{"id":3138,"date":"2022-02-27T12:19:05","date_gmt":"2022-02-27T04:19:05","guid":{"rendered":"https:\/\/egonlin.com\/?p=3138"},"modified":"2022-02-27T12:19:05","modified_gmt":"2022-02-27T04:19:05","slug":"%e7%ac%ac%e4%b8%80%e7%af%87%ef%bc%9aadaboost%e7%ae%97%e6%b3%95%e5%bc%95%e5%85%a5","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3138","title":{"rendered":"\u7b2c\u4e00\u7bc7\uff1aAdaBoost\u7b97\u6cd5\u5f15\u5165"},"content":{"rendered":"

AdaBoost\u7b97\u6cd5<\/h1>\n

  \u96c6\u6210\u5b66\u4e60\u4e2d\u5f31\u5b66\u4e60\u5668\u4e4b\u95f4\u6709\u5f3a\u4f9d\u8d56\u5173\u7cfb\u7684\uff0c\u79f0\u4e4b\u4e3aBoosting\u7cfb\u5217\u7b97\u6cd5\uff0c\u800cAdaBoost\u5219\u662fBoosting\u7cfb\u5217\u7b97\u6cd5\u4e2d\u6700\u8457\u540d\u7684\u7b97\u6cd5\u4e4b\u4e00\u3002<\/p>\n

  AdaBoost\u7b97\u6cd5\u5f3a\u5927\u4e4b\u5904\u5728\u4e8e\u65e2\u53ef\u4ee5\u89e3\u51b3\u5206\u7c7b\u95ee\u9898\uff0c\u53c8\u53ef\u4ee5\u89e3\u51b3\u56de\u5f52\u95ee\u9898\u3002<\/p>\n

AdaBoost\u7b97\u6cd5\u5b66\u4e60\u76ee\u6807<\/h1>\n
    \n
  1. AdaBoost\u7b97\u6cd5\u76ee\u6807\u51fd\u6570\u4f18\u5316<\/li>\n
  2. \u5f3a\u5206\u7c7b\u5668\u548c\u5f3a\u56de\u5f52\u5668\u6d41\u7a0b<\/li>\n
  3. AdaBoost\u7b97\u6cd5\u4f18\u7f3a\u70b9<\/li>\n<\/ol>\n

    AdaBoost\u7b97\u6cd5\u8be6\u89e3<\/h1>\n

    Boosting\u7b97\u6cd5\u56de\u987e<\/h2>\n

      Boosting\u7b97\u6cd5\u7684\u6d41\u7a0b\u662f\uff1a\u9996\u5148\u8bad\u7ec3\u5904\u4e00\u4e2a\u5f31\u5b66\u4e60\u5668\uff0c\u6839\u636e\u5f31\u5b66\u4e60\u5668\u7684\u8bef\u5dee\u7387\u66f4\u65b0\u8bad\u7ec3\u6837\u672c\u7684\u6743\u91cd\uff0c\u7136\u540e\u57fa\u4e8e\u8c03\u6574\u6743\u91cd\u540e\u7684\u8bad\u7ec3\u96c6\u8bad\u7ec3\u7b2c\u4e8c\u4e2a\u5f31\u5b66\u4e60\u5668\uff0c\u76f4\u5230\u5f31\u5b66\u4e60\u5668\u8fbe\u5230\u4e8b\u5148\u6307\u5b9a\u7684\u6570\u76eeT\uff0c\u505c\u6b62\u7b97\u6cd5\u3002<\/p>\n

      \u5bf9\u4e8eBoosting\u7b97\u6cd5\u7684\u6d41\u7a0b\uff0c\u53ef\u4ee5\u770b\u5230\u5982\u679c\u6211\u4eec\u89e3\u51b3\u4ee5\u4e0b4\u4e2a\u95ee\u9898\uff0c\u65e2\u53ef\u4ee5\u5f97\u5230\u5b8c\u6574\u7684Boosting\u7b97\u6cd5<\/p>\n

