{"id":3170,"date":"2022-02-27T12:47:40","date_gmt":"2022-02-27T04:47:40","guid":{"rendered":"https:\/\/egonlin.com\/?p=3170"},"modified":"2022-02-27T12:49:35","modified_gmt":"2022-02-27T04:49:35","slug":"xgboost%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3170","title":{"rendered":"XgBoost\u7b97\u6cd5"},"content":{"rendered":"

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

  XgBoost\u7b97\u6cd5(eXtreme Gradient Boosting)\u5c5e\u4e8eBoosting\u7cfb\u5217\u7b97\u6cd5\uff0c\u66f4\u591a\u7684\u662f\u57fa\u4e8eGBDT\u7b97\u6cd5\u7684\u4e00\u4e2a\u8fdb\u9636\u7b97\u6cd5\u3002\u672c\u6587\u5047\u8bbeXgBoost\u7b97\u6cd5\u4f7f\u7528\u7684\u5f31\u5b66\u4e60\u5668\u4e3a\u51b3\u7b56\u6811\u3002<\/p>\n

XgBoost\u7b97\u6cd5\u5b66\u4e60\u76ee\u6807<\/h1>\n
    \n
  1. XgBoost\u7b97\u6cd5\u76ee\u6807\u51fd\u6570<\/li>\n
  2. XgBoost\u7b97\u6cd5\u6b63\u5219\u5316\u9879<\/li>\n
  3. XgBoost\u7b97\u6cd5\u6700\u5c0f\u5316\u76ee\u6807\u51fd\u6570<\/li>\n
  4. XgBoost\u7b97\u6cd5\u4f18\u7f3a\u70b9<\/li>\n<\/ol>\n

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

    XgBoost\u7b97\u6cd5\u53c2\u6570<\/h2>\n

      \u5047\u8bbe\u6211\u4eec\u83b7\u53d6\u4e86XgBoost\u7684\u6a21\u578b\u548c\u5b83\u7684\u76ee\u6807\u51fd\u6570\uff0c\u73b0\u5728\u6211\u4eec\u7684\u4efb\u52a1\u5c31\u662f\u6700\u5c0f\u5316\u76ee\u6807\u51fd\u6570$J(\\theta)$\u627e\u5230\u6700\u4f73\u7684$\\theta$\uff0c\u4f46\u662f\u8fd9\u4e2a\u53c2\u6570\u662f\u4ec0\u4e48\u5462\uff1fXgBoost\u7531\u4e00\u5806CART\u6811\u7ec4\u6210\uff0c\u56e0\u6b64\u8fd9\u4e2a\u53c2\u6570\u5f88\u660e\u663e\u5b58\u5728\u4e8e\u6bcf\u9897CART\u6811\u4e2d\u3002\u4f46\u662fCART\u6811\u7684\u53c2\u6570\u53c8\u662f\u4ec0\u4e48\u5462\uff1fCART\u6811\u5982\u679c\u88ab\u786e\u5b9a\u4e4b\u540e\uff0c\u5b50\u8282\u70b9\u662f\u53ef\u4ee5\u4e22\u6389\u7684\uff0c\u5269\u4e0b\u7684\u53ea\u6709\u6bcf\u4e00\u4e2a\u53f6\u5b50\u8282\u70b9\u4ee5\u53ca\u6bcf\u4e00\u4e2a\u53f6\u5b50\u8282\u70b9\u4e0a\u7684\u5206\u6570\uff0c\u8fd9\u5c31\u662fCART\u6811\u7684\u53c2\u6570\u5373XgBoost\u7684\u53c2\u6570\uff0c\u8fd8\u662f\u4e0d\u6e05\u695a\u7ee7\u7eed\u5f80\u4e0b\u770b\u3002<\/p>\n

