{"id":3175,"date":"2022-02-27T12:52:38","date_gmt":"2022-02-27T04:52:38","guid":{"rendered":"https:\/\/egonlin.com\/?p=3175"},"modified":"2022-02-27T12:52:38","modified_gmt":"2022-02-27T04:52:38","slug":"%e7%ac%ac%e4%b8%80%e7%af%87%ef%bc%9abagging%e7%ae%97%e6%b3%95%e5%92%8c%e9%9a%8f%e6%9c%ba%e6%a3%ae%e6%9e%97","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3175","title":{"rendered":"\u7b2c\u4e00\u7bc7\uff1aBagging\u7b97\u6cd5\u548c\u968f\u673a\u68ee\u6797"},"content":{"rendered":"<h1>Bagging\u7b97\u6cd5\u548c\u968f\u673a\u68ee\u6797<\/h1>\n<p>&emsp;&emsp;\u96c6\u6210\u5b66\u4e60\u4e3b\u8981\u5206\u6210\u4e24\u4e2a\u6d41\u6d3e\uff0c\u5176\u4e2d\u4e00\u4e2a\u662fBoosting\u7b97\u6cd5\uff0c\u53e6\u4e00\u4e2a\u5219\u662f\u672c\u6587\u8981\u8bb2\u7684Bagging\u7b97\u6cd5\uff0cBagging\u7b97\u6cd5<br \/>\n\u7b97\u6cd5\u7684\u5f31\u5b66\u4e60\u5668\u662f\u6ca1\u6709\u4f9d\u8d56\u5173\u7cfb\u7684\uff0c\u56e0\u6b64\u5f31\u5b66\u4e60\u4e4b\u95f4\u53ef\u4ee5\u5e76\u884c\u62df\u5408\u3002<\/p>\n<p>&emsp;&emsp;Bagging\u7b97\u6cd5\u4e2d\u6700\u8457\u540d\u7684\u7b97\u6cd5\u662f\u968f\u673a\u68ee\u6797\uff0c\u7531\u4e8e\u968f\u673a\u68ee\u6797\u7684\u4e0d\u5bb9\u6613\u8fc7\u62df\u5408\u6027\u4ee5\u53ca\u7b80\u4fbf\u6027\uff0c\u53ef\u4ee5\u8bf4\u662f\u548c\u68af\u5ea6\u63d0\u5347\u6811\u540c\u540d\u7684\u7b97\u6cd5\u3002<\/p>\n<h1>Bagging\u7b97\u6cd5\u548c\u968f\u673a\u68ee\u6797\u5b66\u4e60\u76ee\u6807<\/h1>\n<ol>\n<li>Bagging\u7b97\u6cd5\u539f\u7406<\/li>\n<li>Bagging\u7b97\u6cd5\u6d41\u7a0b<\/li>\n<li>\u968f\u673a\u68ee\u6797\u548cBagging\u7b97\u6cd5\u533a\u522b<\/li>\n<li>\u968f\u673a\u68ee\u6797\u6d41\u7a0b<\/li>\n<\/ol>\n<h1>Bagging\u7b97\u6cd5\u539f\u7406\u56de\u987e<\/h1>\n<p>&emsp;&emsp;Bagging\u7b97\u6cd5\u7684\u5f31\u5b66\u4e60\u5668\u7684\u8bad\u7ec3\u96c6\u662f\u901a\u8fc7\u968f\u673a\u91c7\u6837\u5f97\u5230\u7684\u3002\u901a\u8fc7$T$\u6b21\u7684\u968f\u673a\u91c7\u6837\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u81ea\u4e3b\u91c7\u6837\u6cd5(bootstrap