{"id":3201,"date":"2022-02-27T13:17:32","date_gmt":"2022-02-27T05:17:32","guid":{"rendered":"https:\/\/egonlin.com\/?p=3201"},"modified":"2022-02-27T13:25:33","modified_gmt":"2022-02-27T05:25:33","slug":"%e7%ac%ac%e5%85%ad%e8%8a%82%ef%bc%9a%e6%a8%a1%e5%9e%8b%e9%80%89%e6%8b%a9","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3201","title":{"rendered":"\u7b2c\u516d\u8282\uff1a\u6a21\u578b\u9009\u62e9"},"content":{"rendered":"

\u6a21\u578b\u9009\u62e9<\/h1>\n

  \u673a\u5668\u5b66\u4e60\u662f\u5728\u67d0\u79cd\u5047\u8bbe\u4e0a\u5bf9\u6570\u636e\u7684\u5206\u6790\uff0c\u57fa\u4e8e\u8be5\u5047\u8bbe\u5373\u53ef\u6784\u9020\u591a\u4e2a\u6a21\u578b\u83b7\u5f97\u9884\u6d4b\u503c\uff0c\u901a\u8fc7\u6bd4\u8f83\u591a\u4e2a\u6a21\u578b\u95f4\u771f\u5b9e\u503c\u4e0e\u9884\u6d4b\u503c\u4e4b\u95f4\u7684\u8bef\u5dee\u5373\u53ef\u83b7\u5f97\u4e00\u4e2a\u8f83\u4f18\u7684\u6a21\u578b\u3002<\/p>\n

  \u7531\u4e8e\u673a\u5668\u5b66\u4e60\u4e0d\u662f\u9884\u8a00\u800c\u662f\u9884\u6d4b\u3002\u56e0\u6b64\u673a\u5668\u5b66\u4e60\u53ef\u80fd\u4f1a\u51fa\u73b0\u6b20\u62df\u5408\u548c\u8fc7\u62df\u5408\u7684\u73b0\u8c61\uff0c\u5373\u5982\u679c\u6a21\u578b\u62df\u5408\u6548\u679c\u4e0d\u597d\uff0c\u5219\u662f\u6b20\u62df\u5408\uff0c\u5bf9\u4e8e\u6b20\u62df\u5408\u95ee\u9898\u901a\u5e38\u589e\u5927\u8bad\u7ec3\u6570\u636e\u91cf\u5373\u53ef\uff1b\u4f46\u662f\u5982\u679c\u6a21\u578b\u7684\u62df\u5408\u6548\u679c\u5f88\u597d\uff0c\u4e5f\u5e76\u4e0d\u4e00\u5b9a\u662f\u4e00\u4ef6\u597d\u4e8b\uff0c\u56e0\u4e3a\u8bad\u7ec3\u96c6\u4e2d\u5f80\u5f80\u542b\u6709\u566a\u58f0\uff0c\u5bfc\u81f4\u6a21\u578b\u53ef\u80fd\u51fa\u73b0\u8fc7\u62df\u5408\uff0c\u8fc7\u62df\u5408\u5c06\u4f1a\u662f\u5b66\u4e60\u673a\u5668\u5b66\u4e60\u8def\u4e0a\u7684\u62e6\u8def\u864e\u4e4b\u4e00\u3002<\/p>\n

  \u5728\u672a\u6765\u5f88\u957f\u7684\u4e00\u6bb5\u8def\u4e2d\u9996\u5148\u8981\u8003\u8651\u7684\u5c31\u662f\u6a21\u578b\u4f1a\u4e0d\u4f1a\u8fc7\u62df\u5408\uff0c\u56e0\u6b64\u672c\u6587\u7ed9\u51fa\u4e86\u89e3\u51b3\u8fc7\u62df\u5408\u7684\u51e0\u79cd\u65b9\u6cd5\uff0c\u89e3\u51b3\u8fc7\u62df\u5408\u95ee\u9898\u7684\u540c\u65f6\u5c31\u662f\u5728\u8fdb\u884c\u6a21\u578b\u9009\u62e9\u3002<\/p>\n

  \u9664\u4e86\u8fc7\u62df\u5408\u95ee\u9898\u4e4b\u5916\uff0c\u6a21\u578b\u53ef\u80fd\u8fd8\u4f1a\u56e0\u4e3a\u5176\u4ed6\u7684\u95ee\u9898\u9020\u6210\u6a21\u578b\u4e0d\u4f18\u7684\u60c5\u51b5\uff0c\u901a\u5e38\u56de\u5f52\u95ee\u9898\u53ef\u4ee5\u901a\u8fc7\u504f\u5dee\u548c\u65b9\u5dee\u5ea6\u91cf\u6a21\u578b\u6027\u80fd\uff0c\u4e8c\u5206\u7c7b\u95ee\u9898\u5219\u53ef\u4ee5\u901a\u8fc7\u7cbe\u51c6\u5ea6\u548c\u67e5\u5168\u7387\u7684\u8003\u8651\u6216\u63cf\u7ed8\u5b66\u4e60\u66f2\u7ebfROC\u6765\u5ea6\u91cf\u6a21\u578b\u6027\u80fd\u3002<\/p>\n

  \u603b\u800c\u8a00\u4e4b\uff0c\u603b\u80fd\u901a\u8fc7\u67d0\u79cd\u5de5\u5177\u7684\u5e94\u7528\u8ba9\u6211\u4eec\u627e\u5230\u4e00\u4e2a\u6700\u4f18\u7684\u6a21\u578b\u6765\u9884\u6d4b\u672a\u6765\u65b0\u6570\u636e\u3002<\/p>\n

\u6a21\u578b\u9009\u62e9\u5b66\u4e60\u76ee\u6807<\/h1>\n
    \n
  1. \u635f\u5931\u51fd\u6570\u548c\u76ee\u6807\u51fd\u6570<\/li>\n
  2. \u8fc7\u62df\u5408<\/li>\n
  3. \u89e3\u51b3\u8fc7\u62df\u5408\u7684\u56db\u79cd\u65b9\u6cd5<\/li>\n
  4. \u504f\u5dee\u4e0e\u65b9\u5dee<\/li>\n
  5. \u67e5\u51c6\u7387\u3001\u67e5\u5168\u7387\u548cF1<\/li>\n
  6. ROC\u548cAUC<\/li>\n<\/ol>\n

    \u673a\u5668\u5b66\u4e60\u57fa\u672c\u5047\u8bbe<\/h1>\n

    \u635f\u5931\u51fd\u6570<\/h2>\n

      \u673a\u5668\u5b66\u4e60\u6a21\u578b\u901a\u5e38\u5206\u4e3a\u6982\u7387\u6a21\u578b\u548c\u975e\u6982\u7387\u6a21\u578b\uff0c\u6982\u7387\u6a21\u578b\u7531\u6761\u4ef6\u6982\u7387\u5206\u5e03$p(\\hat{y_i}|x_i)$\u8868\u793a\uff1b\u975e\u6982\u7387\u6a21\u578b\u7531\u51b3\u7b56\u51fd\u6570$\\hat{y_i}=f(x_i)$\u8868\u793a\uff0c\u5176\u4e2d$\\hat{y_i}$\u4e3a\u6a21\u578b\u7684\u8f93\u51fa\u503c\u5373\u9884\u6d4b\u503c\u3002<\/p>\n

      \u901a\u5e38\u60c5\u51b5\u4e0b\u4f7f\u7528\u635f\u5931\u51fd\u6570\u5ea6\u91cf\u6a21\u578b\u5bf9\u5355\u4e2a\u6837\u672c\u9884\u6d4b\u7684\u597d\u574f\uff0c\u5373\u5ea6\u91cf\u771f\u5b9e\u503c\u4e0e\u9884\u6d4b\u503c\u4e4b\u95f4\u7684\u8bef\u5dee\uff0c\u4e00\u822c\u4f7f\u7528\u4e0b\u9762\u7ed9\u51fa\u7684$4$\u79cd\u635f\u5931\u51fd\u6570\u3002<\/p>\n

      \u7ed9\u5b9a\u4e00\u4e2a\u6837\u4f8b$(x_i,y_i)$\uff0c\u5047\u8bbe\u6a21\u578b\u7684\u9884\u6d4b\u503c\u4e3a$\\hat{y_i}$\uff0c\u628a\u635f\u5931\u51fd\u6570\u8bb0\u4f5c$L(yi,\\hat{y_i})$.\u901a\u5e38\u6709\u4ee5\u4e0b4\u79cd\u635f\u5931\u51fd\u6570\u7684\u8868\u73b0\u5f62\u5f0f\u3002<\/p>\n

      \n
    1. 0-1\u635f\u5931\u51fd\u6570\uff1a
      \n$$
      \nL(y_i,\\hat{y_i})= \\begin{cases} 1, &{y_i\\not=\\hat{y_i}} \\ 0, &{y_i=\\hat{y_i}} \\end{cases}
      \n$$<\/li>\n
    2. \u5e73\u65b9\u635f\u5931\u51fd\u6570\uff1a
      \n$$
      \nL(y_i,\\hat{y_i})=(y_i-\\hat{y_i})^2
      \n$$<\/li>\n
    3. \u7edd\u5bf9\u503c\u635f\u5931\u51fd\u6570\uff1a
      \n$$
      \nL(y_i,\\hat{y_i})=|y_i-\\hat{y_i}|
      \n$$<\/li>\n
    4. \u5bf9\u6570\u635f\u5931\u51fd\u6570\u6216\u5bf9\u6570\u4f3c\u7136\u635f\u5931\u51fd\u6570\uff1a
      \n$$
      \nL(y_i,p(\\hat{y_i}|x_i))=-logp(\\hat{y_i}|x_i)
      \n$$<\/li>\n<\/ol>\n