      \n
    1. \u5f31\u5b66\u4e60\u5668\u7684\u8bef\u5dee\u7387<\/li>\n
    2. \u8bad\u7ec3\u6837\u672c\u7684\u6743\u91cd$w$\u66f4\u65b0\u65b9\u6cd5<\/li>\n
    3. \u66f4\u65b0\u6837\u672c\u6743\u91cd\u7684\u65b9\u6cd5<\/li>\n
    4. \u7ed3\u5408\u7b56\u7565<\/li>\n<\/ol>\n

      AdaBoost\u7b97\u6cd5<\/h2>\n

        \u4e0a\u9762\u8bb2\u5230\u4e86Boosting\u7b97\u6cd5\u9700\u8981\u89e3\u51b3\u76844\u4e2a\u95ee\u9898\uff0c\u56e0\u4e3aAdaBoost\u7b97\u6cd5\u96b6\u5c5e\u4e8eBoosting\u7b97\u6cd5\uff0c\u90a3\u4e48AdaBoost\u7b97\u6cd5\u4e5f\u9700\u8981\u89e3\u51b3\u8fd94\u4e2a\u95ee\u9898\uff0c\u5176\u5b9e\u4e5f\u53ef\u4ee5\u8bf4\u6210\u53ea\u8981\u662fBoosting\u7cfb\u5217\u7684\u7b97\u6cd5\uff0c\u90fd\u9700\u8981\u89e3\u51b3\u8fd94\u4e2a\u95ee\u9898\u3002<\/p>\n

      AdaBoost\u7b97\u6cd5\u76ee\u6807\u51fd\u6570\u4f18\u5316<\/h2>\n

        AdaBoost\u7b97\u6cd5\u53ef\u4ee5\u7406\u89e3\u6210\u6a21\u578b\u662f\u52a0\u6cd5\u6a21\u578b\u3001\u76ee\u6807\u51fd\u6570\u662f\u6307\u6570\u51fd\u6570\u3001\u5b66\u4e60\u7b97\u6cd5\u662f\u524d\u5411\u5206\u6b65\u7b97\u6cd5\u65f6\u7684\u5b66\u4e60\u65b9\u6cd5\u3002\u5176\u4e2d\u52a0\u6cd5\u6a21\u578b\u53ef\u4ee5\u7406\u89e3\u6210\u5f3a\u5b66\u4e60\u5668\u662f\u7531\u4e4b\u524d\u6240\u6709\u7684\u5f31\u5b66\u4e60\u5668\u52a0\u6743\u5e73\u5747\u5f97\u5230\u7684\uff1b\u524d\u5411\u5206\u6b65\u7b97\u6cd5\u5219\u53ef\u4ee5\u7406\u89e3\u6210\u5f31\u5b66\u4e60\u5668\u8bad\u7ec3\u6570\u636e\u7684\u6743\u91cd\u901a\u8fc7\u524d\u4e00\u4e2a\u5f31\u5b66\u4e60\u5668\u66f4\u65b0\u3002<\/p>\n

        AdaBoost\u7b97\u6cd5\u7684\u6a21\u578b\u662f\u52a0\u6cd5\u6a21\u578b\uff0c\u5373\u5f3a\u5b66\u4e60\u5668\u7684\u6a21\u578b\u4e3a
      \n$$
      \nf(x) = \\sum_{k=1}^K \\alpha_kG_k(x)
      \n$$
      \n\u5176\u4e2d$K$\u662f$K$\u4e2a\u5f31\u5b66\u4e60\u5668\u3002<\/p>\n