sampling)\u5f97\u5230$T$\u4e2a\u91c7\u6837\u96c6\uff0c\u7136\u540e\u5bf9\u4e8e\u8fd9$T$\u4e2a\u91c7\u6837\u96c6\u72ec\u7acb\u7684\u8bad\u7ec3\u51fa$T$\u4e2a\u5f31\u5b66\u4e60\u5668\uff0c\u4e4b\u540e\u6211\u4eec\u901a\u8fc7\u67d0\u79cd\u7ed3\u5408\u7b56\u7565\u5c06\u8fd9$T$\u4e2a\u5f31\u5b66\u4e60\u5668\u6784\u9020\u6210\u4e00\u4e2a\u5f3a\u5b66\u4e60\u5668\u3002<\/p>\n<p>&emsp;&emsp;\u5728\u4e00\u4e2a\u6709$m$\u4e2a\u6837\u672c\u7684\u8bad\u7ec3\u6570\u636e\u4e2d\u968f\u673a\u91c7\u6837\uff0c\u4e00\u4e2a\u6837\u672c\u6bcf\u6b21\u88ab\u91c7\u6837\u7684\u6982\u7387\u4e3a${\\frac{1}{m}}$\uff0c\u4e0d\u88ab\u91c7\u96c6\u7684\u6982\u7387\u4e3a$1-{\\frac{1}{m}}$\uff0c\u5982\u679c$m$\u6b21\u91c7\u6837\u90fd\u6ca1\u6709\u91c7\u4e2d\u7684\u6982\u7387\u4e3a$(1-{\\frac{1}{m}})^m$\uff0c\u5f53$m\\rightarrow{\\infty}$\uff0c$(1-{\\frac{1}{m}})^m\\rightarrow{\\frac{1}{e}}\\approx0.368$\uff0c\u5373\u5728Bagging\u7b97\u6cd5\u7684\u968f\u673a\u91c7\u6837\u4e2d\uff0c\u5927\u7ea6\u6709$36.8%$\u7684\u6570\u636e\u6ca1\u6709\u88ab\u91c7\u4e2d\u3002<\/p>\n<p>&emsp;&emsp;Bagging\u7b97\u6cd5\u7684\u7ed3\u5408\u7b56\u7565\uff0c\u5bf9\u4e8e\u5206\u7c7b\u95ee\u9898\uff0c\u4e00\u822c\u4f7f\u7528\u76f8\u5bf9\u591a\u6570\u6295\u7968\u6cd5\uff0c\u5373\u7968\u6570\u6700\u591a\u7684\u7c7b\u522b\u5373\u4e3a\u6837\u672c\u9884\u6d4b\u7c7b\u522b\uff1b\u5bf9\u4e8e\u56de\u5f52\u95ee\u9898\uff0c\u4e00\u822c\u4f7f\u7528\u7b80\u5355\u5e73\u5747\u6cd5\uff0c\u5373\u5bf9$T$\u4e2a\u5f31\u5b66\u4e60\u7684\u8f93\u51fa\u505a\u7b97\u672f\u5e73\u5747\u5f97\u5230\u6837\u672c\u9884\u6d4b\u503c\u3002<\/p>\n<h1>Bagging\u7b97\u6cd5\u6d41\u7a0b<\/h1>\n<h2>\u8f93\u5165<\/h2>\n<p>&emsp;&emsp;$m$\u4e2a\u6837\u672c$n$\u4e2a\u7279\u5f81\u7684\u8bad\u7ec3\u6570\u636e\u96c6$D={(x_1,y_1),(x_2,y_2),\\cdots,(x_m,y_m)}$\uff1b\u5f31\u5b66\u4e60\u5668\u8fed\u4ee3\u6b21\u6570\u4e3a$T$\u3002<\/p>\n<h2>\u8f93\u51fa<\/h2>\n<p>&emsp;&emsp;\u6700\u7ec8\u5f3a\u5b66\u4e60\u5668$f(x)$\u3002<\/p>\n<h2>\u6d41\u7a0b<\/h2>\n<ol>\n<li>\u5bf9\u8bad\u7ec3\u96c6\u8fdb\u884c\u7b2c$t\\quad(t=1,2,\\cdots,T)$\u6b21\u968f\u673a\u91c7\u6837\uff0c\u5171\u91c7\u96c6$m$\u6b21\uff0c\u5f97\u5230\u6709$m$\u4e2a\u6837\u672c\u7684\u91c7\u6837\u96c6$D_t$<\/li>\n<li>\u7528\u91c7\u6837\u96c6$D_t$\u8bad\u7ec3\u7b2c$t$\u4e2a\u5f31\u5b66\u4e60\u5668$G_t(x)$<\/li>\n<li>\u5bf9\u4e8e\u5206\u7c7b\u95ee\u9898\uff0c\u4f7f\u7528\u76f8\u5bf9\u591a\u6570\u6295\u7968\u6cd5\u9884\u6d4b\u5206\u7c7b\u7ed3\u679c\uff1b\u5bf9\u4e8e\u56de\u5f52\u95ee\u9898\uff0c\u4f7f\u7528\u7b80\u5355\u5e73\u5747\u6cd5\u5f97\u5230\u9884\u6d4b\u503c<\/li>\n<\/ol>\n<h1>\u968f\u673a\u68ee\u6797\u8be6\u89e3<\/h1>\n<h2>\u968f\u673a\u68ee\u6797\u548cBagging\u7b97\u6cd5\u533a\u522b<\/h2>\n<p>&emsp;&emsp;\u968f\u673a\u68ee\u6797(random