      \u76ee\u6807\u51fd\u6570<\/h2>\n

        \u901a\u8fc7\u635f\u5931\u51fd\u6570\u5373\u53ef\u5f97\u5230\u6a21\u578b\u7684\u76ee\u6807\u51fd\u6570\uff0c\u76ee\u6807\u51fd\u6570\u662f\u6570\u636e\u96c6\u7684\u5e73\u5747\u635f\u5931\uff0c\u5b83\u8868\u793a\u8bad\u7ec3\u96c6\u7684\u5e73\u5747\u8bad\u7ec3\u8bef\u5dee\uff0c\u6709\u65f6\u5019\u4e5f\u88ab\u79f0\u4e3a\u8bad\u7ec3\u8bef\u5dee\uff0c\u5bf9\u4e8e\u6d4b\u8bd5\u96c6\u5219\u79f0\u4e3a\u6d4b\u8bd5\u8bef\u5dee\u3002<\/p>\n

        \u6709\u4e00\u4e2a$n$\u4e2a\u9e22\u5c3e\u82b1\u6837\u672c\u7684\u8bad\u7ec3\u96c6$T={(x_1,y_1),(x_2,y_2),\\cdots,(x_i,y_i),\\cdots,(x_n,yn)}$\uff0c\u53ef\u4ee5\u7ed9\u51fa\u76ee\u6807\u51fd\u6570\u7684\u516c\u5f0f\uff1a
      \n$$
      \nJ={\\frac{1}{n}}\\sum<\/em>{i=1}^nL(y_i,\\hat{y_i})
      \n$$
      \n  \u5f53\u635f\u5931\u51fd\u6570\u662f0-1\u635f\u5931\u51fd\u6570\u65f6\uff0c\u76ee\u6807\u51fd\u6570\u5c06\u53d8\u6210\u8bef\u5dee\u7387\u6216\u51c6\u786e\u7387\uff0c$I(y_i \\not= \\hat{yi})$\u662f\u6307\u793a\u51fd\u6570\uff0c\u5373$y_i \\not= \\hat{yi}$\u65f6\u4e3a1\uff0c\u5426\u5219\u4e3a0\u3002
      \n$$
      \nJe={\\frac{1}{n}} \\sum<\/em>{i=1}^n I(y_i\\not=\\hat{y_i}) \\text{\u8bef\u5dee\u7387}\\
      \nJa={\\frac{1}{n}} \\sum<\/em>{i=1}^n I(y_i = \\hat(y_i)) \\text{\u51c6\u786e\u7387}\\
      \nJ_e + J_a = 1
      \n$$<\/p>\n

      \u53c2\u6570\u6a21\u578b\u548c\u975e\u53c2\u6570\u6a21\u578b<\/h1>\n

      \u53c2\u6570\u6a21\u578b<\/h2>\n

        \u53c2\u6570\u6a21\u578b\u662f\u901a\u8fc7\u8bad\u7ec3\u5927\u91cf\u7684\u8bad\u7ec3\u96c6\u5f97\u5230\u4e00\u4e2a\u7684\u5e26\u6709\u53c2\u6570\u7684\u51fd\u6570\uff0c\u9884\u6d4b\u672a\u6765\u65b0\u6570\u636e\u65f6\u53ea\u9700\u8981\u628a\u7279\u5f81\u503c\u8f93\u5165\u51fd\u6570\u5373\u53ef\u83b7\u5f97\u9884\u6d4b\u503c\u3002\u53c2\u6570\u6a21\u578b\u7684\u5178\u578b\u4f8b\u5b50\u6709\u611f\u77e5\u673a\u3001\u903b\u8f91\u56de\u5f52\u3002<\/p>\n

      \u975e\u53c2\u6570\u6a21\u578b<\/h2>\n

        \u975e\u53c2\u6570\u6a21\u578b\u65e0\u6cd5\u7528\u4e00\u7ec4\u56fa\u5b9a\u7684\u53c2\u6570\u6765\u63cf\u8ff0\uff0c\u901a\u5e38\u60c5\u51b5\u4e0b\u5229\u7528\u6570\u636e\u672c\u8eab\u8fdb\u884c\u8bad\u7ec3\u3002\u975e\u53c2\u6570\u6a21\u578b\u7684\u5178\u578b\u4f8b\u5b50\u6709\u51b3\u7b56\u6811\u3001k-\u8fd1\u90bb\u7b97\u6cd5\u3002<\/p>\n

      \u8fc7\u62df\u5408<\/h1>\n

        \u4e0a\u4e00\u8282\u8bb2\u4e86\u901a\u8fc7\u8bad\u7ec3\u8bef\u5dee\u9009\u62e9\u6700\u4f18\u6a21\u578b\uff0c\u4e5f\u8bb8\u5df2\u7ecf\u627e\u5230\u4e86$0$\u8bef\u5dee\u7684\u6a21\u578b\uff0c\u4f46\u662f\u8fd9\u5c31\u662f\u6700\u597d\u7684\u5417\uff1f<\/p>\n

        \u4e8b\u5b9e\u4e0a$0$\u8bef\u5dee\u7684\u6a21\u578b\u4e5f\u8bb8\u5e76\u4e0d\u662f\u6700\u597d\u7684\uff0c\u56e0\u4e3a\u6a21\u578b\u662f\u901a\u8fc7\u8bad\u7ec3\u96c6\u5f97\u5230\u7684\uff0c\u7531\u4e8e\u8bad\u7ec3\u96c6\u53ef\u80fd\u5b58\u5728\u566a\u58f0\uff0c\u56e0\u6b64\u8bad\u7ec3\u96c6\u5e76\u4e0d\u4e00\u5b9a\u80fd\u4ee3\u8868\u6d4b\u8bd5\u96c6\uff0c\u66f4\u4e0d\u4e00\u5b9a\u80fd\u4ee3\u8868\u672a\u6765\u65b0\u6570\u636e\u3002\u867d\u7136\u8fd9\u6837\u7684\u6a21\u578b\u53ef\u80fd\u5f88\u597d\u7684\u62df\u5408\u8bad\u7ec3\u6570\u636e\uff0c\u4f46\u662f\u5bf9\u672a\u6765\u6570\u636e\u53ef\u80fd\u5e76\u6ca1\u6709\u8f83\u597d\u7684\u62df\u5408\u80fd\u529b\uff0c\u8fd9\u79cd\u73b0\u8c61\u6210\u4e3a\u8fc7\u62df\u5408\u3002<\/p>\n

      \u8fc7\u62df\u5408\u89e3\u51b3\u65b9\u6cd5<\/h1>\n
        \n
      1. \u6536\u96c6\u66f4\u591a\u8bad\u7ec3\u6570\u636e<\/li>\n
      2. \u9009\u62e9\u53c2\u6570\u8f83\u5c11\u7684\u7b80\u5355\u6a21\u578b<\/li>\n
      3. \u901a\u8fc7\u6b63\u5219\u5316\u5f15\u5165\u5bf9\u590d\u6742\u6027\u7684\u60e9\u7f5a<\/li>\n
      4. \u5207\u5272\u8bad\u7ec3\u6570\u636e\u96c6\u4ea4\u53c9\u9a8c\u8bc1<\/li>\n
      5. \u51cf\u5c11\u6570\u636e\u7684\u7ef4\u5ea6\u6216\u8005\u5220\u9664\u6389\u65e0\u610f\u4e49\u7684\u7279\u5f81(\u4f1a\u6709\u5355\u72ec\u7684\u6587\u7ae0\u4ecb\u7ecd\u6570\u636e\u964d\u7ef4)<\/li>\n<\/ol>\n

        \u6536\u96c6\u66f4\u591a\u8bad\u7ec3\u6570\u636e<\/h2>\n

          \u7531\u4e8e\u8fd8\u6ca1\u6709\u5b9e\u6218\u7ecf\u9a8c\uff0c\u4f60\u53ef\u80fd\u65e0\u6cd5\u60f3\u8c61\u3002<\/p>\n

          \u4f46\u662f\u4f60\u53ef\u4ee5\u8fd9\u6837\u5047\u60f3\u5f53\u8bad\u7ec3\u6570\u636e\u591a\u7684\u80fd\u591f\u7a77\u5c3d\u672a\u6765\u65b0\u6570\u636e\u7684\u65f6\u5019\uff0c\u90a3\u4e48\u7528\u8be5\u8bad\u7ec3\u6570\u636e\u5f97\u5230\u7684\u6a21\u578b\u53bb\u6d4b\u8bd5\u672a\u6765\u65b0\u6570\u636e\uff0c\u90a3\u4e48\u5bf9\u672a\u6765\u65b0\u6570\u636e\u7684\u9884\u6d4b\u4e00\u5b9a\u80fd\u591f\u5f97\u5230\u4e00\u4e2a\u5f88\u597d\u7684\u9884\u6d4b\u503c\uff1b\u8bad\u7ec3\u6570\u636e\u8fc7\u591a\u4e5f\u4f1a\u9002\u5f53\u51cf\u8f7b\u566a\u58f0\u7684\u5f71\u54cd\u3002<\/p>\n

        \u9009\u62e9\u7b80\u5355\u6a21\u578b<\/h2>\n

          \u7ed9\u5b9a\u4e00\u4e2a\u8bad\u7ec3\u96c6$T={(x_1,y_1),(x_2,y_2),\\cdots,(x_i,y_i),\\cdots,(x_n,y_n)}$\uff0c\u7b2c$i$\u4e2a\u6837\u672c$x_i$\u53ef\u4ee5\u7531\u4e00\u4e2a$m$\u6b21\u591a\u9879\u5f0f\u51fd\u6570\u5f97\u5230\u4e00\u4e2a\u9884\u6d4b\u503c$\\hat{y_i}$\u3002\u5047\u8bbe$m$\u6b21\u591a\u9879\u5f0f\u4e3a
        \n$$
        \n\\hat{y_i}=f(x,\\omega)=\\omega_1x_i^{(1)}+\\omega_2x_i^{(2)}+\\cdots+\\omega_nx_i^{(n)}
        \n$$<\/p>\n