    XgBoost\u7b97\u6cd5\u76ee\u6807\u51fd\u6570<\/h2>\n

      \u901a\u8fc7\u771f\u5b9e\u503c\u548c\u9884\u6d4b\u503c\u4ee5\u53caxboost\u6a21\u578b\u6211\u4eec\u80fd\u5f97\u5230\u4e00\u4e2a\u76ee\u6807\u51fd\u6570\uff0c\u8be5\u76ee\u6807\u51fd\u6570\u5047\u8bbe\u5b58\u5728\u4e00\u4e2a$L$\u4ee3\u4ef7\u51fd\u6570\u548c\u4e00\u4e2a\u6b63\u5219\u9879$\\sum_{i=1}^t\\Omega(fk)$(\u7c7b\u4f3c\u4e8e\u7ebf\u6027\u56de\u5f52\u7684L1\u3001L2\u6b63\u5219\u5316\uff0c\u4e4b\u540e\u4f1a\u8be6\u7ec6\u89e3\u91ca\uff0c\u6b64\u5904\u662ft\u68f5\u6811\u7684\u6b63\u5219\u5316\u9879\u52a0\u548c\uff0c\u73b0\u5728\u5047\u8bbe\u6211\u4eec\u6709t\u68f5\u6811\uff0cn\u4e2a\u8bad\u7ec3\u6837\u672c\uff0c\u65e2\u5f97\u4e00\u4e2a\u76ee\u6807\u51fd\u6570
    \n$$
    \nJ(\\theta)=\\sum<\/em>{i=1}^nL(y_i^t,\\hat{y}i^{(t)}))+\\sum<\/em>{i=1}^t\\Omega(fi)
    \n$$
    \n  \u5982\u679c\u6211\u4eec\u5047\u8bbe$C$\u662ft-1\u68f5\u6811\u7684\u6b63\u5219\u5316\u9879\u52a0\u548c\uff0c\u5e76\u4e14\u4ee3\u5165XgBoost\u7684\u6a21\u578b\uff0c\u5f97
    \n$$
    \nJ(\\theta)=\\sum<\/em>{i=1}^nL(y_i^t,\\hat{y}_i^{(t-1)}+f_t(x_i))+\\Omega(f_t)+C
    \n$$
    \n\u6cf0\u52d2\u5c55\u5f00\u5f0f\u516c\u5f0f\u4e3a\uff1a
    \n$$
    \nf(x+\\Delta{x})\\approx{f(x)}+f'(x)\\Delta{x}+{\\frac{1}{2}}f”(x)\\Delta{x^2}
    \n$$
    \n\u5047\u8bbe
    \n$$
    \n\\begin{align}
    \n& f(x)=\\hat{y}_i^{(t-1)} \\
    \n& \\Delta=f_t(xi) \\
    \n& gi=\\partial<\/em>{\\hat{y}_i^{(t-1)}}L(y_i^t,\\hat{y}i^{(t-1)}) \\
    \n& hi=\\partial<\/em>{\\hat{y}_i^{(t-1)}}^2L(y_i^t,\\hat{y}i^{(t-1)})
    \n\\end{align}
    \n$$
    \n  \u5728\u8fd9\u4e9b\u5047\u8bbe\u7684\u57fa\u7840\u4e0a\uff0c\u6211\u4eec\u5047\u8bbe\u5b58\u5728\u4e00\u4e2a\u4ee3\u4ef7\u51fd\u6570$L$\uff0c\u6211\u4eec\u53ef\u4ee5\u628a$J(\\theta)$\u6cf0\u52d2\u4e8c\u9636\u5c55\u5f00\uff1a
    \n$$
    \n\\begin{align}
    \nJ(\\theta) & = \\sum<\/em>{i=1}^nL(y_i^t,\\hat{y}i^{(t)}))+\\sum<\/em>{i=1}^t\\Omega(fi) \\
    \n& = \\sum<\/em>{i=1}^nL(y_i^t,\\hat{y}_i^{(t-1)}+f_t(x_i))+\\Omega(ft)+C \\
    \n& = \\sum<\/em>{i=1}^n[L(y_i^t,\\hat{y}_i^{(t-1)})+g_if_t(x_i)+{\\frac{1}{2}}h_if_t^2(x_i)]+\\Omega(f_t)+C
    \n\\end{align}
    \n$$
    \n\u5176\u4e2d$y_i^t$\u548c$\\hat{y}_i^{(t-1)}$\u5df2\u77e5\uff0c\u5373$L(y_i^t,\\hat{y}i^{(t-1)})$\u662f\u4e00\u4e2a\u5e38\u6570\u9879(\u56e0\u4e3a\u6211\u4eec\u5047\u8bbe\u4e86\u8fd9\u4e2a\u4ee3\u4ef7\u51fd\u6570$L$\u662f\u5df2\u77e5\u7684\u4e00\u4e2a\u4ee3\u4ef7\u51fd\u6570\uff0c\u53ef\u4ee5\u662fMSE\uff0c\u53ef\u4ee5\u662fMSA\uff0c\u53ef\u4ee5\u662f\u4efb\u4f55\u4e00\u4e2a\u5df2\u77e5\u7684\u4ee3\u4ef7\u51fd\u6570)\uff1b$C$\u662f\u524dt-1\u68f5\u6811\u7684\u6b63\u5219\u5316\u9879\u52a0\u548c\uff0c\u4e5f\u662f\u4e00\u4e2a\u5e38\u6570\uff0c\u8fd9\u4e24\u4e2a\u5e38\u6570\u9879\u5bf9\u76ee\u6807\u51fd\u6570\u6c42\u6700\u5c0f\u503c\u65e0\u610f\u4e49\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u53bb\u6389\uff0c\u65e2\u5f97
    \n$$
    \nJ(\\theta)=\\sum<\/em>{i=1}^n[g_if_t(x_i)+{\\frac{1}{2}}h_if_t^2(x_i)]+\\Omega(ft)
    \n$$
    \n  \u73b0\u5728\u5982\u679c\u6211\u4eec\u5047\u8bbe\u635f\u5931\u51fd\u6570$L$\u4f7f\u7528\u7684\u662fMSE\uff0c\u90a3\u4e48\u4e0a\u8ff0\u5f0f\u5b50\u4f1a\u53d8\u6210
    \n$$
    \n\\begin{align}
    \nJ(\\theta) & = \\sum<\/em>{i=1}^n(y_i^t-(\\hat{y}_i^{(t-1)}+f_t(x_i)))^2+\\Omega(ft)+C \\
    \n& = \\sum<\/em>{i=1}^n((y_i^t-\\hat{y}_i^{(t-1)})-f_t(x_i))^2+\\Omega(ft)+C \\
    \n& =\\sum<\/em>{i=1}^n[(y_i^t-\\hat{y}_i^{(t-1)})^2-2(y_i^t-\\hat{y}_i^{(t-1)})f_t(x_i)+f_t(x_i)^2]+\\Omega(ft)+C
    \n\\end{align}
    \n$$
    \n\u53bb\u6389\u5e38\u6570\u9879\u53ef\u4ee5\u5f97\u5230
    \n$$
    \nJ(\\theta)=\\sum<\/em>{i=1}^n[-2(y_i^t-\\hat{y}_i^{(t-1)})f_t(x_i)+f_t(x_i)^2]+\\Omega(f_t)
    \n$$
    \n  \u5982\u679c\u4f60\u4ee3\u5165\u9a8c\u8bc1\u5f88\u660e\u663e\u53ef\u4ee5\u53d1\u73b0\u6211\u4eec\u4f7f\u7528\u6cf0\u52d2\u5c55\u5f00\u5f0f\u5f97\u5230\u7684\u5f0f\u5b50\u662f\u6ca1\u6709\u95ee\u9898\u7684<\/p>\n