forest\uff0cRF)\u57fa\u4e8eBagging\u7b97\u6cd5\u7684\u601d\u60f3\uff0c\u505a\u4e86\u4e00\u5b9a\u7684\u6539\u8fdb\uff0c\u5373\u5bf9\u7279\u5f81\u8fdb\u884c\u4e86\u9009\u62e9\u3002<\/p>\n<p>&emsp;&emsp;RF\u4f7f\u7528CART\u51b3\u7b56\u6811\u4f5c\u4e3a\u5f31\u5b66\u4e60\u5668\uff0c\u4f46\u662fRF\u5bf9\u666e\u901a\u7684CART\u51b3\u7b56\u6811\u505a\u4e86\u6539\u8fdb\uff0c\u666e\u901a\u7684CART\u6811\u9009\u62e9\u6700\u4f18\u7279\u5f81\u4f5c\u4e3a\u51b3\u7b56\u6811\u5212\u5206\u7684\u6761\u4ef6\uff1bRF\u7684CART\u51b3\u7b56\u6811\u5219\u662f\u5728\u8bad\u7ec3\u6570\u636e\u7684$n$\u4e2a\u7279\u5f81\u4e2d\u968f\u673a\u9009\u62e9$n<em>{sub}$\u7279\u5f81\uff0c\u4e00\u822c\u60c5\u51b5\u4e0b$n<\/em>{sub}&lt;n$\uff0c\u7136\u540e\u5728\u8fd9$n_{sub}$\u4e2a\u7279\u5f81\u4e2d\u9009\u62e9\u6700\u4f18\u7279\u5f81\u4f5c\u4e3a\u51b3\u7b56\u6811\u5212\u5206\u7684\u6761\u4ef6\u3002<\/p>\n<p>&emsp;&emsp;\u5982\u679c$n<em>{sub}=n$\uff0c\u5219RF\u7684\u51b3\u7b56\u6811\u4e3a\u666e\u901a\u7684\u51b3\u7b56\u6811\uff1b$n<\/em>{sub}$\u8d8a\u5c0f\uff0c\u5219\u6a21\u578b\u9c81\u68d2\u6027\u8d8a\u597d\uff0c\u6a21\u578b\u65b9\u5dee\u4e5f\u4f1a\u51cf\u5c0f\uff0c\u4f46\u6a21\u578b\u5bf9\u8bad\u7ec3\u96c6\u7684\u62df\u5408\u7a0b\u5ea6\u4f1a\u53d8\u5dee\uff0c\u53cd\u4e4b\uff0c\u6a21\u578b\u7684\u504f\u5dee\u4f1a\u53d8\u5c0f\uff0c\u6a21\u578b\u5bf9\u8bad\u7ec3\u96c6\u7684\u6cdb\u5316\u80fd\u529b\u4f1a\u53d8\u5dee\u3002<\/p>\n<h1>\u968f\u673a\u68ee\u6797\u62d3\u5c55<\/h1>\n<p>&emsp;&emsp;RF\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u4e0d\u4ec5\u80fd\u89e3\u51b3\u5206\u7c7b\u548c\u56de\u5f52\u95ee\u9898\uff0c\u8fd8\u53ef\u4ee5\u7528\u4e8e\u7279\u5f81\u8f6c\u6362\u3001\u5f02\u5e38\u70b9\u68c0\u6d4b\u7b49\u3002<\/p>\n<h2>Extra Trees<\/h2>\n<p>&emsp;&emsp;Extra Trees\u548cRF\u7684\u533a\u522b\u6709\u4ee5\u4e0b\u4e24\u70b9\uff1a<\/p>\n<ol>\n<li>\u5bf9\u4e8e\u6bcf\u4e2a\u51b3\u7b56\u6811\u7684\u8bad\u7ec3\u96c6\uff0cRF\u91c7\u7528\u7684\u968f\u673a\u91c7\u6837\u96c6\uff1b\u5bf9\u4e8eextra