        \u793a\u4f8b<\/h4>\n
        # \u8fc7\u62df\u5408\u56fe\u4f8b\nimport pandas as pd\nimport matplotlib.pyplot as plt\nfrom matplotlib.font_manager import FontProperties\nfrom sklearn.preprocessing import PolynomialFeatures\nfrom sklearn.linear_model import LinearRegression\nfont = FontProperties(fname='\/Library\/Fonts\/Heiti.ttc')\n%matplotlib inline\n\n# \u81ea\u5b9a\u4e49\u6570\u636e\u5e76\u5904\u7406\u6570\u636e\ndata_frame = {'x': [2, 1.5, 3, 3.2, 4.22, 5.2, 6, 6.7],\n              'y': [0.5, 3.5, 5.5, 5.2, 5.5, 5.7, 5.5, 6.25]}\ndf = pd.DataFrame(data_frame)\nX, y = df.iloc[:, 0].values.reshape(-1, 1), df.iloc[:, 1].values.reshape(-1, 1)\n\n# \u7ebf\u6027\u56de\u5f52\nlr = LinearRegression()\nlr.fit(X, y)\n\ndef poly_lr(degree):\n    """\u591a\u9879\u5f0f\u56de\u5f52"""\n    poly = PolynomialFeatures(degree=degree)\n    X_poly = poly.fit_transform(X)\n    lr_poly = LinearRegression()\n    lr_poly.fit(X_poly, y)\n    y_pred_poly = lr_poly.predict(X_poly)\n\n    return y_pred_poly\n\ndef plot_lr():\n    """\u5bf9\u7ebf\u6027\u56de\u5f52\u751f\u6210\u7684\u56fe\u7ebf\u753b\u56fe"""\n    plt.scatter(X, y, c='k', edgecolors='white', s=50)\n    plt.plot(X, lr.predict(X), color='r', label='lr')\n    # \u566a\u58f0\n    plt.scatter(2, 0.5, c='r')\n    plt.text(2, 0.5, s='$(2,0.5)$')\n\n    plt.xlim(0, 7)\n    plt.ylim(0, 8)\n    plt.xlabel('x')\n    plt.ylabel('y')\n    plt.legend()\n\ndef plot_poly(degree, color):\n    """\u5bf9\u591a\u9879\u5f0f\u56de\u5f52\u751f\u6210\u7684\u56fe\u7ebf\u753b\u56fe"""\n    plt.scatter(X, y, c='k', edgecolors='white', s=50)\n    plt.plot(X, poly_lr(degree), color=color, label='m={}'.format(degree))\n    # \u566a\u58f0\n    plt.scatter(2, 0.5, c='r')\n    plt.text(2, 0.5, s='$(2,0.5)$')\n\n    plt.xlim(0, 7)\n    plt.ylim(0, 8)\n    plt.xlabel('x')\n    plt.ylabel('y')\n    plt.legend()\n\ndef run():\n    plt.figure()\n    plt.subplot(231)\n    plt.title('\u56fe1(\u7ebf\u6027\u56de\u5f52)', fontproperties=font, color='r', fontsize=12)\n    plot_lr()\n    plt.subplot(232)\n    plt.title('\u56fe2(\u4e00\u9636\u591a\u9879\u5f0f\u56de\u5f52)', fontproperties=font, color='r', fontsize=12)\n    plot_poly(1, 'orange')\n    plt.subplot(233)\n    plt.title('\u56fe3(\u4e09\u9636\u591a\u9879\u5f0f\u56de\u5f52)', fontproperties=font, color='r', fontsize=12)\n    plot_poly(3, 'gold')\n    plt.subplot(234)\n    plt.title('\u56fe4(\u4e94\u9636\u591a\u9879\u5f0f\u56de\u5f52)', fontproperties=font, color='r', fontsize=12)\n    plot_poly(5, 'green')\n    plt.subplot(235)\n    plt.title('\u56fe5(\u4e03\u9636\u591a\u9879\u5f0f\u56de\u5f52)', fontproperties=font, color='r', fontsize=12)\n    plot_poly(7, 'blue')\n    plt.subplot(236)\n    plt.title('\u56fe6(\u5341\u9636\u591a\u9879\u5f0f\u56de\u5f52)', fontproperties=font, color='r', fontsize=12)\n    plot_poly(10, 'violet')\n    plt.show()\n\nrun()<\/code><\/pre>\n
        \"\"<\/div><\/p>\n
          \u5982\u4e0a\u56fe\u6240\u793a\u6bcf\u5f20\u56fe\u90fd\u6709\u76f8\u540c\u5206\u5e03\u76848\u4e2a\u6837\u672c\u70b9\uff0c\u7ea2\u70b9\u660e\u663e\u662f\u4e00\u4e2a\u566a\u58f0\u70b9\uff0c\u63a5\u4e0b\u6765\u5c06\u8bb2\u89e3\u4e0a\u8ff08\u5f20\u56fe\u3002\u6682\u65f6\u4e0d\u7528\u592a\u5173\u5fc3\u7ebf\u6027\u56de\u5f52\u548c\u591a\u9879\u5f0f\u56de\u5f52\u662f\u4ec0\u4e48\uff0c\u8fd9\u4e24\u4e2a\u4ee5\u540e\u4f60\u90fd\u4f1a\u5b66\u4e60\u5230\uff0c\u6b64\u5904\u5f15\u7528\u53ea\u662f\u4e3a\u4e86\u65b9\u4fbf\u4e3e\u4f8b\u3002<\/p>\n
          \n
        • \u56fe1\uff1a\u7ebf\u6027\u56de\u5f52\u62df\u5408\u6837\u672c\u70b9\uff0c\u53ef\u4ee5\u53d1\u73b0\u6837\u672c\u70b9\u8ddd\u79bb\u62df\u5408\u66f2\u7ebf\u5f88\u8fdc\uff0c\u8fd9\u4e2a\u65f6\u5019\u4e00\u822c\u79f0\u4f5c\u6b20\u62df\u5408\uff08underfitting\uff09<\/li>\n
        • \u56fe2\uff1a\u4e00\u9636\u591a\u9879\u5f0f\u56de\u5f52\u62df\u5408\u6837\u672c\u70b9\uff0c\u7b49\u540c\u4e8e\u7ebf\u6027\u56de\u5f52<\/li>\n
        • \u56fe3\uff1a\u4e09\u9636\u591a\u9879\u5f0f\u56de\u5f52\u62df\u5408\u6837\u672c\u70b9\uff0c\u8868\u73b0\u8fd8\u4e0d\u9519<\/li>\n
        • \u56fe4\uff1a\u4e94\u9636\u591a\u9879\u5f0f\u56de\u5f52\u62df\u5408\u6837\u672c\u70b9\uff0c\u660e\u663e\u8fc7\u62df\u5408<\/li>\n
        • \u56fe5\uff1a\u4e03\u9636\u591a\u9879\u5f0f\u56de\u5f52\u62df\u5408\u6837\u672c\u70b9\uff0c\u5df2\u7ecf\u62df\u5408\u4e86\u6240\u6709\u7684\u6837\u672c\u70b9\uff0c\u6bcb\u5eb8\u7f6e\u7591\u7684\u8fc7\u62df\u5408<\/li>\n
        • \u56fe7\uff1a\u5341\u9636\u591a\u9879\u5f0f\u56de\u5f52\u62df\u5408\u6837\u672c\u70b9\uff0c\u62df\u5408\u6837\u672c\u70b9\u7684\u66f2\u7ebf\u548c\u4e03\u9636\u591a\u9879\u5f0f\u5df2\u7ecf\u6ca1\u6709\u4e86\u533a\u522b\uff0c\u53ef\u4ee5\u60f3\u8c61\u5341\u9636\u4e4b\u540e\u7684\u66f2\u7ebf\u4e5f\u7c7b\u4f3c\u4e8e\u4e03\u9636\u591a\u9879\u5f0f\u7684\u62df\u5408\u66f2\u7ebf<\/li>\n<\/ul>\n
            \u4ece\u4e0a\u56fe\u53ef\u4ee5\u770b\u51fa\uff0c\u8fc7\u62df\u5408\u6a21\u578b\u5c06\u4f1a\u53d8\u5f97\u590d\u6742\uff0c\u5bf9\u4e8e\u7ebf\u6027\u56de\u5f52\u800c\u8a00\uff0c\u5b83\u53ef\u80fd\u9700\u8981\u66f4\u9ad8\u9636\u7684\u591a\u9879\u5f0f\u53bb\u62df\u5408\u6837\u672c\u70b9\uff0c\u5bf9\u4e8e\u5176\u4ed6\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\uff0c\u4e5f\u662f\u5982\u6b64\u3002\u8fd9\u4e2a\u65f6\u5019\u4f60\u4e5f\u53ef\u4ee5\u60f3\u8c61\uff0c\u8fc7\u62df\u5408\u867d\u7136\u5bf9\u62df\u5408\u7684\u6837\u672c\u70b9\u7684\u8bef\u5dee\u63a5\u8fd10\uff0c\u4f46\u662f\u5bf9\u4e8e\u672a\u6765\u65b0\u6570\u636e\u800c\u8a00\uff0c\u5982\u679c\u65b0\u6570\u636e\u7684$x=2$\uff0c\u5982\u679c\u4f7f\u7528\u8fc7\u62df\u5408\u7684\u66f2\u7ebf\u8fdb\u884c\u62df\u5408\u65b0\u6570\u636e\uff0c\u90a3\u4e48\u4f1a\u7ed9\u51fa$y=0.5$\u7684\u9884\u6d4b\u503c\uff0c\u4e5f\u5c31\u662f\u8bf4\u628a\u566a\u58f0\u7684\u503c\u7ed9\u4e86\u65b0\u6570\u636e\uff0c\u8fd9\u6837\u660e\u663e\u662f\u4e0d\u5408\u7406\u7684\u3002<\/p>\n
          \u6b63\u5219\u5316<\/h2>\n
            \u9488\u5bf9\u8fc7\u62df\u5408\u6709\u65f6\u5019\u53ef\u4ee5\u51cf\u5c11\u6a21\u578b\u7684\u53c2\u6570\uff0c\u8fd8\u6709\u4e00\u4e2a\u5178\u578b\u7684\u65b9\u6cd5\u662f\u5bf9\u76ee\u6807\u51fd\u6570\u6b63\u5219\u5316\uff08regularization\uff09\uff0c\u5373\u5728\u76ee\u6807\u51fd\u6570\u4e0a\u52a0\u4e0a\u4e00\u4e2a\u6b63\u5219\u5316\u9879\uff08regularizer\uff09\u6216\u60e9\u7f5a\u9879\uff08penalty term\uff09\uff0c\u5373\u65b0\u7684\u76ee\u6807\u51fd\u6570\u53d8\u6210