      \u5176\u5b9e\u8d70\u5230\u8fd9\u91cc\u6211\u4eec\u7684XgBoost\u5df2\u7ecf\u7b97\u662f\u7ed3\u675f\u4e86\uff0c\u662f\u4e0d\u662f\u5fd8\u4e86\u6211\u4eec\u5728\u505a\u4ec0\u4e48\uff0c\u54c8\u54c8\uff01\u6211\u4eec\u5728\u505a\u7684\u662f\u901a\u8fc7\u524dt-1\u68f5\u7684\u9884\u6d4b\u503c\u52a0\u548c\u6211\u4eec\u662f\u5426\u80fd\u7b97\u51fa\u7b2ct\u68f5\u6811\u7684\u6700\u4f18\u9884\u6d4b\u503c\u3002<\/p>\n

    XgBoost\u7b97\u6cd5\u6b63\u5219\u5316\u9879<\/h2>\n

      \u5982\u7ebf\u6027\u56de\u5f52\u7684\u6b63\u5219\u5316\u9879\u4e00\u6837\uff0c\u4f60\u53ef\u4ee5\u4f7f\u7528L1\u6b63\u5219\u5316\uff0c\u4f60\u4e5f\u53ef\u4ee5\u4f7f\u7528L2\u6b63\u5219\u5316\u3002\u8fd9\u91cc\u6211\u5c31\u8bb2\u8bb2\u6211\u5bf9XgBoost\u4f7f\u7528\u7684\u6b63\u5219\u5316\u9879\u3002<\/p>\n