        AdaBoost\u7b97\u6cd5\u7684\u4e8b\u524d\u5411\u5206\u6b65\u7b97\u6cd5\uff0c\u5373\u7ecf\u8fc7$k-1$\u6b21\u8fed\u4ee3\u540e\uff0c\u7b2c$k-1$\u8f6e\u540e\u5f3a\u5b66\u4e60\u5668\u4e3a
      \n$$
      \n\\begin{align}
      \nf_{k-1}(x) & = \\alpha_1G_1(x)+\\alpha_2G2(x)+\\cdots+\\alpha<\/em>{k-1}G{k-1}(x)\\
      \n& = f<\/em>{k-2}(x) + \\alpha{k-1} G<\/em>{k-1}(x)
      \n\\end{align}
      \n$$
      \n\u7ecf\u8fc7$k$\u6b21\u8fed\u4ee3\u540e\uff0c\u7b2c$k$\u8f6e\u540e\u5f3a\u5b66\u4e60\u5668\u4e3a
      \n$$
      \nfk(x) = \\sum<\/em>{i=1}^k \\alpha_i Gi(x) = f<\/em>{k-1}(x) + \\alpha_kG_k(x)
      \n$$
      \n  \u5f97\u5230\u7b2c$k$\u8f6e\u5f3a\u5b66\u4e60\u5668\u540e\uff0c\u6211\u4eec\u77e5\u9053AdaBoost\u7684\u76ee\u6807\u51fd\u6570\u662f\u6307\u6570\u51fd\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u7684\u76ee\u6807\u662f\u4f7f\u524d\u5411\u5206\u6b65\u7b97\u6cd5\u5f97\u5230\u7684$\\alpha_k$\u548c$G_k(x)$\u4f7f$f_k(x)$\u5728\u8bad\u7ec3\u6570\u636e\u96c6\u4e0a\u7684\u6307\u6570\u635f\u5931\u6700\u5c0f\uff0c\u5373AdaBoost\u7684\u76ee\u6807\u51fd\u6570\u4e3a
      \n$$
      \n\\begin{align}
      \n(\\alpha_k,Gk(x)) & = \\underbrace{\\arg\\,min}<\/em>{\\alpha,G}\\sum_{i=1}^m e^{-y_ifk(x)}\\
      \n& = \\underbrace{\\arg\\,min}<\/em>{\\alpha,G}\\sum_{i=1}^m e^{[{-yi(f<\/em>{k-1}(x_i)+\\alpha{G(xi)}})]} \\
      \n& = \\underbrace{\\arg\\,min}<\/em>{\\alpha,G}\\sum_{i=1}^m e^{[{-yi(f<\/em>{k-1}(x_i))}]} e^{[{-y_i(\\alpha{G(x_i)}})]}
      \n\\end{align}
      \n$$
      \n  \u7531\u4e8e$e^{[{-yi(f<\/em>{k-1}(xi))}]}$\u7684\u503c\u4e0d\u4f9d\u8d56$\\alpha,G$\uff0c\u56e0\u6b64\u4ed6\u4e0e\u6700\u5c0f\u5316\u65e0\u5173\uff0c\u5b83\u4ec5\u4ec5\u4f9d\u8d56\u4e8e\u968f\u7740\u6bcf\u4e00\u8f6e\u8fed\u4ee3\u800c\u53d8\u5316\u7684$f<\/em>{k-1}(x)$\uff0c\u56e0\u6b64\u53ef\u4ee5\u628a$e^{[{-yi(f<\/em>{k-1}(xi))}]}$\u770b\u505a$\\overline{w}<\/em>{ki}$\uff0c\u5373\u76ee\u6807\u51fd\u6570\u53d8\u4e3a
      \n$$
      \n(\\alpha_k,Gk(x)) = \\underbrace{\\arg\\,min}<\/em>{\\alpha,G}\\sum{i=1}^m \\overline{w}<\/em>{ki} e^{[{-y_i(\\alpha{G(x_i)}})]}
      \n$$
      \n  \u73b0\u5728\u7684\u76ee\u6807\u5c31\u662f\u6700\u4f18\u5316AdaBoost\u7684\u76ee\u6807\u51fd\u6570\u5f97\u5230\u80fd\u4f7f\u76ee\u6807\u51fd\u6570\u6700\u5c0f\u5316\u7684$\\alpha_k^$\u548c$G_k^<\/em>(x)$\u3002<\/p>\n