          \n$$
          \nJ(\\omega)=\\frac{1}{m} \\sum_{i=1}^m L(yi,f<\/em>{\\omega_i}(x_i)) + \\lambda(R(f))
          \n$$
          \n\u5176\u4e2d$\\lambda\\geq0$\u4e3a\u8d85\u53c2\u6570\uff0c\u7c7b\u4f3c\u4e8e\u53c2\u6570\uff0c\u4f46\u662f\u53c2\u6570\u53ef\u4ee5\u901a\u8fc7\u7b97\u6cd5\u6c42\u89e3\uff0c\u8d85\u53c2\u6570\u9700\u8981\u4eba\u5de5\u624b\u52a8\u8c03\u6574\uff1b$\\lambda(R(f))$\u4e3a\u6b63\u5219\u5316\u9879\u3002<\/p>\n
            \u6b63\u5219\u5316\u9879\u4e00\u822c\u662f\u4e00\u4e2a\u5355\u8c03\u9012\u589e\u7684\u51fd\u6570\uff0c\u6a21\u578b\u8d8a\u590d\u6742\uff0c\u6b63\u5219\u5316\u503c\u8d8a\u5927\uff0c\u60e9\u7f5a\u8d8a\u5927\u3002<\/p>\n
          L1\u6b63\u5219\u5316<\/h3>\n
            L1\u6b63\u5219\u5316\uff08Lasso\uff09\u662f\u5728\u76ee\u6807\u51fd\u6570\u4e0a\u52a0\u4e0aL1\u6b63\u5219\u5316\u9879\uff0c\u4e00\u822c\u7528\u4e8e\u7279\u5f81\u9009\u62e9\uff0c\u4e5f\u53ef\u4ee5\u9632\u6b62\u8fc7\u62df\u5408\uff0c\u5373\u65b0\u7684\u76ee\u6807\u51fd\u6570\u4e3a
          \n$$
          \nJ(\\omega) =\\frac{1}{m} \\sum_{i=1}^m L(yi,f<\/em>{\\omega_i}(x_i)) + \\lambda||\\omega||_1
          \n$$
          \n\u5176\u4e2d$||\\omega||_1$\u4e3a\u53c2\u6570\u5411\u91cf$\\omega$\u76841\u8303\u6570\u3002<\/p>\n
            \u5047\u8bbe\u6837\u672c\u6709$n$\u7279\u5f81\uff0c\u5219$\\omega$\u4e3a$n$\u7ef4\u5411\u91cf\uff0c1\u8303\u6570\u4e3a
          \n$$
          \n||\\omega||1=\\sum<\/em>{j=1}^n|\\omega_j|
          \n$$<\/p>\n
          L2\u6b63\u5219\u5316<\/h3>\n
            L2\u6b63\u5219\u5316\uff08Ridge\uff09\u662f\u5728\u76ee\u6807\u51fd\u6570\u4e0a\u52a0\u4e0aL2\u6b63\u5219\u5316\u9879\uff0c\u4e00\u822c\u53ea\u7528\u4e8e\u8fc7\u62df\u5408\uff0c\u5373\u65b0\u7684\u76ee\u6807\u51fd\u6570\u4e3a
          \n$$
          \nJ(\\omega)=\\frac{1}{m} \\sum_{i=1}^m L(yi,f<\/em>{\\omega_i}(x_i)) + \\frac{\\lambda}{2}||\\omega||_2^2
          \n$$
          \n\u5176\u4e2d$||\\omega||_2^2$\u4e3a\u53c2\u6570\u5411\u91cf$\\omega$\u76842\u8303\u6570\u7684\u5e73\u65b9\u3002<\/p>\n
            \u5047\u8bbe\u6837\u672c\u6709$n$\u7279\u5f81\uff0c\u5219$\\omega$\u4e3a$n$\u7ef4\u5411\u91cf\uff0c2\u8303\u6570\u4e3a
          \n$$
          \n||\\omega||2=\\sqrt{\\sum<\/em>{j=1}^n{\\omega_j}^2}
          \n$$<\/p>\n
            \u591a\u8bf4\u4e00\u5634\uff0c\u5047\u8bbe\u6837\u672c\u6709$n$\u7279\u5f81\uff0c\u5219$\\omega$\u4e3a$n$\u7ef4\u5411\u91cf\uff0cp\u8303\u6570\u4e3a
          \n$$
          \n||\\omega||p=\\sqrt[p]{\\sum<\/em>{j=1}^n{\\omega_j}^p}
          \n$$<\/p>\n
          \u4ea4\u53c9\u9a8c\u8bc1<\/h2>\n
            \u5bf9\u8bad\u7ec3\u6570\u636e\u96c6\u5207\u5272\u505a\u4ea4\u53c9\u9a8c\u8bc1\u4e5f\u662f\u9632\u6b62\u6a21\u578b\u8fc7\u62df\u5408\u7684\u4e00\u4e2a\u5f88\u597d\u7684\u65b9\u6cd5\u3002<\/p>\n
            \u4e00\u822c\u4f1a\u628a\u6570\u636e\u6309\u7167\u67d0\u79cd\u6bd4\u4f8b\u5206\u4e3a\u8bad\u7ec3\u96c6\u3001\u6d4b\u8bd5\u96c6\u3002\u8bad\u7ec3\u96c6\u7528\u6765\u8bad\u7ec3\u6a21\u578b\uff0c\u628a\u6d4b\u8bd5\u96c6\u5f53\u505a\u672a\u6765\u65b0\u6837\u672c\u7684\u6837\u672c\u96c6\u7528\u6765\u8bc4\u4f30\u6a21\u578b\u3002\u7136\u540e\u4ea4\u53c9\u9a8c\u8bc1\u53ef\u4ee5\u8ba4\u4e3a\u5c31\u662f\u4e0d\u65ad\u5730\u91cd\u590d\u8bad\u7ec3\u6a21\u578b\u3001\u6d4b\u8bd5\u6a21\u578b\u3002<\/p>\n
          \u7b80\u5355\u4ea4\u53c9\u9a8c\u8bc1<\/h3>\n
            \u628a\u6570\u636e\u96c6\u6309\u7167\u67d0\u79cd\u6bd4\u4f8b\uff0c\u5c06\u6570\u636e\u96c6\u4e2d\u7684\u6570\u636e\u968f\u673a\u7684\u5206\u4e3a\u8bad\u7ec3\u96c6\u548c\u6d4b\u8bd5\u96c6\u3002\u7136\u540e\u4e0d\u65ad\u7684\u6539\u53d8\u6a21\u578b\u53c2\u6570\u8bad\u7ec3\u51fa\u4e00\u7ec4\u6a21\u578b\uff0c\u6bcf\u8bad\u7ec3\u5b8c\u4e00\u4e2a\u6a21\u578b\u5c31\u7528\u6d4b\u8bd5\u96c6\u6d4b\u8bd5\uff0c\u6700\u540e\u5f97\u5230\u6027\u80fd\u6700\u597d\u7684\u6a21\u578b\u3002<\/p>\n
            \n
          1. \u521d\u59cb\u503c$c=1$ <\/li>\n
          2. \u8bad\u7ec3\u6a21\u578b<\/li>\n
          3. \u6d4b\u8bd5\u6a21\u578b\uff0c$c+1$<\/li>\n
          4. \u5982\u679c$c<11$\u6539\u53d8\u6a21\u578b\u53c2\u6570\uff0c\u8df3\u8f6c\u5230\u6b65\u9aa41\uff1b\u53cd\u4e4b\uff0c\u505c\u6b62\u8bad\u7ec3<\/li>\n
          5. \u4ece\u6a21\u578b\u96c6${c_1,c2,\\cdots,c<\/em>{10}}$\u4e2d\u9009\u62e9\u6027\u80fd\u6700\u4f18\u7684\u6a21\u578b<\/li>\n<\/ol>\n
            # \u7b80\u5355\u4ea4\u53c9\u9a8c\u8bc1\nimport numpy as np\nfrom sklearn import datasets\nfrom sklearn.model_selection import train_test_split\n\n# \u5bfc\u5165\u9e22\u5c3e\u82b1\u6570\u636e\niris_data = datasets.load_iris()\nX = iris_data.data[:, [0, 1]]\ny = iris_data.target\n\n# random_state=1\u53ef\u4ee5\u786e\u4fdd\u7ed3\u679c\u4e0d\u968f\u673a\uff0cstratify=y\u53ef\u4ee5\u786e\u4fdd\u6bcf\u4e2a\u5206\u7c7b\u7684\u7ed3\u679c\u90fd\u6709\u76f8\u540c\u7684\u6bd4\u4f8b\nX_train, X_test, y_train, y_test = train_test_split(\n    X, y, test_size=0.3, random_state=1, stratify=y)\n\nprint('\u4e0d\u540c\u7c7b\u522b\u6240\u6709\u6837\u672c\u6570\u91cf:{}'.format(np.bincount(y)))\nprint('\u4e0d\u540c\u7c7b\u522b\u8bad\u7ec3\u6570\u636e\u6570\u91cf:{}'.format(np.bincount(y_train)))\nprint('\u4e0d\u540c\u7c7b\u522b\u6d4b\u8bd5\u6570\u636e\u6570\u91cf:{}'.format(np.bincount(y_test)))<\/code><\/pre>\n
            \u4e0d\u540c\u7c7b\u522b\u6240\u6709\u6837\u672c\u6570\u91cf:[50 50 50]\n\u4e0d\u540c\u7c7b\u522b\u8bad\u7ec3\u6570\u636e\u6570\u91cf:[35 35 35]\n\u4e0d\u540c\u7c7b\u522b\u6d4b\u8bd5\u6570\u636e\u6570\u91cf:[15 15 15]<\/code><\/pre>\n
            k\u6298\u4ea4\u53c9\u9a8c\u8bc1<\/h3>\n
              \u5c06\u6570\u636e\u968f\u673a\u7684\u5206\u4e3a$k$\u4e2a\u5b50\u96c6\uff08$k$\u7684\u53d6\u503c\u8303\u56f4\u4e00\u822c\u5728$[1-20]$\u4e4b\u95f4\uff09\uff0c\u7136\u540e\u53d6\u51fa$k-1$\u4e2a\u5b50\u96c6\u8fdb\u884c\u8bad\u7ec3\uff0c\u53e6\u4e00\u4e2a\u5b50\u96c6\u7528\u4f5c\u6d4b\u8bd5\u6a21\u578b\uff0c\u91cd\u590d$k$\u6b21\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u5f97\u5230\u6700\u4f18\u6a21\u578b\u3002<\/p>\n
              \n
            1. \u5c06\u6570\u636e\u5206\u4e3a$k$\u4e2a\u5b50\u96c6<\/li>\n