trees\uff0c\u6bcf\u4e2a\u51b3\u7b56\u6811\u91c7\u7528\u539f\u59cb\u6570\u636e\u96c6<\/li>\n<li>RF\u4f1a\u57fa\u4e8e\u57fa\u5c3c\u7cfb\u6570\u3001\u4fe1\u606f\u71b5\u7684\u65b9\u5f0f\uff0c\u9009\u62e9\u4e00\u4e2a\u6700\u4f18\u7684\u7279\u5f81\u503c\u5212\u5206\uff1bextra teees\u5219\u4f1a\u968f\u673a\u9009\u62e9\u4e00\u4e2a\u7279\u5f81\u503c\u5212\u5206\u7279\u5f81\u6570<\/li>\n<\/ol>\n<p>&emsp;&emsp;\u4ee5\u4e0a\u4e24\u70b9\u5bfc\u81f4extra trees\u751f\u6210\u7684\u968f\u673a\u68ee\u6797\u7684\u51b3\u7b56\u6811\u89c4\u6a21\u4e00\u822c\u4f1a\u5927\u4e8eRF\u3002\u5373\u53ef\u4ee5\u4e00\u5b9a\u7a0b\u5ea6\u7684\u51cf\u5c0f\u6a21\u578b\u7684\u65b9\u5dee\uff0c\u589e\u5f3a\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n<pre><code class=\"language-python\"># \u4f7f\u7528ExtraTree\u5224\u65ad\u7279\u5f81\u91cd\u8981\u6027\u7a0b\u5ea6\nfrom sklearn.datasets import make_friedman1\nfrom sklearn.ensemble import ExtraTreesRegressor\n\nX, y = make_friedman1(n_samples=100, n_features=10, random_state=0)\n\n# \u901a\u8fc7ExtraTreesRegressor\u6a21\u578b\u83b7\u53d6\u6bcf\u4e2a\u7279\u5f81\u7684\u91cd\u8981\u6027\net = ExtraTreesRegressor(n_estimators=10)\net = et.fit(X, y)\nprint(&#039;10\u4e2a\u7279\u5f81\u5404\u81ea\u7684\u91cd\u8981\u6027:{}&#039;.format(et.feature_importances_))<\/code><\/pre>\n<pre><code>10\u4e2a\u7279\u5f81\u5404\u81ea\u7684\u91cd\u8981\u6027:[0.11488041 0.12557425 0.08477273 0.45483849 0.09753123 0.01384401\n 0.0364967  0.0256125  0.01965904 0.02679065]<\/code><\/pre>\n<h2>Totally Random Trees Embedding<\/h2>\n<p>&emsp;&emsp; Totally Random Trees Embedding(TRTE)\u662f\u4e00\u79cd\u65e0\u76d1\u7763\u5b66\u4e60\u7684\u6570\u636e\u8f6c\u6362\u65b9\u5f0f\uff0c\u5b83\u53ef\u4ee5\u5c06\u4f4e\u7ef4\u7684\u6570\u636e\u96c6\u6620\u5c04\u5230\u9ad8\u7ef4\uff0c\u5728\u652f\u6301\u5411\u91cf\u673a\u4e2d\u4f7f\u7528\u4e86\u6838\u6280\u5de7\u5c06\u4f4e\u7ef4\u7684\u6570\u636e\u6620\u5c04\u5230\u9ad8\u7ef4\uff0cTRTE\u63d0\u4f9b\u4e86\u4e0d\u540c\u4e8e\u6838\u6280\u5de7\u7684\u65b9\u6cd5\u3002<\/p>\n<p>&emsp;&emsp;TRTE\u9996\u5148\u4f1a\u6784\u6210\u4e00\u4e2a\u7c7b\u4f3cRF\u7684\u968f\u673a\u68ee\u6797\u6a21\u578b\uff0c\u6a21\u578b\u5b9a\u4e0b\u6765\u540e\u6a21\u578b\u4e2d$T$\u4e2a\u51b3\u7b56\u6811\u7684\u53f6\u5b50\u8282\u70b9\u4f4d\u7f6e\u4e5f\u4f1a\u88ab\u786e\u5b9a\u3002<\/p>\n<p>&emsp;&emsp;\u73b0\u5728\u5047\u8bbe\u6211\u4eec\u67093\u68f5\u51b3\u7b56\u6811