        \u9996\u5148\uff0c\u5bf9\u4e8e\u4efb\u610f\u7684$\\alpha>0$\uff0c$G_k^(x)$\u8868\u793a\u7b2c$k$\u8f6e\u80fd\u591f\u4f7f\u5f97\u52a0\u8bad\u7ec3\u6570\u636e\u5206\u7c7b\u8bef\u5dee\u7387\u6700\u5c0f\u7684\u57fa\u672c\u5206\u7c7b\u5668\uff0c\u5206\u7c7b\u8bef\u5dee\u7387\u4e3a
      \n$$
      \nek = {\\frac{\\sum<\/em>{i=1}^m\\overline{w}_{ki}I(y_i\\neq{G_k(xi)})}{\\sum<\/em>{i=1}^m\\overline{w}{ki}}} = \\sum<\/em>{i=1}^m\\overline{w}_{ki}I(y_i\\neq{G_k(xi)}) = \\sum<\/em>{{y_i}\\neq{G_k(xi)}}\\overline{w}<\/em>{ki}
      \n$$
      \n$G_k^<\/em>(x)$\u4e3a
      \n$$
      \nGk^*(x) = \\underbrace{arg\\,\\min}<\/em>{G}\\sum{i=1}^m \\overline{w}<\/em>{ki} I(y_i\\neq{G(x_i))}
      \n$$
      \n  $G_k^(x)$\u5373\u4e3a\u5b66\u4e60\u5668\u7684$G_k(x)$\uff0c\u628a$G_k(x)$\u4ee3\u5165\u76ee\u6807\u51fd\u6570\u5bf9$\\alpha$\u6c42\u5bfc\u5e76\u4f7f\u5bfc\u6570\u4e3a0\uff0c\u53ef\u4ee5\u628a\u4e0a\u8ff0\u7684\u76ee\u6807\u51fd\u6570\u4f18\u5316\u6210
      \n$$
      \n\\begin{align}
      \n(\\alpha_k,Gk(x)) & = \\underbrace{\\arg\\,min}<\/em>{\\alpha,G}\\sum{i=1}^m \\overline{w}<\/em>{ki} e^{[{-y_i(\\alpha{G(xi)}})]} \\
      \n& = \\underbrace{\\arg\\,min}<\/em>{\\alpha,G}\\sum_{y_i=G_k(xi)}\\overline{w}<\/em>{ki}e^{-\\alpha}+\\sum_{y_i\\neq{G_k(xi)}}\\overline{w}<\/em>{ki}e^{\\alpha} \\
      \n& = \\underbrace{\\arg\\,min}_{\\alpha,G} (1-e_k)e^{-\\alpha} + e_ke^{\\alpha}
      \n\\end{align}
      \n$$
      \n\u65e2\u5f97\u6700\u5c0f\u7684$\\alpha$\u4e3a
      \n$$
      \n\\alpha_k^<\/em> = {\\frac{1}{2}}\\log{\\frac{1-e_k}{e_k}}
      \n$$
      \n  \u6700\u540e\u770b\u6837\u672c\u7684\u6743\u91cd\u66f4\u65b0\uff0c\u5229\u7528$fk(x)=f<\/em>{k-1}(x)+\\alpha_kGk(x)$\u548c$\\overline{w}<\/em>{ki}=e^{[-yif<\/em>{k-1}(xi)]}$\u53ef\u5f97
      \n$$
      \n\\begin{align}
      \n\\overline{w}<\/em>{k+1,i} & = e^{[-yif<\/em>{k}(x_i)]} \\
      \n& = e^{[-yi(f<\/em>{k-1}(x_i))-y_i(\\alpha_kG_k(xi))]} \\
      \n& = \\overline{w}<\/em>{ki}e^{[-y_i\\alpha_kGk(x)]}
      \n\\end{align}
      \n$$
      \n  $\\overline{w}<\/em>{k+1,i}$\u5373\u63a5\u4e0b\u6765\u8981\u8bb2\u5230\u7684AdaBoost\u7b97\u6cd5\u7684\u8bad\u7ec3\u6570\u636e\u6743\u91cd\u7684\u66f4\u65b0\u516c\u5f0f\u3002<\/p>\n