      \u6b63\u5219\u5316\u524d\u6211\u4eec\u5148\u5bf9CART\u6811\u505a\u5904\u7406\uff1a\u5047\u8bbe\u4e00\u68f5\u6811\u6709T\u4e2a\u53f6\u5b50\u8282\u70b9\uff0c\u8fd9T\u4e2a\u53f6\u5b50\u8282\u70b9\u7ec4\u6210\u4e86\u4e00\u4e2aT\u7ef4\u5411\u91cf$w$\uff0c\u800c$q(x)$\u662f\u4e00\u4e2a\u6620\u5c04\uff0c\u7528\u6765\u5c06\u6837\u672c\u6620\u5c04\u62101\u5230T\u7684\u67d0\u4e2a\u503c\uff0c\u5373$q(x)$\u8868\u793a\u4e86CART\u6811\u7684\u7ed3\u6784\uff0c$w_q(x)$\u8868\u793a\u4e86\u8fd9\u68f5\u6811\u5bf9\u6837\u672cx\u7684\u9884\u6d4b\u503c
    \n$$
    \nft(x)=w<\/em>{q(x)},w\\in{R^T},a:R^d\\rightarrow{1,2,\\cdots,T}
    \n$$
    \n  \u7531\u6b64\u6211\u4eec\u53ef\u4ee5\u5047\u8bbeXgBoost\u7684\u6b63\u5219\u5316\u9879
    \n$$
    \n\\Omega(ft)=\\gamma{T}+{\\frac{1}{2}}\\lambda\\sum<\/em>{j=1}^T{w_j^2}
    \n$$
    \n\u5176\u4e2d$\\gamma$\u548c$\\lambda$\u662f\u6211\u4eec\u81ea\u5b9a\u4e49\u7684\u4e00\u4e2a\u6570(\u7c7b\u4f3c\u7ebf\u6027\u56de\u5f52\u7684\u5b66\u4e60\u7387)\uff0c\u5982\u679c$\\gamma$\u8d8a\u5927\uff0c\u8868\u793a\u5e0c\u671b\u83b7\u5f97\u7ed3\u6784\u7b80\u5355\u7684\u6811\uff0c\u56e0\u4e3a$\\gamma$\u8d8a\u5927\u5bf9\u53f6\u5b50\u8282\u70b9\u591a\u7684\u6811\u60e9\u7f5a\u66f4\u5927\uff1b$\\lambda$\u8d8a\u5927\u4e5f\u662f\u5982\u6b64\u3002<\/p>\n