\uff0c\u6bcf\u4e2a\u51b3\u7b56\u6811\u67094\u4e2a\u53f6\u5b50\u8282\u70b9\uff0c\u67d0\u4e2a\u6570\u636e\u7279\u5f81$x$\u5212\u5206\u5230\u7b2c1\u4e2a\u51b3\u7b56\u6811\u7684\u7b2c1\u4e2a\u53f6\u5b50\u8282\u70b9\uff0c\u7b2c2\u68f5\u51b3\u7b56\u6811\u7684\u7b2c2\u4e2a\u8282\u70b9\uff0c\u7b2c3\u68f5\u51b3\u7b56\u6811\u7684\u7b2c4\u4e2a\u8282\u70b9\uff0c\u5219$x$\u6620\u5c04\u540e\u7684\u7279\u5f81\u7f16\u7801\u4e3a$(1,0,0,0\\quad0,1,0,0\\quad0,0,0,1)$\uff0c\u7531\u6b64\u65e2\u53ef\u4ee5\u5f97\u523012\u7ef4\u7684\u9ad8\u7ef4\u7279\u5f81\u3002<\/p>\n<h2>Isolation Forest<\/h2>\n<p>&emsp;&emsp;Isolation Forest(IForest)\u53ef\u4ee5\u68c0\u6d4b\u5f02\u5e38\u70b9\u3002<\/p>\n<p>&emsp;&emsp;IForest\u7c7b\u4f3c\u4e8eRF\uff0c\u4f46\u5728\u968f\u673a\u91c7\u6837\u7684\u65f6\u5019\uff0cIForest\u968f\u673a\u91c7\u6837\u7684\u6570\u91cf\u5e76\u4e0d\u662f$m$\u4e2a\uff0c\u800c\u662f\u8fdc\u8fdc\u5c0f\u4e8e\u8bad\u7ec3\u96c6\u4e2a\u6570\uff0c\u56e0\u4e3aIForest\u7684\u4f5c\u7528\u662f\u68c0\u6d4b\u5f02\u5e38\u70b9\uff0c\u5982\u679c\u91c7\u6837\u8fc7\u591a\u6b63\u786e\u6837\u672c\u4f1a\u63a9\u76d6\u6389\u5f02\u5e38\u70b9\u3002<\/p>\n<p>&emsp;&emsp;\u5728\u5212\u5206\u7279\u5f81\u7684\u65f6\u5019\uff0cIForest\u5bf9\u5212\u5206\u7279\u5f81\u968f\u673a\u9009\u62e9\u4e00\u4e2a\u5212\u5206\u9608\u503c\uff0c\u5e76\u968f\u673a\u9009\u62e9\u4e00\u4e2a\u7279\u5f81\u5212\u5206\u51b3\u7b56\u6811\u3002<\/p>\n<p>&emsp;&emsp;\u7531\u4e8eIForest\u7684\u6837\u672c\u6570\u8fc7\u5c11\uff0cIForest\u4e5f\u4f1a\u9009\u62e9\u4e00\u4e2a\u8f83\u5c0f\u7684\u6700\u5927\u51b3\u7b56\u6811\u6df1\u5ea6\u63a7\u5236\u51b3\u7b56\u6811\u7684\u6df1\u5ea6\u3002<\/p>\n<p>&emsp;&emsp;\u5c06\u6d4b\u8bd5\u6837\u672c$x$\u62df\u5408\u5230$T$\u68f5\u51b3\u7b56\u6811\uff0c\u8ba1\u7b97\u6bcf\u9897\u51b3\u7b56\u6811\u4e0a\u8be5\u6837\u672c\u7684\u53f6\u5b50\u8282\u70b9\u7684\u6df1\u5ea6$h_t(x)$\uff0c\u4ece\u800c\u8ba1\u7b97\u51fa\u5e73\u5747\u9ad8\u5ea6\uff0c\u5219\u6837\u672c\u70b9$x$\u7684\u5f02\u5e38\u6982\u7387\u4e3a<br \/>\n$$<br \/>\ns(x,m) = 2^{-{\\frac{h(x)}{c(m)}}}<br \/>\n$$<br \/>\n\u5176\u4e2d$m$\u4e3a\u6837\u672c\u4e2a\u6570\uff0c$c(m)$\u7684\u8868\u8fbe\u5f0f\u4e3a<br \/>\n$$<br \/>\nc(m) = 2\\ln(m-1)+\\xi-2{\\frac{m-1}{m}}<br \/>\n$$<br 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