\u5bf9\u4e8e\u5206\u7c7b\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u80fd\u4f1a\u4f7f\u7528k\u8fd1\u90bb\u7b97\u6cd5\u3001\u51b3\u7b56\u6811\u3001\u903b\u8f91\u56de\u5f52\u3001\u6734\u7d20\u8d1d\u53f6\u65af\u6cd5\u3001\u652f\u6301\u5411\u91cf\u673a\u3001\u968f\u673a\u68ee\u6797\uff1b\u5bf9\u4e8e\u56de\u5f52\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u80fd\u4f1a\u4f7f\u7528\u7ebf\u6027\u56de\u5f52\u3001\u51b3\u7b56\u6811\u3001\u968f\u673a\u68ee\u6797\u3002\u5728\u5de5\u4e1a\u4e0a\uff0c\u6211\u4eec\u4e0d\u53ef\u80fd\u4f1a\u5bf9\u5ba2\u6237\u8bf4\uff0c\u8fd9\u662f\u6211\u8bad\u7ec3\u7684\u51e0\u4e2a\u6a21\u578b\uff0c\u4f60\u60f3\u7528\u54ea\u4e2a\u6211\u5c31\u7ed9\u4f60\u54ea\u4e2a\u3002\u4e00\u822c\u800c\u8a00\u8fd9\u662f\u4e0d\u53ef\u80fd\u7684\uff0c\u901a\u5e38\u5bf9\u4e8e\u8fd9\u51e0\u4e2a\u6a21\u578b\uff0c\u6211\u4eec\u4f1a\u901a\u8fc7\u67d0\u79cd\u5ea6\u91cf\u6a21\u578b\u7684\u5de5\u5177\uff0c\u9009\u62e9\u4e00\u4e2a\u6700\u4f18\u7684\u6a21\u578b\u63a8\u7ed9\u5ba2\u6237\u3002<\/p>\n
\u5728\u8bad\u7ec3\u6a21\u578b\u90a3\u4e00\u7ae0\u8282\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u6a21\u578b\u6211\u4eec\u90fd\u4f7f\u7528\u4e86\u6a21\u578b\u81ea\u5e26\u7684score()\u65b9\u6cd5\u5bf9\u6a21\u578b\u7684\u6027\u80fd\u8fdb\u884c\u4e86\u4e00\u4e2a\u5ea6\u91cf\uff0c\u4f46\u662fscore()\u65b9\u6cd5\u5bf9\u4e8e\u5206\u7c7b\u6a21\u578b\uff0c\u53ea\u662f\u7b80\u5355\u7684\u5ea6\u91cf\u4e86\u6a21\u578b\u7684\u6027\u80fd\uff1b\u5bf9\u4e8e\u56de\u5f52\u6a21\u578b\uff0cscore()\u65b9\u6cd5\u53ea\u662f\u8ba1\u7b97\u4e86R2\u62a5\u544a\u5206\u6570\u3002\u8fd9\u6837\u7684\u5ea6\u91cf\u662f\u5f88\u7247\u9762\u7684\uff0c\u901a\u5e38\u6211\u4eec\u4f1a\u4f7f\u7528sklearn.metics\u548csklearn.model_selection\u5e93\u4e0b\u7684\u6a21\u5757\u5bf9\u5ea6\u91cf\u6a21\u578b\u6027\u80fd\u3002<\/p>\n
\u6a21\u5757\u63d0\u4f9b\u4e86\u5404\u79cd\u8bc4\u4f30\u6307\u6807\uff0c\u5e76\u4e14\u7528\u6237\u53ef\u4ee5\u81ea\u5b9a\u4e49\u8bc4\u4f30\u6307\u6807\uff0c\u5bf9\u4e8emetrics\u8bc4\u4f30\u6307\u6807\uff0c\u4e3b\u8981\u5206\u4e3a\u4ee5\u4e0b\u4e24\u79cd\u7c7b\u578b\uff1a<\/p>\n
* \u4ee5_score\u7ed3\u5c3e\u7684\u4e3a\u6a21\u578b\u5f97\u5206\uff0c\u4e00\u822c\u60c5\u51b5\u8d8a\u5927\u8d8a\u597d\n* \u4ee5_error\u6216_loss\u7ed3\u5c3e\u7684\u4e3a\u6a21\u578b\u7684\u504f\u5dee\uff0c\u4e00\u822c\u60c5\u51b5\u8d8a\u5c0f\u8d8a\u597d<\/code><\/pre>\n \u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u901a\u8fc7\u5206\u7c7b\u6a21\u578b\u3001\u56de\u5f52\u6a21\u578b\u6765\u8be6\u7ec6\u8bb2\u89e3metrics\u8bc4\u4f30\u6307\u6807\u3002<\/p>\n