      AdaBoost\u7b97\u6cd5\u6d41\u7a0b<\/h1>\n

        AdaBoost\u7b97\u6cd5\u65e2\u53ef\u4ee5\u89e3\u51b3\u5206\u7c7b\u95ee\u9898\uff0c\u53c8\u53ef\u4ee5\u89e3\u51b3\u56de\u5f52\u95ee\u9898\u3002\u5bf9\u4e8e\u5206\u7c7b\u95ee\u9898\uff0c\u6b64\u5904\u6211\u4eec\u8bb2\u8ff0\u7684AdaBoost\u7b97\u6cd5\u6d41\u7a0b\u4e3b\u8981\u662f\u9488\u5bf9\u4e8c\u5206\u7c7b\u95ee\u9898\uff0c\u4e8c\u5206\u7c7b\u95ee\u9898\u548c\u591a\u5206\u7c7b\u95ee\u9898\u7684\u533a\u522b\u4e3b\u8981\u5728\u4e8e\u5f31\u5206\u7c7b\u5668\u7684\u7cfb\u6570\u4e0a\uff0c\u672c\u6587\u4f1a\u4ecb\u7ecdAdaBoost SAMME\u7b97\u6cd5\u5982\u4f55\u8ba1\u7b97\u5f31\u5206\u7c7b\u5668\u7684\u7cfb\u6570\uff1b\u5bf9\u4e8e\u56de\u5f52\u95ee\u9898\uff0c\u7531\u4e8eAdaBoost\u7528\u6765\u89e3\u51b3\u56de\u5f52\u95ee\u9898\u7684\u53d8\u79cd\u6709\u5f88\u591a\uff0c\u672c\u6587\u53ea\u5bf9AdaBoost R2\u7b97\u6cd5\u505a\u4e00\u4e2a\u4ecb\u7ecd\u3002<\/p>\n

      \u8f93\u5165<\/h2>\n

        $m$\u4e2a\u6837\u672c$n$\u4e2a\u7279\u5f81\u7684\u8bad\u7ec3\u6570\u636e\u96c6$T={(x_1,y_1),(x_2,y_2),\\cdots,(x_m,y_m)}$\u3002<\/p>\n

        \u9488\u5bf9\u4e8c\u5206\u7c7b\u95ee\u9898\uff0c$y_i\\in{Y={1,-1}}$\u3002<\/p>\n

      \u8f93\u51fa<\/h2>\n

        \u6700\u7ec8\u5f3a\u5b66\u4e60\u5668$G(x)$\u3002<\/p>\n

      \u5f3a\u5206\u7c7b\u5668\u6d41\u7a0b<\/h2>\n
        \n
      1. \u521d\u59cb\u5316\u8bad\u7ec3\u6570\u636e\u7684\u6743\u91cd
        \n$$
        \nD1 = (w<\/em>{11},\\cdots,w{1i},\\cdots,w<\/em>{1m}),\\quad{w_{1i}={\\frac{1}{m}},\\quad{i=1,2,\\cdots,m}}
        \n$$<\/li>\n
      2. \u751f\u6210\u5f31\u5206\u7c7b\u5668
        \n$$
        \nG_k(x),\\quad{k=1,2,\\cdots,K}
        \n$$<\/li>\n
      3. \u8ba1\u7b97\u5f31\u5206\u7c7b\u5668$G_k(x)$\u5728\u8bad\u7ec3\u96c6\u4e0a\u7684\u5206\u7c7b\u8bef\u5dee\u7387\u4e3a
        \n$$
        \n\\begin{align}
        \nek & = \\sum<\/em>{i=1}^m P(G_k(x_i)\\neq{yi}) \\
        \n& = \\sum<\/em>{i=1}^m w_{k_i} I(G_k(x_i)\\neq{y_i})
        \n\\end{align}
        \n$$<\/li>\n
      4. \u8ba1\u7b97$G_k(x)$\u7684\u6743\u91cd\u7cfb\u6570
        \n$$
        \n\\begin{align}
        \n& \\alpha_k={\\frac{1}{2}}\\log{\\frac{1-e_k}{e_k}}\\quad\\text{\u4e8c\u5206\u7c7b\u95ee\u9898} \\
        \n& \\alpha_k={\\frac{1}{2}}\\log{\\frac{1-e_k}{e_k}}+\\log(R-1)\\quad\\text{\u591a\u5206\u7c7b\u95ee\u9898}
        \n\\end{align}
        \n$$
        \n  \u4e8c\u5206\u7c7b\u95ee\u9898\u7684\u6743\u91cd\u7cfb\u6570\u4e2d\uff0c\u53ef\u4ee5\u770b\u51fa\u5982\u679c\u5206\u7c7b\u8bef\u5dee\u7387$e_k$\u8d8a\u5927\uff0c\u5219\u5bf9\u5e94\u7684\u5f31\u5206\u7c7b\u5668\u7684\u6743\u91cd\u7cfb\u6570$\\alpha_k$\u8d8a\u5c0f\uff0c\u5373\u8bef\u5dee\u7387\u5c0f\u7684\u5f31\u5206\u7c7b\u5668\u6743\u91cd\u7cfb\u6570\u8d8a\u5927\u3002<\/li>\n<\/ol>\n