    XgBoost\u7b97\u6cd5\u6700\u5c0f\u5316\u76ee\u6807\u51fd\u6570<\/h2>\n

      \u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u6709\u4e86\u6cf0\u52d2\u4e8c\u9636\u5c55\u5f00\u7684\u76ee\u6807\u51fd\u6570\uff0c\u6709\u4e86\u81ea\u5b9a\u4e49\u7684\u6b63\u5219\u5316\u9879\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u81ea\u5b9a\u4e49\u7684\u6b63\u5219\u9879\u4ee3\u5165\u76ee\u6807\u51fd\u6570\u4e2d
    \n$$
    \nJ(\\theta)=\\sum_{i=1}^n[g_if_t(x_i)+{\\frac{1}{2}}h_if_t^2(xi)]+\\gamma{T}+{\\frac{1}{2}}\\lambda\\sum<\/em>{j=1}^T{w_j^2}
    \n$$
    \n\u4ee3\u5165$ft(x)=w<\/em>{q(x)}$\uff0c\u5f97
    \n$$
    \nJ(\\theta)=\\sum_{i=1}^n[giw<\/em>{q(x_i)}+{\\frac{1}{2}}hi{w<\/em>{q(xi)}^2}]+\\gamma{T}+{\\frac{1}{2}}\\lambda\\sum<\/em>{j=1}^T{w_j^2}
    \n$$
    \n  \u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u9700\u8981\u8003\u8651\uff0c\u5982\u679c\u4e00\u4e2a\u53f6\u5b50\u8282\u70b9\u4e0a\u96be\u9053\u53ea\u4f1a\u5bf9\u5e94\u4e00\u4e2a\u6837\u672c\u5417\uff1f\u5f88\u660e\u663e\u5982\u679c\u6837\u672c\u5f88\u591a\uff0c\u4e00\u4e2a\u53f6\u5b50\u53ef\u80fd\u4f1a\u5bf9\u5e94\u591a\u4e2a\u6837\u672c\u3002\u56e0\u6b64\u6211\u4eec\u7528$Ij$\u8868\u793a\u4e00\u4e2a\u53f6\u5b50\u8282\u70b9\u4e0a\u7684\u6240\u6709\u6837\u672c\uff0c\u5373$\\sum<\/em>{i\\in{Ij}}$\u5bf9\u5e94\u4e00\u4e2a\u53f6\u5b50\u8282\u70b9\u4e0a\u6240\u6709\u6837\u672c\u7684\u5bf9\u5e94\u503c\u7684\u52a0\u548c\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u7684\u5c31\u662fT\u4e2a\u53f6\u5b50\u8282\u70b9\u4e0a\u7684\u6837\u672c\u9884\u6d4b\u503c\u7684\u52a0\u548c\uff0c\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u7528$\\sum<\/em>{j=1}^T$\u5f00\u5934\u7684\u539f\u56e0
    \n$$
    \n\\begin{align}
    \nJ(\\theta) & =\\sum{j=1}^T{[(\\sum<\/em>{i\\in{I_j}}g_i)wj+{\\frac{1}{2}}(\\sum<\/em>{i\\in{I_j}}hi)wj^2]+\\gamma{T}+{\\frac{1}{2}}\\lambda\\sum<\/em>{j=1}^T{wj^2}} \\
    \n& = \\sum<\/em>{j=1}^T{[(\\sum_{i\\in{I_j}}g_i)wj+{\\frac{1}{2}}(\\sum<\/em>{i\\in{I_j}}hi+\\lambda)w_j^2]+\\gamma{T}}
    \n\\end{align}
    \n$$
    \n\u5047\u8bbe$Gj=\\sum<\/em>{i\\in{I_j}}g_i,Hj=\\sum<\/em>{i\\in{I_j}}hi$
    \n$$
    \nJ(\\theta)=\\sum<\/em>{j=1}^T[G_jw_j+{\\frac{1}{2}}(H_j+\\lambda)w_j^2]+\\gamma{T}
    \n$$
    \n  \u901a\u8fc7\u4e0a\u5f0f\u6211\u4eec\u53ef\u4ee5\u5bf9\u76ee\u6807\u51fd\u6570\u5bf9$w$\u6c42\u504f\u5bfc\u627e\u5230\u6700\u4f18$w^{}$\u4e3a
    \n$$
    \n{\\frac{\\partial{J(f_t)}}{\\partial{w_J}}}=G_j+(H_j+\\lambda)w_j==0\\Rightarrow{w_j^<\/em>}=-{\\frac{G_j}{Hj+\\lambda}}
    \n$$
    \n\u56de\u4ee3\u6700\u4f18$w^{}$\u5f97
    \n$$
    \nJ(\\theta)^<\/em>=-{\\frac{1}{2}}\\sum<\/em>{j=1}^T{\\frac{G_j^2}{H_j+\\lambda}}+\\gamma{T}
    \n$$
    \n  \u56e0\u4e3a$J(\\theta)^$\u7684\u63a8\u5bfc\u8fc7\u7a0b\u4e2d\u53ea\u548c$G_j$\u548c$H_j$\u548c\u6709\u5173\uff0c\u800c\u5b83\u4eec\u53c8\u53ea\u548c\u6811\u7684\u7ed3\u6784$q(x)$\u6709\u5173\uff0c\u8fd9\u8868\u793a$J(\\theta)^<\/em>$\u4ee3\u8868\u4e86\u8fd9\u9897\u6811\u7684\u7ed3\u6784\u6709\u591a\u597d\uff0c\u503c\u8d8a\u5c0f\uff0c\u4ee3\u8868\u8fd9\u6837\u7684\u7ed3\u6784\u8d8a\u597d\u3002<\/p>\n

      \u5176\u5b9e\u806a\u660e\u7684\u540c\u5b66\u5df2\u7ecf\u53d1\u73b0\u4e86\u6211\u4eec\u7684$\\theta$\u8fd9\u4e2a\u53c2\u6570\u5b8c\u5168\u53ef\u4ee5\u770b\u6210$f_t$\uff0c\u5b83\u8868\u793a\u7684\u662f\u7b2ct\u9897\u6811\u7684\u7ed3\u6784\uff0c\u4e5f\u5c31\u53ef\u4ee5\u770b\u6210\u6211\u4eec\u7684$\\theta$\u5440\uff1f\u4e0d\u662f\u5417\uff1f\u563b\u563b\uff0c\u4f60\u4ed4\u7ec6\u601d\u8003\u4e0b\u3002\u5f53\u7136$f_t$\u4e5f\u662f\u6211\u4eec\u81ea\u5df1\u5b9a\u4e49\u7684\u3002<\/p>\n