            2. \u9009\u62e9$k-1$\u4e2a\u5b50\u96c6\u8bad\u7ec3\u6a21\u578b<\/li>\n
            3. \u9009\u62e9\u53e6\u4e00\u4e2a\u5b50\u96c6\u6d4b\u8bd5\u6a21\u578b<\/li>\n
            4. \u91cd\u590d2-3\u6b65\uff0c\u76f4\u81f3\u6709$k$\u4e2a\u6a21\u578b<\/li>\n
            5. \u9009\u62e9$k$\u4e2a\u6a21\u578b\u4e2d\u6027\u80fd\u6700\u4f18\u7684\u6a21\u578b<\/li>\n<\/ol>\n
              # k\u6298\u4ea4\u53c9\u9a8c\u8bc1\nimport numpy as np\nfrom sklearn import datasets\nfrom sklearn.model_selection import StratifiedKFold\n\n# \u5bfc\u5165\u9e22\u5c3e\u82b1\u6570\u636e\niris_data = datasets.load_iris()\nX = iris_data.data[:, [0, 1]]\ny = iris_data.target\n\n# n_splits=10\u76f8\u5f53\u4e8ek=10\nkfold = StratifiedKFold(n_splits=10, random_state=1)\nkfold = kfold.split(X, y)\n\nfor k, (train_data, test_data) in enumerate(kfold):\n    print('\u8fed\u4ee3\u6b21\u6570:{}'.format(k), '\u8bad\u7ec3\u6570\u636e\u957f\u5ea6:{}'.format(\n        len(train_data)), '\u6d4b\u8bd5\u6570\u636e\u957f\u5ea6:{}'.format(len(test_data)))<\/code><\/pre>\n
              \u8fed\u4ee3\u6b21\u6570:0 \u8bad\u7ec3\u6570\u636e\u957f\u5ea6:135 \u6d4b\u8bd5\u6570\u636e\u957f\u5ea6:15\n\u8fed\u4ee3\u6b21\u6570:1 \u8bad\u7ec3\u6570\u636e\u957f\u5ea6:135 \u6d4b\u8bd5\u6570\u636e\u957f\u5ea6:15\n\u8fed\u4ee3\u6b21\u6570:2 \u8bad\u7ec3\u6570\u636e\u957f\u5ea6:135 \u6d4b\u8bd5\u6570\u636e\u957f\u5ea6:15\n\u8fed\u4ee3\u6b21\u6570:3 \u8bad\u7ec3\u6570\u636e\u957f\u5ea6:135 \u6d4b\u8bd5\u6570\u636e\u957f\u5ea6:15\n\u8fed\u4ee3\u6b21\u6570:4 \u8bad\u7ec3\u6570\u636e\u957f\u5ea6:135 \u6d4b\u8bd5\u6570\u636e\u957f\u5ea6:15\n\u8fed\u4ee3\u6b21\u6570:5 \u8bad\u7ec3\u6570\u636e\u957f\u5ea6:135 \u6d4b\u8bd5\u6570\u636e\u957f\u5ea6:15\n\u8fed\u4ee3\u6b21\u6570:6 \u8bad\u7ec3\u6570\u636e\u957f\u5ea6:135 \u6d4b\u8bd5\u6570\u636e\u957f\u5ea6:15\n\u8fed\u4ee3\u6b21\u6570:7 \u8bad\u7ec3\u6570\u636e\u957f\u5ea6:135 \u6d4b\u8bd5\u6570\u636e\u957f\u5ea6:15\n\u8fed\u4ee3\u6b21\u6570:8 \u8bad\u7ec3\u6570\u636e\u957f\u5ea6:135 \u6d4b\u8bd5\u6570\u636e\u957f\u5ea6:15\n\u8fed\u4ee3\u6b21\u6570:9 \u8bad\u7ec3\u6570\u636e\u957f\u5ea6:135 \u6d4b\u8bd5\u6570\u636e\u957f\u5ea6:15<\/code><\/pre>\n
              \u7559\u4e00\u6cd5\u4ea4\u53c9\u9a8c\u8bc1<\/h3>\n
                \u4e0e$k$\u6298\u4ea4\u53c9\u9a8c\u8bc1\u7c7b\u4f3c\uff0c\u5c5e\u4e8e$k$\u6298\u4ea4\u53c9\u9a8c\u8bc1\u7684\u7279\u4f8b\uff0c\u5373\u4e00\u4e2a\u6570\u636e\u96c6$T$\u4e2d\u6709$n$\u4e2a\u6570\u636e\uff0c\u5f53$k=n-1$\u65f6\uff0c$k$\u6298\u4ea4\u53c9\u9a8c\u8bc1\u5373\u4e3a\u7559\u4e00\u6cd5\u4ea4\u53c9\u9a8c\u8bc1\u3002<\/p>\n
              # \u7559\u4e00\u6cd5\u4ea4\u53c9\u9a8c\u8bc1\nimport numpy as np\nfrom sklearn import datasets\nfrom sklearn.model_selection import LeaveOneOut\n\n# \u5bfc\u5165\u9e22\u5c3e\u82b1\u6570\u636e\niris_data = datasets.load_iris()\nX = iris_data.data[:, [0, 1]]\ny = iris_data.target\n\nloo = LeaveOneOut()\nloo<\/code><\/pre>\n
              LeaveOneOut()<\/code><\/pre>\n
              loo.get_n_splits(X)<\/code><\/pre>\n
              150<\/code><\/pre>\n
              count = 0\nfor train_index, test_index in loo.split(X):\n    if count < 10:\n        print("\u8bad\u7ec3\u96c6\u957f\u5ea6:", len(train_index), "\u6d4b\u8bd5\u96c6\u957f\u5ea6:", len(test_index))\n    count += 1\n    if count == loo.get_n_splits(X)-1:\n        print('...\\n\u8fed\u4ee3\u6b21\u6570:', count)<\/code><\/pre>\n
              \u8bad\u7ec3\u96c6\u957f\u5ea6: 149 \u6d4b\u8bd5\u96c6\u957f\u5ea6: 1\n\u8bad\u7ec3\u96c6\u957f\u5ea6: 149 \u6d4b\u8bd5\u96c6\u957f\u5ea6: 1\n\u8bad\u7ec3\u96c6\u957f\u5ea6: 149 \u6d4b\u8bd5\u96c6\u957f\u5ea6: 1\n\u8bad\u7ec3\u96c6\u957f\u5ea6: 149 \u6d4b\u8bd5\u96c6\u957f\u5ea6: 1\n\u8bad\u7ec3\u96c6\u957f\u5ea6: 149 \u6d4b\u8bd5\u96c6\u957f\u5ea6: 1\n\u8bad\u7ec3\u96c6\u957f\u5ea6: 149 \u6d4b\u8bd5\u96c6\u957f\u5ea6: 1\n\u8bad\u7ec3\u96c6\u957f\u5ea6: 149 \u6d4b\u8bd5\u96c6\u957f\u5ea6: 1\n\u8bad\u7ec3\u96c6\u957f\u5ea6: 149 \u6d4b\u8bd5\u96c6\u957f\u5ea6: 1\n\u8bad\u7ec3\u96c6\u957f\u5ea6: 149 \u6d4b\u8bd5\u96c6\u957f\u5ea6: 1\n\u8bad\u7ec3\u96c6\u957f\u5ea6: 149 \u6d4b\u8bd5\u96c6\u957f\u5ea6: 1\n...\n\u8fed\u4ee3\u6b21\u6570: 149<\/code><\/pre>\n
              \u65f6\u95f4\u5e8f\u5217\u5206\u5272<\/h3>\n
                \u65f6\u95f4\u5e8f\u5217\u5206\u5272\u4e00\u822c\u5bf9\u65f6\u95f4\u5e8f\u5217\u7b97\u6cd5\u505a\u6d4b\u8bd5\uff0c\u4ed6\u5207\u5272\u7684\u539f\u7406\u662f\uff1a\u6d4b\u8bd5\u96c6\u7684\u6570\u636e\u548c\u4e0a\u51e0\u4e2a\u6570\u636e\u4f1a\u6709\u4e00\u5b9a\u7684\u8054\u7cfb\u3002<\/p>\n
              from sklearn.model_selection import TimeSeriesSplit\nX = np.array([[1, 2], [2, 4], [3, 2], [2, 4], [1, 2], [3, 2]])\ny = np.array([1, 3, 3, 4, 5, 4])\n# max_train_size\u6307\u8bad\u7ec3\u6570\u636e\u4e2a\u6570\uff0cn_splits\u6307\u5207\u5272\u6b21\u6570\ntscv = TimeSeriesSplit(n_splits=5, max_train_size=3)\ntscv<\/code><\/pre>\n
              TimeSeriesSplit(max_train_size=3, n_splits=5)<\/code><\/pre>\n
              for train_index, test_index in tscv.split(X):\n    print("\u8bad\u7ec3\u6570\u636e\u7d22\u5f15:", train_index, "\u6d4b\u8bd5\u6570\u7d22\u5f15:", test_index)\n    X_train, X_test = X[train_index], X[test_index]\n    y_train, y_test = y[train_index], y[test_index]<\/code><\/pre>\n
              \u8bad\u7ec3\u6570\u636e\u7d22\u5f15: [0] \u6d4b\u8bd5\u6570\u7d22\u5f15: [1]\n\u8bad\u7ec3\u6570\u636e\u7d22\u5f15: [0 1] \u6d4b\u8bd5\u6570\u7d22\u5f15: [2]\n\u8bad\u7ec3\u6570\u636e\u7d22\u5f15: [0 1 2] \u6d4b\u8bd5\u6570\u7d22\u5f15: [3]\n\u8bad\u7ec3\u6570\u636e\u7d22\u5f15: [1 2 3] \u6d4b\u8bd5\u6570\u7d22\u5f15: [4]\n\u8bad\u7ec3\u6570\u636e\u7d22\u5f15: [2 3 4] \u6d4b\u8bd5\u6570\u7d22\u5f15: [5]<\/code><\/pre>\n
              \u4ea4\u53c9\u9a8c\u8bc1\u548c\u6a21\u578b\u4e00\u8d77\u4f7f\u7528<\/h2>\n
                \u5982\u679c\u53ea\u662f\u5bf9\u4ea4\u53c9\u9a8c\u8bc1\u6709\u4e00\u5b9a\u7684\u4e86\u89e3\uff0c\u90a3\u4e48\u95ee\u9898\u5219\u662f\uff0c\u6211\u4eec\u5982\u4f55\u628a\u4f7f\u7528\u4ea4\u53c9\u9a8c\u8bc1\u7684\u601d\u60f3\uff0c\u8bad\u7ec3\u6a21\u578b\u5462\uff1f\u4f7f\u7528for\u5faa\u73af\u5417\uff1f\u4e0d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528sklearn\u81ea\u5e26\u7684\u4ea4\u53c9\u9a8c\u8bc1\u8bc4\u5206\u65b9\u6cd5\u3002<\/p>\n