          \u591a\u5206\u7c7b\u95ee\u9898\u4f7f\u7528\u7684\u662fAdaBoost SAMME\u7b97\u6cd5\uff0c\u5176\u4e2d$R$\u4e3a\u7c7b\u522b\u6570\uff0c\u5982\u679c$R=2$\uff0c\u5219\u8be5\u591a\u5143\u5206\u7c7b\u7684\u6743\u91cd\u7cfb\u6570\u5c06\u53d8\u6210\u4e8c\u5143\u5206\u7c7b\u7684\u6743\u91cd\u7cfb\u6570\u3002<\/p>\n

          \n
        1. \u66f4\u65b0\u8bad\u7ec3\u6570\u636e\u7684\u6743\u91cd
          \n$$
          \n\\begin{align}
          \n& D{k+1} = (w<\/em>{k+1,1},\\cdots,w{k+1,i},\\cdots,w<\/em>{k+1,m}) \\
          \n& w{k+1,i} = {\\frac{w<\/em>{ki}}{Z_k}}e^{-\\alpha_ky_iG_k(x_i)},\\quad{i=1,2,\\cdots,m}\\
          \n\\end{align}
          \n$$
          \n  \u5176\u4e2d$Z_k$\u662f\u89c4\u8303\u56e0\u5b50
          \n$$
          \nZk=\\sum<\/em>{i=1}^mw_{ki}e^{-\\alpha_ky_iG_k(xi)}
          \n$$
          \n  \u4ece$w<\/em>{k+1,i}$\u7684\u8ba1\u7b97\u516c\u5f0f\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u5982\u679c\u7b2c$i$\u4e2a\u6837\u672c\u5206\u7c7b\u9519\u8bef\uff0c\u5219$y_iG_k(x_i)<0$\uff0c\u5bfc\u81f4\u6837\u672c\u7684\u6743\u91cd\u5728\u7b2c$k+1$\u4e2a\u5f31\u5206\u7c7b\u5668\u4e2d\u53d8\u5927\uff0c\u53cd\u4e4b\uff0c\u5219\u6837\u672c\u6743\u91cd\u5728\u7b2c$k+1$\u4e2a\u5f31\u5206\u7c7b\u5668\u4e2d\u53d8\u5c0f\u3002<\/li>\n
        2. \u7ed3\u5408\u7b56\u7565
          \n$$
          \n\\begin{align}
          \n& f(x)=\\sum_{k=1}^K\\alpha_kGk(X)\\quad\\text{\u7ebf\u6027\u6a21\u578b} \\
          \n& G(x)=sign(\\sum<\/em>{k=1}^K\\alpha_kG_k(X))\\quad\\text{\u6700\u7ec8\u5f3a\u5206\u7c7b\u5668}G(x)
          \n\\end{align}
          \n$$<\/li>\n<\/ol>\n

