentry","category-c"],"_links":{"self":[{"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/posts\/45021","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/comments?post=45021"}],"version-history":[{"count":1,"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/posts\/45021\/revisions"}],"predecessor-version":[{"id":45022,"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/posts\/45021\/revisions\/45022"}],"wp:attachment":[{"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/media?parent=45021"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/categories?post=45021"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/wx.kaifamiao.info\/index.php\/wp-json\/wp\/v2\/tags?post=45021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}