              cross_val_score<\/h3>\n
                \u4ea4\u53c9\u9a8c\u8bc1\u4e2d\u7684cross_val_score\uff0c\u5373\u6700\u666e\u901a\u7684\u4ea4\u53c9\u9a8c\u8bc1\u548c\u6a21\u578b\u4e00\u8d77\u4f7f\u7528\u7684\u65b9\u6cd5\uff0c\u8be5\u65b9\u6cd5\u9700\u8981\u6307\u5b9a\u6a21\u578b\u3001\u8bad\u7ec3\u96c6\u6570\u636e\u548c\u8bc4\u5206\u65b9\u6cd5\uff0c\u7136\u540e\u53ef\u4ee5\u5f97\u51fa\u6bcf\u4e00\u6b21\u6d4b\u8bd5\u6a21\u578b\u7684\u5206\u6570\u3002<\/p>\n
              from sklearn.metrics import SCORERS\n\n# \u53ef\u4ee5\u4f7f\u7528\u7684\u8bc4\u5206\u65b9\u6cd5\nSCORERS.keys()<\/code><\/pre>\n
              dict_keys(['explained_variance', 'r2', 'neg_median_absolute_error', 'neg_mean_absolute_error', 'neg_mean_squared_error', 'neg_mean_squared_log_error', 'accuracy', 'roc_auc', 'balanced_accuracy', 'average_precision', 'neg_log_loss', 'brier_score_loss', 'adjusted_rand_score', 'homogeneity_score', 'completeness_score', 'v_measure_score', 'mutual_info_score', 'adjusted_mutual_info_score', 'normalized_mutual_info_score', 'fowlkes_mallows_score', 'precision', 'precision_macro', 'precision_micro', 'precision_samples', 'precision_weighted', 'recall', 'recall_macro', 'recall_micro', 'recall_samples', 'recall_weighted', 'f1', 'f1_macro', 'f1_micro', 'f1_samples', 'f1_weighted'])<\/code><\/pre>\n
              from sklearn.model_selection import cross_val_score\nfrom sklearn.linear_model import LogisticRegression\nfrom sklearn import datasets\n\niris = datasets.load_iris()\nX = iris.data\ny = iris.target\n\nclf = LogisticRegression(solver='lbfgs', multi_class='auto', max_iter=1000)\nscores = cross_val_score(clf, X, y, cv=10, scoring='accuracy')\nscores<\/code><\/pre>\n
              LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n          intercept_scaling=1, max_iter=1000, multi_class='auto',\n          n_jobs=None, penalty='l2', random_state=None, solver='lbfgs',\n          tol=0.0001, verbose=0, warm_start=False)<\/code><\/pre>\n
              print('\u51c6\u786e\u7387:{:.4f}(+\/-{:.4f})'.format(scores.mean(), scores.std()*2))<\/code><\/pre>\n
              cross_validate<\/h3>\n
                \u4ea4\u53c9\u9a8c\u8bc1\u4e2dcross_validate\u65b9\u6cd5\uff0c\u76f8\u6bd4\u8f83cross_val_score\u65b9\u6cd5\u53ef\u4ee5\u6307\u5b9a\u591a\u4e2a\u6307\u6807\uff0c\u5e76\u4e14cross_validate\u65b9\u6cd5\u4f1a\u8fd4\u56de\u6a21\u578bfit_time\u8bad\u7ec3\u548cscore_time\u8bc4\u5206\u7684\u65f6\u95f4\u3002<\/p>\n
              from sklearn.model_selection import cross_validate\nfrom sklearn.linear_model import LogisticRegression\nfrom sklearn import datasets\n\niris = datasets.load_iris()\nX = iris.data\ny = iris.target\n\nclf = LogisticRegression(solver='lbfgs', multi_class='auto', max_iter=1000)\ncross_validate(clf, X, y, cv=10, scoring=[\n    'accuracy', 'recall_weighted'], return_train_score=True)<\/code><\/pre>\n
              {'fit_time': array([0.03741813, 0.03649879, 0.0418241 , 0.03404689, 0.02642822,\n        0.02773309, 0.02451205, 0.02093697, 0.03865075, 0.06034207]),\n 'score_time': array([0.00159192, 0.00155306, 0.00085807, 0.00101495, 0.00089979,\n        0.000772  , 0.00068307, 0.00121713, 0.00101519, 0.00123286]),\n 'test_accuracy': array([1.        , 0.93333333, 1.        , 1.        , 0.93333333,\n        0.93333333, 0.93333333, 1.        , 1.        , 1.        ]),\n 'train_accuracy': array([0.97037037, 0.97777778, 0.97037037, 0.97037037, 0.97777778,\n        0.97777778, 0.98518519, 0.97037037, 0.97037037, 0.97777778]),\n 'test_recall_weighted': array([1.        , 0.93333333, 1.        , 1.        , 0.93333333,\n        0.93333333, 0.93333333, 1.        , 1.        , 1.        ]),\n 'train_recall_weighted': array([0.97037037, 0.97777778, 0.97037037, 0.97037037, 0.97777778,\n        0.97777778, 0.98518519, 0.97037037, 0.97037037, 0.97777778])}<\/code><\/pre>\n
              cross_val_predict<\/h3>\n
                \u4ea4\u53c9\u9a8c\u8bc1\u4e2d\u7684cross_val_predict\u65b9\u6cd5\u53ef\u4ee5\u83b7\u53d6\u6bcf\u4e2a\u6837\u672c\u7684\u9884\u6d4b\u7ed3\u679c\uff0c\u5373\u6bcf\u4e00\u4e2a\u6837\u672c\u90fd\u4f1a\u88ab\u4f5c\u4e3a\u6d4b\u8bd5\u6570\u636e\u3002<\/p>\n
              from sklearn.model_selection import cross_val_predict\nfrom sklearn.linear_model import LogisticRegression\nfrom sklearn import datasets\n\niris = datasets.load_iris()\nX = iris.data\ny = iris.target\n\nclf = LogisticRegression(solver='lbfgs', multi_class='auto', max_iter=1000)\ncross_val_predict(clf, X, y, cv=10)<\/code><\/pre>\n
              array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n       1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1,\n       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2,\n       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])<\/code><\/pre>\n
              from sklearn.metrics import accuracy_score\n\naccuracy_score(y, per_sample)<\/code><\/pre>\n
              0.9733333333333334<\/code><\/pre>\n
              \u504f\u5dee\u4e0e\u65b9\u5dee<\/h1>\n
                \u901a\u5e38\u628a\u6a21\u578b\u5bf9\u672a\u6765\u65b0\u6570\u636e\u7684\u9884\u6d4b\u80fd\u529b\u79f0\u4e3a\u6cdb\u5316\u80fd\u529b\uff0c\u800c\u6a21\u578b\u5bf9\u4f4d\u7f6e\u65b0\u6570\u636e\u9884\u6d4b\u7684\u8bef\u5dee\u79f0\u4e3a\u6cdb\u5316\u8bef\u5dee\u3002\u504f\u5dee\u5219\u8868\u8fbe\u4e86\u6a21\u578b\u7684\u671f\u671b\u9884\u6d4b\u4e0e\u771f\u5b9e\u7ed3\u679c\u7684\u504f\u79bb\u7a0b\u5ea6\uff0c\u5373\u6a21\u578b\u7684\u62df\u5408\u80fd\u529b\uff1b\u65b9\u5dee\u8868\u8fbe\u4e86\u540c\u6837\u5927\u5c0f\u7684\u8bad\u7ec3\u96c6\u53d8\u52a8\u6240\u5bfc\u81f4\u7684\u5b66\u4e60\u6027\u80fd\u7684\u53d8\u5316\uff0c\u5373\u6570\u636e\u6270\u52a8\u9020\u6210\u7684\u5f71\u54cd\uff1b\u566a\u58f0\u8868\u8fbe\u4e86\u671f\u671b\u6cdb\u5316\u8bef\u5dee\u7684\u4e0b\u9650\uff0c\u5373\u5bf9\u672a\u6765\u9884\u6d4b\u65b0\u6570\u636e\u7684\u96be\u5ea6\u3002<\/p>\n