          \u5f3a\u56de\u5f52\u5668\u6d41\u7a0b<\/h2>\n
            \n
          1. \u521d\u59cb\u5316\u8bad\u7ec3\u6570\u636e\u7684\u6743\u91cd
            \n$$
            \nD1 = (w<\/em>{11},\\cdots,w{1i},\\cdots,w<\/em>{1m}),\\quad{w_{1i}={\\frac{1}{m}},\\quad{i=1,2,\\cdots,m}}
            \n$$<\/li>\n
          2. \u751f\u6210\u5f31\u5206\u7c7b\u5668
            \n$$
            \nG_k(x),\\quad{k=1,2,\\cdots,K}
            \n$$<\/li>\n
          3. \u8ba1\u7b97\u5f31\u56de\u5f52\u5668$G_k(x)$\u5728\u8bad\u7ec3\u96c6\u4e0a\u7684\u6700\u5927\u8bef\u5dee
            \n$$
            \nE_k = \\max|y_i-G_k(x_i)|,\\quad{i=1,2,\\cdots,m}
            \n$$<\/li>\n
          4. \u8ba1\u7b97\u6bcf\u4e2a\u6837\u672c\u4e4b\u95f4\u7684\u76f8\u5bf9\u8bef\u5dee
            \n$$
            \ne_{ki}={\\frac{|y_i-G_k(x_i)|}{Ek}}
            \n$$
            \n  \u6b64\u5904\u4e5f\u53ef\u4ee5\u4f7f\u7528\u5747\u65b9\u8bef\u5dee\uff0c\u5373$e<\/em>{ki}={\\frac{(y_i-G_k(x_i))^2}{E_k^2}}$<\/li>\n
          5. \u8ba1\u7b97\u7b2c$k$\u5f31\u56de\u5f52\u5668\u7684\u8bef\u5dee\u7387\u548c\u6743\u91cd\u7cfb\u6570
            \n$$
            \n\\begin{align}
            \n& ek = \\sum<\/em>{i=1}^m w{ki} e<\/em>{ki}\\quad\\text{\u8bef\u5dee\u7387} \\
            \n& \\alpha_k = {\\frac{e_k}{1-e_k}}\\quad\\text{\u6743\u91cd\u7cfb\u6570}
            \n\\end{align}
            \n$$<\/li>\n
          6. \u66f4\u65b0\u8bad\u7ec3\u6570\u636e\u7684\u6743\u91cd
            \n$$
            \nw{k+1,i} = {\\frac{w<\/em>{ki}}{Z_k}\\alphak^{1-e<\/em>{ki}}}
            \n$$
            \n  \u5176\u4e2d$Z_k$\u662f\u89c4\u8303\u56e0\u5b50
            \n$$
            \nZk = \\sum<\/em>{i=1}^m w_{ki}\\alphak^{1-e<\/em>{ki}}
            \n$$<\/li>\n
          7. \u7ed3\u5408\u7b56\u7565
            \n$$
            \nG(x) = G{k^*}(x)
            \n$$
            \n  \u5176\u4e2d$G<\/em>{k^}(x)$\u662f\u6240\u6709$\\ln{\\frac{1}{\\alpha_k}},\\quad{k=1,2,\\cdots,K}$\u7684\u4e2d\u4f4d\u6570\u5bf9\u5e94\u5e8f\u53f7$k^<\/em>$\u5bf9\u5e94\u7684\u5f31\u56de\u5f52\u5668<\/li>\n<\/ol>\n

            AdaBoost\u7b97\u6cd5\u4f18\u7f3a\u70b9<\/h1>\n

            \u4f18\u70b9<\/h2>\n
              \n
            1. \u4e0d\u5bb9\u6613\u8fc7\u62df\u5408<\/li>\n
            2. \u5206\u7c7b\u7cbe\u51c6\u5ea6\u9ad8<\/li>\n
            3. \u7531\u4e8e\u5f31\u5206\u7c7b\u5668\u65e2\u53ef\u4ee5\u662f\u5206\u7c7b\u5668\u53c8\u53ef\u4ee5\u662f\u56de\u5f52\u5668\uff0c\u4f7f\u7528\u7075\u6d3b<\/li>\n<\/ol>\n