    XgBoost\u7b97\u6cd5\u4e3e\u4f8b<\/h2>\n

      \u73b0\u5728\u6211\u4eec\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u5bb6\u4e94\u53e3\u7684\u6570\u636e\uff0c\u89c1\u4e0b\u8868<\/p>\n\n\n\n\n\n
    \u513f\u5b50<\/th>\n\u5988\u5988<\/th>\n\u7238\u7238<\/th>\n\u5976\u5976<\/th>\n\u7237\u7237<\/th>\n<\/tr>\n<\/thead>\n
    g1,h1<\/td>\ng2,h2<\/td>\ng3,h3<\/td>\ng4,h4<\/td>\ng5,h5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \u513f\u5b50+\u5988\u5988
    \n$$
    \nG_L=g_1+g_2
    \n$$
    \n  \u7238\u7238+\u5976\u5976+\u7237\u7237
    \n$$
    \nG_R=g_3+g_4+g5
    \n$$
    \n$$
    \nJ(\\theta)^*=-{\\frac{1}{2}}\\sum<\/em>{j=1}^T{\\frac{G_j^2}{H_j+\\lambda}}+\\gamma{T}
    \n$$
    \n  \u5982\u679c\u6211\u4eec\u4e0d\u5bf9\u8fd95\u4e2a\u6837\u672c\u5206\u5f00\uff0c\u628a\u6570\u636e\u4ee3\u5165$J(\\theta)$\uff0c\u4ed6\u4eec\u7684\u76ee\u6807\u503c\u662f
    \n$$
    \n{\\frac{1}{2}}{\\frac{(G_L+G_R)^2}{H_L+H_R+\\lambda}}
    \n$$
    \n  \u5982\u679c\u6211\u4eec\u628a\u4ed6\u4eec\u4e94\u4e2a\u4eba\u6309\u7167\u5e74\u9f84\u6392\u5217\u5e76\u4ece\u7a7a\u683c\u5217\u5206\u5f00\uff0c\u5373\u8be5\u51b3\u7b56\u6811\u4f1a\u6709\u4e24\u4e2a\u53f6\u5b50\uff0c\u4e00\u4e2a\u53f6\u5b50\u4f1a\u6709\u513f\u5b50+\u5988\u5988\u7684\u5206\u6570\uff1b\u53e6\u4e00\u4e2a\u53f6\u5b50\u4f1a\u6709\u7238\u7238+\u5976\u5976+\u7237\u7237\u7684\u5206\u6570<\/p>\n

    \u628a\u6570\u636e\u4ee3\u5165$J(\\theta)$\u76ee\u6807\u503c\u662f
    \n$$
    \n{\\frac{1}{2}}[{\\frac{G_L^2}{H_L+\\lambda}}+{\\frac{G_R^2}{H_R+\\lambda}}]
    \n$$
    \n  \u7531\u6b64\u53ef\u4ee5\u8ba1\u7b97Gain\u503c
    \n$$
    \nGain={\\frac{1}{2}}[{\\frac{G_L^2}{H_L+\\lambda}}+{\\frac{G_R^2}{H_R+\\lambda}}-{\\frac{(G_L+G_R)^2}{H_L+H_R+\\lambda}}]+\\gamma
    \n$$
    \n  \u603b\u7ed3\uff1a\u8be5Gain\u503c\u662f\u5355\u8282\u70b9\u7684\u76ee\u6807\u503c\u51cf\u53bb\u5207\u5206\u540e\u7684\u6240\u6709\u8282\u70b9\u7684\u76ee\u6807\u503c\uff0cGain\u503c\u5982\u679c\u662f\u6b63\u7684\uff0c\u5e76\u4e14Gain\u503c\u8d8a\u5927\uff0c\u5c31\u8d8a\u503c\u5f97\u5207\u5206\uff0c\u7136\u540e\u4e0d\u65ad\u91cd\u590d\u4e0a\u8ff0\u8fc7\u7a0b\uff1b\u5982\u679cGain\u503c\u662f\u8d1f\u7684\uff0c\u8868\u660e\u5207\u5206\u540e\u76ee\u6807\u503c\u53d8\u5927\u4e86\u3002\u800c$\\gamma$\u5728\u8fd9\u91cc\u63a7\u5236\u76ee\u6807\u503c\u7684\u4e0b\u964d\u5e45\u5ea6\u3002Gain\u503c\u7c7b\u4f3c\u4e8e\u4fe1\u606f\u589e\u76ca\uff0c\u5e76\u4e14\u76f8\u6bd4\u8f83\u4f20\u7edf\u7684GBDT\uff0cXgBoost\u4f7f\u7528\u4e86\u4e8c\u9636\u6cf0\u52d2\u5c55\u5f00\uff0c\u53ef\u4ee5\u66f4\u5feb\u7684\u5728\u8bad\u7ec3\u96c6\u4e0a\u6536\u655b\uff0c\u867d\u7136XgBoost\u9700\u8981\u8ba1\u7b97\u6bcf\u4e2a\u6837\u672c\u7684g\u548ch\u503c\uff0c\u4f46\u662fXgBoost\u4f7f\u7528\u4e86\u5e76\u884c\/\u591a\u6838\u8fd0\u7b97\uff0c\u8fd9\u90fd\u4e0d\u662f\u95ee\u9898\u3002<\/p>\n