                \u56de\u5f52\u4efb\u52a1\u4e2d\u6cdb\u5316\u8bef\u5dee\u901a\u8fc7\u67d0\u79cd\u8ba1\u7b97\u53ef\u4ee5\u5206\u89e3\u4e3a\u504f\u5dee\u3001\u65b9\u5dee\u4e0e\u566a\u58f0\u4e4b\u548c\uff0c\u5982\u4f55\u5206\u89e3\u4e0d\u5728\u672c\u6587\u8ba8\u8bba\u8303\u56f4\u5185\u3002\u566a\u58f0\u4e0d\u53ef\u907f\u514d\uff0c\u56e0\u6b64\u4e3b\u8981\u5173\u6ce8\u504f\u5dee\u4e0e\u65b9\u5dee\uff0c\u504f\u5dee\u8d8a\u5927\uff0c\u9884\u6d4b\u503c\u4e0e\u771f\u5b9e\u7ed3\u679c\u7684\u504f\u79bb\u7a0b\u5ea6\u8d8a\u5927\uff0c\u6a21\u578b\u7684\u62df\u5408\u80fd\u529b\u8d8a\u5f31\uff0c\u6cdb\u5316\u8bef\u5dee\u8d8a\u5927\uff1b\u65b9\u5dee\u8d8a\u5927\uff0c\u5bf9\u6570\u636e\u6270\u52a8\u9020\u6210\u7684\u5f71\u54cd\u8d8a\u5f3a\uff0c\u6a21\u578b\u7684\u62df\u5408\u80fd\u529b\u8d8a\u5dee\uff0c\u6cdb\u5316\u8bef\u5dee\u8d8a\u5927\u3002\u5982\u6b64\u770b\u6765\uff0c\u504f\u5dee\u4e0e\u65b9\u5dee\u8d8a\u5c0f\u8d8a\u597d\uff0c\u4f46\u662f\u504f\u5dee\u548c\u65b9\u5dee\u901a\u5e38\u60c5\u51b5\u4e0b\u662f\u6709\u51b2\u7a81\u7684\uff0c\u79f0\u4e3a\u504f\u5dee-\u65b9\u5dee\u7a98\u5883\u3002<\/p>\n
              \u504f\u5dee-\u65b9\u5dee\u7a98\u5883<\/h2>\n
                \u504f\u5dee-\u65b9\u5dee\u7a98\u5883\uff1a\u8bad\u7ec3\u521d\u671f\uff0c\u7531\u4e8e\u8bad\u7ec3\u4e0d\u8db3\uff0c\u4f1a\u9020\u6210\u6b20\u62df\u5408\uff0c\u6570\u636e\u62df\u5408\u6548\u679c\u5f88\u5dee\uff0c\u504f\u5dee\u8f83\u5927\uff0c\u6570\u636e\u96c6\u7684\u6270\u52a8\u4e5f\u65e0\u6cd5\u4f7f\u6a21\u578b\u9020\u6210\u8f83\u5927\u5f71\u54cd\uff1b\u968f\u7740\u8bad\u7ec3\u7a0b\u5ea6\u7684\u52a0\u6df1\uff0c\u6570\u636e\u62df\u5408\u6548\u679c\u5f88\u597d\uff0c\u5373\u8fc7\u62df\u5408\uff0c\u504f\u5dee\u53d8\u5c0f\uff0c\u4f46\u662f\u6570\u636e\u96c6\u8f7b\u5fae\u7684\u6270\u52a8\u90fd\u4f1a\u4f7f\u6a21\u578b\u53d1\u751f\u8f83\u5927\u7684\u5f71\u54cd\uff0c\u65b9\u5dee\u504f\u5927\u3002\u7b80\u800c\u8a00\u4e4b\uff0c\u6b20\u62df\u5408\u72b6\u6001\uff0c\u504f\u5dee\u5927\uff0c\u65b9\u5dee\u5c0f\uff1b\u8fc7\u62df\u5408\u72b6\u6001\uff0c\u504f\u5dee\u5c0f\uff0c\u65b9\u5dee\u5927\u3002<\/p>\n
              \u67e5\u51c6\u7387\u3001\u67e5\u5168\u7387\u548cF1<\/h1>\n
                \u4e8c\u5206\u7c7b\u95ee\u9898\u4e2d\u6839\u636e\u6837\u4f8b\u7684\u771f\u5b9e\u7c7b\u522b\u548c\u6a21\u578b\u9884\u6d4b\u7c7b\u522b\u7684\u7ec4\u5408\u5212\u5206\u4e3a\u771f\u6b63\u4f8b(true positive)\u3001\u5047\u6b63\u4f8b(false positive)\u3001\u771f\u53cd\u4f8b(true negative)\u3001\u5047\u53cd\u4f8b(false negative)\u56db\u79cd\u60c5\u5f62\uff0c\u4ee4TP\u3001FP\u3001TN\u3001FN\u5206\u522b\u8868\u793a\u5bf9\u5e94\u7684\u6837\u4f8b\u6570\uff0c$\u6837\u4f8b\u603b\u6570 = TP+FP+TN+FN$\u3002<\/p>\n
                  TP\u2014\u2014\u5c06\u6b63\u7c7b\u9884\u6d4b\u4e3a\u6b63\u7c7b\u6570<\/p>\n
                  FP\u2014\u2014\u5c06\u8d1f\u7c7b\u9884\u6d4b\u4e3a\u6b63\u7c7b\u6570<\/p>\n
                  TN\u2014\u2014\u5c06\u8d1f\u7c7b\u9884\u6d4b\u4e3a\u8d1f\u7c7b\u6570<\/p>\n
                  FN\u2014\u2014\u5c06\u6b63\u7c7b\u9884\u6d4b\u4e3a\u8d1f\u7c7b\u6570<\/p>\n
              \u51c6\u786e\u5ea6<\/h3>\n
              \u51c6\u786e\u5ea6\uff08accuracy_socre\uff09\u5b9a\u4e49\u4e3a
              \n$$
              \nP = {\\frac{TP+FN}{TP+FP+TN+FN}} = \\frac{\u6b63\u786e\u9884\u6d4b\u7684\u6837\u672c\u6570}{\u6837\u672c\u603b\u6570}
              \n$$<\/p>\n
              # \u67e5\u51c6\u7387\u793a\u4f8b\nfrom sklearn import datasets\nfrom sklearn.metrics import accuracy_score\nfrom sklearn.linear_model import LogisticRegression\n\niris_data = datasets.load_iris()\nX = iris_data.data\ny = iris_data.target\n\nlr = LogisticRegression(solver='lbfgs', multi_class='auto', max_iter=200)\nlr = lr.fit(X, y)\n\ny_pred = lr.predict(X)\nprint('\u51c6\u786e\u5ea6:{:.2f}'.format(\n    accuracy_score(y, y_pred)))<\/code><\/pre>\n
              \u51c6\u786e\u5ea6:0.97<\/code><\/pre>\n
              \u67e5\u51c6\u7387<\/h2>\n
                \u67e5\u51c6\u7387\u5b9a\u4e49\u4e3a
              \n$$
              \nP = {\\frac{TP}{TP+FP}} = \\frac{\u6b63\u786e\u9884\u6d4b\u4e3a\u6b63\u7c7b\u7684\u6837\u672c\u6570}{\u9884\u6d4b\u4e3a\u6b63\u7c7b\u7684\u6837\u672c\u603b\u6570}
              \n$$<\/p>\n
              # \u67e5\u51c6\u7387\u793a\u4f8b\nfrom sklearn import datasets\nfrom sklearn.metrics import precision_score\nfrom sklearn.linear_model import LogisticRegression\n\niris_data = datasets.load_iris()\nX = iris_data.data\ny = iris_data.target\n\nlr = LogisticRegression(solver='lbfgs', multi_class='auto', max_iter=200)\nlr = lr.fit(X, y)\n\ny_pred = lr.predict(X)\nprint('\u67e5\u51c6\u7387:{:.2f}'.format(\n    precision_score(y, y_pred, average='weighted')))<\/code><\/pre>\n
              \u67e5\u51c6\u7387:0.97<\/code><\/pre>\n
              \u67e5\u5168\u7387<\/h2>\n
                \u67e5\u5168\u7387\u5b9a\u4e49\u4e3a
              \n$$
              \nR = {\\frac{TP}{TP+FN}} = \\frac{\u6b63\u786e\u9884\u6d4b\u4e3a\u6b63\u7c7b\u7684\u6837\u672c\u6570}{\u6b63\u7c7b\u603b\u6837\u672c\u6570}
              \n$$<\/p>\n
              # \u67e5\u5168\u7387\u793a\u4f8b\nfrom sklearn.metrics import recall_score\nfrom sklearn import datasets\nfrom sklearn.linear_model import LogisticRegression\n\niris_data = datasets.load_iris()\nX = iris_data.data\ny = iris_data.target\n\nlr = LogisticRegression(solver='lbfgs', multi_class='auto', max_iter=200)\nlr = lr.fit(X, y)\n\ny_pred = lr.predict(X)\nprint('\u67e5\u5168\u7387:{:.2f}'.format(recall_score(y, y_pred, average='weighted')))<\/code><\/pre>\n
              \u67e5\u5168\u7387:0.97<\/code><\/pre>\n
              F1\u503c<\/h2>\n
                \u901a\u5e38\u60c5\u51b5\u4e0b\u901a\u8fc7\u67e5\u51c6\u7387\u548c\u67e5\u5168\u7387\u5ea6\u91cf\u6a21\u578b\u7684\u597d\u574f\uff0c\u4f46\u662f\u67e5\u51c6\u7387\u548c\u67e5\u5168\u7387\u662f\u4e00\u5bf9\u77db\u76fe\u7684\u5ea6\u91cf\u5de5\u5177\uff0c\u67e5\u51c6\u7387\u9ad8\u7684\u65f6\u5019\u67e5\u5168\u7387\u4f4e\uff1b\u67e5\u5168\u7387\u9ad8\u7684\u65f6\u5019\u67e5\u51c6\u7387\u4f4e\uff0c\u56e0\u6b64\u5de5\u4e1a\u4e0a\u5bf9\u4e0d\u4e0d\u540c\u7684\u95ee\u9898\u5bf9\u67e5\u51c6\u7387\u548c\u67e5\u5168\u7387\u7684\u4fa7\u91cd\u70b9\u4f1a\u6709\u6240\u4e0d\u540c\u3002<\/p>\n
                \u4f8b\u5982\u764c\u75c7\u7684\u9884\u6d4b\u4e2d\uff0c\u6b63\u7c7b\u662f\u5065\u5eb7\uff0c\u53cd\u7c7b\u662f\u60a3\u6709\u764c\u75c7\u3002\u8f83\u9ad8\u7684\u67e5\u51c6\u7387\u53ef\u80fd\u4f1a\u5bfc\u81f4\u5065\u5eb7\u7684\u4eba\u88ab\u544a\u77e5\u60a3\u6709\u764c\u75c7\uff1b\u8f83\u9ad8\u7684\u67e5\u5168\u7387\u53ef\u80fd\u4f1a\u5bfc\u81f4\u60a3\u6709\u764c\u75c7\u7684\u60a3\u8005\u4f1a\u88ab\u544a\u77e5\u5065\u5eb7\u3002<\/p>\n