              \u7f3a\u70b9<\/h2>\n
                \n
              1. \u7531\u4e8e\u662f\u5bf9\u8bad\u7ec3\u6570\u636e\u52a0\u6743\uff0c\u6709\u53ef\u80fd\u4f1a\u8d4b\u4e88\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u5f02\u5e38\u503c\u8f83\u9ad8\u7684\u6743\u91cd\uff0c\u5f71\u54cd\u6a21\u578b\u7684\u51c6\u786e\u5ea6<\/li>\n<\/ol>\n

                \u5c0f\u7ed3<\/h1>\n

                  AdaBoost\u7b97\u6cd5\u5e76\u6ca1\u6709\u4f7f\u7528\u8f83\u6df1\u7684\u6570\u5b66\u77e5\u8bc6\uff0c\u800c\u662f\u63a8\u5bfc\u8fc7\u7a0b\u6d89\u53ca\u8f83\u4e3a\u590d\u6742\u7684\u903b\u8f91\u3002\u5982\u679c\u770b\u5b8c\u4e00\u904d\u8fd8\u4e0d\u662f\u5f88\u7406\u89e3\uff0c\u9700\u8981\u81ea\u5df1\u591a\u591a\u63e3\u6469\u3002<\/p>\n

                  AdaBoost\u7b97\u6cd5\u76ee\u524d\u662f\u4e00\u4e2a\u6bd4\u8f83\u6d41\u884c\u7684Boosting\u7b97\u6cd5\uff0c\u4ed6\u7684\u5f31\u5b66\u4e60\u5668\u65e2\u53ef\u4ee5\u662f\u56de\u5f52\u5668\uff0c\u53c8\u53ef\u4ee5\u662f\u5206\u7c7b\u5668\uff0c\u8fd9\u4e5f\u662fAdaBoost\u8f83\u4e3a\u5f3a\u5927\u7684\u4e00\u70b9\u3002\u867d\u7136\u7406\u8bba\u4e0a\u4efb\u4f55\u5b66\u4e60\u5668\u90fd\u53ef\u4ee5\u4f5c\u4e3aAdaBoost\u7684\u5f31\u5b66\u4e60\u5668\uff0c\u4f46\u662fAdaBoost\u7b97\u6cd5\u7528\u7684\u8f83\u591a\u7684\u5f31\u5b66\u4e60\u5668\u4e00\u822c\u8fd8\u662f\u51b3\u7b56\u6811\u548c\u795e\u7ecf\u7f51\u7edc\u3002<\/p>\n

                  \u76f8\u4fe1\u6709\u4e86\u7b2c\u4e00\u4e2a\u96c6\u6210\u7b97\u6cd5AdaBoost\u7684\u57fa\u7840\uff0c\u5bf9\u4e8e\u63a5\u4e0b\u6765\u7684\u7b2c\u4e8c\u4e2a\u7528\u7684\u8f83\u4e3a\u5e7f\u6cdb\u7684Boosting\u7cfb\u5217\u7b97\u6cd5\u4f60\u4e5f\u80fd\u5f88\u5feb\u719f\u6089\u4ed6\uff0c\u5373\u68af\u5ea6\u63d0\u5347\u6811(gradient boosting decision tree\uff0cGBDT)<\/p>\n","protected":false},"excerpt":{"rendered":"

                AdaBoost\u7b97\u6cd5   \u96c6\u6210\u5b66\u4e60\u4e2d\u5f31\u5b66\u4e60\u5668\u4e4b\u95f4\u6709\u5f3a\u4f9d\u8d56\u5173\u7cfb\u7684\uff0c\u79f0\u4e4b\u4e3aBoosting\u7cfb\u5217 […]<\/p>\n","protected":false},"author":3,"featured_media":3136,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[276,294],"tags":[],"_links":{"self":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3138"}],"collection":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3138"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3138\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/media\/3136"}],"wp:attachment":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3138"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3138"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}