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

    \u4f18\u70b9<\/h2>\n
      \n
    1. \u53ef\u4ee5\u4f7f\u7528\u6b63\u5219\u5316\u9879\u7b49\u7b56\u7565\u9632\u6b62\u8fc7\u62df\u5408<\/li>\n
    2. \u76ee\u6807\u51fd\u6570\u4f18\u5316\u5229\u7528\u4e86\u635f\u5931\u51fd\u6570\u5173\u4e8e\u5f85\u6c42\u51fd\u6570\u7684\u4e8c\u9636\u5bfc\u6570\uff0c\u76f8\u6bd4\u8f83GBDT\uff0c\u8fed\u4ee3\u901f\u5ea6\u66f4\u5feb<\/li>\n
    3. \u652f\u6301\u5e76\u884c\u5316\uff0c\u8bad\u7ec3\u901f\u5ea6\u5feb<\/li>\n
    4. \u6dfb\u52a0\u4e86\u5bf9\u7a00\u758f\u6570\u636e\u7684\u5904\u7406<\/li>\n
    5. \u652f\u6301\u8bbe\u7f6e\u6837\u672c\u6743\u91cd\uff0c\u8be5\u6743\u91cd\u4f53\u73b0\u5728\u4e00\u9636\u5bfc\u6570g\u548c\u4e8c\u9636\u5bfc\u6570h\uff0c\u901a\u8fc7\u8c03\u6574\u6743\u91cd\u53ef\u4ee5\u53bb\u66f4\u52a0\u5173\u6ce8\u4e00\u4e9b\u6837\u672c<\/li>\n<\/ol>\n

      \u7f3a\u70b9<\/h2>\n
        \n
      1. \u6570\u636e\u91cf\u5927\u65f6\uff0c\u7531\u4e8e\u9009\u62e9\u5212\u5206\u70b9\u9700\u8981\u5bf9\u7279\u5f81\u505a\u9884\u6392\u5e8f\uff0c\u8ba1\u7b97\u5f00\u9500\u8fc7\u5927<\/li>\n<\/ol>\n

        \u5c0f\u7ed3<\/h1>\n

          XgBoost\u7b97\u6cd5\u662fGBDT\u7b97\u6cd5\u7684\u4e00\u4e2a\u63d0\u5347\uff0c\u4ed6\u4eec\u4e24\u8005\u4e4b\u95f4\u7684\u4e3b\u8981\u533a\u522b\u5728\u4e8e\u76ee\u6807\u51fd\u6570\u5f62\u5f0f\u4e0d\u540c\u3002\u5e76\u4e14XgBoost\u4f7f\u7528\u4e86\u4e8c\u9636\u6cf0\u52d2\u5c55\u5f00\uff0c\u4f7f\u5f97XgBoost\u7b97\u6cd5\u6536\u655b\u901f\u5ea6\u66f4\u5feb\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

        XgBoost\u7b97\u6cd5   XgBoost\u7b97\u6cd5(eXtreme Gradient Boosti […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[276,293,297],"tags":[],"_links":{"self":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3170"}],"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=3170"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3170\/revisions"}],"wp:attachment":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3170"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3170"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3170"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}