                $F_1$\u503c\u5b9a\u4e49\u4e3a
              \n$$
              \nF1 = {\\frac{2P<\/em>R}{P+R}} = {\\frac{2TP}{2TP+FP+FN}} = {\\frac{2<\/em>TP}{\u6837\u4f8b\u603b\u6570+TP-TN}}
              \n$$
              \n  $F<\/em>\\beta$\u5b9a\u4e49\u4e3a\uff1a
              \n$$
              \nF\\beta = {\\frac{(1+\\beta^2)P<\/em>R}{\\beta^2*P+R}}
              \n$$
              \n  $F<\/em>\\beta$\u662f\u5728$F_1$\u503c\u7684\u57fa\u7840\u4e0a\u52a0\u6743\u5f97\u5230\u7684\uff0c\u5b83\u53ef\u4ee5\u66f4\u597d\u7684\u6743\u8861\u67e5\u51c6\u7387\u548c\u67e5\u5168\u7387\u3002<\/p>\n
                \n
              1. \u5f53$\\beta<1$\u65f6\uff0c$P$\u7684\u6743\u91cd\u51cf\u5c0f\uff0c\u5373$R$\u67e5\u51c6\u7387\u66f4\u91cd\u8981<\/li>\n
              2. \u5f53$\\beta=1$\u65f6\uff0c$F_\\beta = F_1$<\/li>\n
              3. \u5f53$\\beta>1$\u65f6\uff0c$P$\u7684\u6743\u91cd\u589e\u5927\uff0c\u5373$P$\u67e5\u5168\u7387\u66f4\u91cd\u8981\u3002<\/li>\n<\/ol>\n
                # F1\u503c\u793a\u4f8b\nfrom sklearn import datasets\nfrom sklearn.metrics import f1_score\nfrom sklearn.linear_model import LogisticRegression\n\niris_data = datasets.load_iris()\nX = iris_data.data\ny = iris_data.target\n\nlr = LogisticRegression(solver='lbfgs', multi_class='auto', max_iter=200)\nlr = lr.fit(X, y)\n\ny_pred = lr.predict(X)\nprint('F1\u503c:{:.2f}'.format(f1_score(y, y_pred, average='weighted')))<\/code><\/pre>\n
                F1\u503c:0.97<\/code><\/pre>\n
                ROC\u66f2\u7ebf<\/h2>\n
                  \u4e0b\u56fe\u5373ROC\u66f2\u7ebf\u7684\u56fe\u5f62\uff0c\u5bf9\u4e8e\u4ee5\u4e0b\u4e09\u6761ROC\u66f2\u7ebf\uff0c\u4e00\u822c\u60c5\u51b5\u53ef\u4ee5\u770b\u8fc7$(0,0)$\u7684\u865a\u7ebf\u4e0eROC\u66f2\u7ebf\u7684\u4ea4\u70b9\uff0c\u5982\u679c\u4ea4\u70b9\u8d8a\u9760\u5916\u9762\uff0c\u5219\u6a21\u578b\u6027\u80fd\u8d8a\u597d\u3002\u4f46\u662f\u4e00\u822c\u60c5\u51b5\u662f\u901a\u8fc7\u5224\u65adROC\u66f2\u7ebf\u56f4\u6210\u7684\u9762\u79efAUC\u9762\u79ef\u6765\u5224\u65ad\u6a21\u578b\u7684\u6027\u80fd\u3002<\/p>\n
                  \u901a\u5e38\u60c5\u51b5\u4e0b\u4e5f\u4f1a\u4f7f\u7528ROC(receiver operating characteristic\uff0cROC)\u66f2\u7ebf\u5ea6\u91cf\u6a21\u578b\u6027\u80fd\u7684\u597d\u574f\uff0cROC\u66f2\u7ebf\u987e\u540d\u601d\u4e49\u662f\u4e00\u6761\u66f2\u7ebf\uff0c\u5b83\u7684\u6a2a\u8f74\u662f\u5047\u6b63\u4f8b\u7387(false positive rate\uff0cFPR)\uff0c\u7eb5\u8f74\u662f\u771f\u6b63\u4f8b\u7387(true positive rate\uff0cTPR)\uff0c\u5047\u6b63\u4f8b\u7387\u548c\u771f\u6b63\u4f8b\u7387\u5206\u522b\u5b9a\u4e49\u4e3a\uff1a
                \n$$
                \nFPR = {\\frac{FP}{TN+FP}} \\text{\u5047\u6b63\u4f8b\u7387} \\
                \nTPR = {\\frac{TP}{TP+FN}} \\text{\u771f\u6b63\u4f8b\u7387}
                \n$$<\/p>\n
                # ROC\u793a\u4f8b\nfrom sklearn import datasets\nfrom sklearn.metrics import roc_curve\nfrom sklearn.linear_model import LogisticRegression\n\niris_data = datasets.load_iris()\nX = iris_data.data[0:100, :]\ny = iris_data.target[0:100]\n\nlr = LogisticRegression(solver='lbfgs', multi_class='auto', max_iter=200)\nlr = lr.fit(X, y)\n\ny_pred = lr.predict(X)\nfpr, tpr, thresholds = roc_curve(y, y_pred)\nplt.xlabel('FPR', fontsize=15)\nplt.ylabel('TPR', fontsize=15)\nplt.title('FPR-TPR', fontsize=20)\nplt.plot(fpr, tpr) \nplt.show()<\/code><\/pre>\n
                \"\"<\/div><\/p>\n
                AUC\u9762\u79ef<\/h2>\n
                  \u7531\u4e8eROC\u66f2\u7ebf\u6709\u65f6\u5019\u65e0\u6cd5\u7cbe\u51c6\u5ea6\u91cf\u6a21\u578b\u7684\u597d\u574f\uff0c\u56e0\u6b64\u4f1a\u4f7f\u7528ROC\u66f2\u7ebf\u5173\u4e8e\u6a2a\u7eb5\u8f74\u56f4\u6210\u7684\u9762\u79ef\u79f0\u4e3aAUC(area under ROC curve\uff0cAUC)\u6765\u5ea6\u91cf\u6a21\u578b\u7684\u597d\u574f\uff0cAUC\u503c\u8d8a\u5927\u7684\u6a21\u578b\uff0c\u5219\u6a21\u578b\u8d8a\u4f18\u3002<\/p>\n
                # AUC\u793a\u4f8b\nfrom sklearn import datasets\nfrom sklearn.metrics import roc_auc_score\nfrom sklearn.linear_model import LogisticRegression\n\niris_data = datasets.load_iris()\nX = iris_data.data[0:100, :]\ny = iris_data.target[0:100]\n\nlr = LogisticRegression(solver='lbfgs', multi_class='auto', max_iter=200)\nlr = lr.fit(X, y)\n\ny_pred = lr.predict(X)\n# \u8ba1\u7b97AUC\u503c\nprint('AUC\u503c:{:.2f}'.format(roc_auc_score(y, y_pred, average='weighted')))<\/code><\/pre>\n
                AUC\u503c:1.00<\/code><\/pre>\n
                \u5c0f\u7ed3<\/h1>\n
                  \u5728\u8bad\u7ec3\u6a21\u578b\u7684\u65f6\u5019\uff0c\u603b\u4f1a\u6709\u5404\u79cd\u5404\u6837\u7684\u539f\u56e0\u5bfc\u81f4\u6211\u4eec\u7684\u6a21\u578b\u53ef\u80fd\u6709\u4e00\u4e9b\u8f83\u5927\u7684\u8bef\u5dee\u3002\u53c8\u7531\u4e8e\u8bef\u5dee\u662f\u65e0\u6cd5\u907f\u514d\u7684\uff0c\u53ea\u80fd\u51cf\u5c0f\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u61c2\u5f97\u5982\u4f55\u53bb\u9762\u5bf9\u5e76\u89e3\u51b3\u8fd9\u4e9b\u8bef\u5dee\uff0c\u800c\u4e0d\u80fd\u8ba9\u8bef\u5dee\u5bfc\u81f4\u6211\u4eec\u5728\u6784\u9020\u6a21\u578b\u4e4b\u524d\u7684\u52aa\u529b\u529f\u4e8f\u4e00\u7bd1\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
                \u6a21\u578b\u9009\u62e9   \u673a\u5668\u5b66\u4e60\u662f\u5728\u67d0\u79cd\u5047\u8bbe\u4e0a\u5bf9\u6570\u636e\u7684\u5206\u6790\uff0c\u57fa\u4e8e\u8be5\u5047\u8bbe\u5373\u53ef\u6784\u9020\u591a\u4e2a\u6a21\u578b\u83b7\u5f97\u9884\u6d4b\u503c\uff0c\u901a […]<\/p>\n","protected":false},"author":3,"featured_media":3189,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[276,299],"tags":[],"_links":{"self":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3201"}],"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=3201"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3201\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/media\/3189"}],"wp:attachment":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3201"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3201"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3201"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}