1.2 \u6d4b\u8bd5\u56de\u5f52\u6a21\u578b<\/h1>\nimport numpy as np\nimport pandas as pd\nimport matplotlib.pyplot as plt\nfrom matplotlib.font_manager import FontProperties\nfrom sklearn import datasets\n%matplotlib inline\nfont = FontProperties(fname='\/Library\/Fonts\/Heiti.ttc')<\/code><\/pre>\n\/Applications\/anaconda3\/lib\/python3.7\/importlib\/_bootstrap.py:219: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n return f(*args, **kwds)\n\/Applications\/anaconda3\/lib\/python3.7\/importlib\/_bootstrap.py:219: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n return f(*args, **kwds)<\/code><\/pre>\n \u56de\u5f52\u6a21\u578b\u5e38\u7528\u7684metrics\u8bc4\u4f30\u6307\u6807\u6709\uff1ar2_score\u3001explained_variance_score\u7b49<\/p>\n
* explained_variance_score(y_true, y_pred, sample_weight=None, multioutput='uniform_average')\uff1a\u56de\u5f52\u65b9\u5dee(\u53cd\u5e94\u81ea\u53d8\u91cf\u4e0e\u56e0\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u7a0b\u5ea6)\n* mean_absolute_error(y_true, y_pred, sample_weight=None, multioutput='uniform_average')\uff1a\u5e73\u5747\u7edd\u5bf9\u503c\u8bef\u5dee\n* mean_squared_error(y_true, y_pred, sample_weight=None, multioutput='uniform_average')\uff1a\u5747\u65b9\u5dee\n* median_absolute_error(y_true, y_pred)\uff1a\u4e2d\u503c\u7edd\u5bf9\u8bef\u5dee\n* r2_score(y_true, y_pred, sample_weight=None, multioutput='uniform_average')\uff1aR\u5e73\u65b9\u503c<\/code><\/pre>\n1.2.1 r2_socre<\/h2>\n
r2score\u5373\u62a5\u544a\u51b3\u5b9a\u7cfb\u6570$(R^2)$\uff0c\u53ef\u4ee5\u7406\u89e3\u6210MSE\u7684\u6807\u51c6\u7248\uff0c$R^2$\u7684\u516c\u5f0f\u4e3a
\n$$
\nR^2 = 1-{\\frac {{\\frac{1}{n}\\sum<\/em>{i=1}^n(y^{(i)}-\\hat{y^{(i)}})^2}} {{\\frac{1}{n}}\\sum{i=1}^n(y^{(i)}-\\mu<\/em>{(y)})^2} }
\n$$
\n\u5176\u4e2d$\\mu{(y)}$\u662f$y$\u7684\u5e73\u5747\u503c\uff0c\u5373${{\\frac{1}{n}}\\sum<\/em>{i=1}^n(y^{(i)}-\\mu_{(y)})^2}$\u4e3a$y$\u7684\u65b9\u5dee\uff0c\u516c\u5f0f\u53ef\u4ee5\u5199\u6210
\n$$
\nR^2 = 1-{\\frac{MSE}{Var(y)}}
\n$$
\n $R^2$\u7684\u53d6\u503c\u8303\u56f4\u5728$0-1$\u4e4b\u95f4\uff0c\u5982\u679c$R^2=1$\uff0c\u5219\u5747\u65b9\u8bef\u5dee$MSE=0$\uff0c\u5373\u6a21\u578b\u5b8c\u7f8e\u7684\u62df\u5408\u6570\u636e\u3002<\/p>\n# \u62a5\u544a\u51b3\u5b9a\u7cfb\u6570\u5f97\u5206\nfrom sklearn.linear_model import LinearRegression\nfrom sklearn.metrics import r2_score\n\nboston = datasets.load_boston()\nX = boston.data\ny = boston.target\n\nlr = LinearRegression()\nlr.fit(X, y)\nlr_predict = lr.predict(X)\n\nlr_r2 = r2_score(y, lr_predict)\nprint('\u62a5\u544a\u51b3\u5b9a\u7cfb\u6570:{:.2f}'.format(lr_r2))<\/code><\/pre>\n\u62a5\u544a\u51b3\u5b9a\u7cfb\u6570:0.74<\/code><\/pre>\n1.2.1 explained_variance_score<\/h2>\n# \u89e3\u91ca\u65b9\u5dee\u793a\u4f8b\nfrom sklearn.linear_model import LinearRegression\nfrom sklearn.metrics import explained_variance_score\n\nboston = datasets.load_boston()\nX = boston.data\ny = boston.target\n\nlr = LinearRegression()\nlr.fit(X, y)\nlr_predict = lr.predict(X)\n\nex_var = explained_variance_score(y, lr_predict)\nprint('\u89e3\u91ca\u65b9\u5dee:{:.2f}'.format(ex_var))<\/code><\/pre>\n\u89e3\u91ca\u65b9\u5dee:0.74<\/code><\/pre>\n1.3 \u6d4b\u8bd5\u5206\u7c7b\u6a21\u578b<\/h1>\n
\u56de\u5f52\u6a21\u578b\u5e38\u7528\u7684metrics\u8bc4\u4f30\u6307\u6807\u6709\uff1aaccuracy_socre\u3001precision_score\u3001recall_score\u3001f1_score\u7b49<\/p>\n
* accuracy_score(y_true,y_pre): \u7cbe\u5ea6 \n* auc(x, y, reorder=False): ROC\u66f2\u7ebf\u4e0b\u7684\u9762\u79ef;\u8f83\u5927\u7684AUC\u4ee3\u8868\u4e86\u8f83\u597d\u7684performance\u3002\n* average_precision_score(y_true, y_score, average='macro', sample_weight=None):\u6839\u636e\u9884\u6d4b\u5f97\u5206\u8ba1\u7b97\u5e73\u5747\u7cbe\u5ea6(AP)\n* brier_score_loss(y_true, y_prob, sample_weight=None, pos_label=None):\u8d8a\u5c0f\u7684brier_score\uff0c\u6a21\u578b\u6548\u679c\u8d8a\u597d\n* confusion_matrix(y_true, y_pred, labels=None, sample_weight=None):\u901a\u8fc7\u8ba1\u7b97\u6df7\u6dc6\u77e9\u9635\u6765\u8bc4\u4f30\u5206\u7c7b\u7684\u51c6\u786e\u6027 \u8fd4\u56de\u6df7\u6dc6\u77e9\u9635\n* f1_score(y_true, y_pred, labels=None, pos_label=1, average='binary', sample_weight=None): F1\u503c\n* log_loss(y_true, y_pred, eps=1e-15, normalize=True, sample_weight=None, labels=None)\uff1a\u5bf9\u6570\u635f\u8017\uff0c\u53c8\u79f0\u903b\u8f91\u635f\u8017\u6216\u4ea4\u53c9\u71b5\u635f\u8017\n* precision_score(y_true, y_pred, labels=None, pos_label=1, average='binary',)\uff1a\u67e5\u51c6\u7387\u6216\u8005\u7cbe\u5ea6\uff1b precision(\u67e5\u51c6\u7387)=TP\/(TP+FP)\n* recall_score(y_true, y_pred, labels=None, pos_label=1, average='binary', sample_weight=None)\uff1a\u67e5\u5168\u7387 \uff1brecall(\u67e5\u5168\u7387)=TP\/(TP+FN)\n* roc_auc_score(y_true, y_score, average='macro', sample_weight=None)\uff1a\u8ba1\u7b97ROC\u66f2\u7ebf\u4e0b\u7684\u9762\u79ef\u5c31\u662fAUC\u7684\u503c\uff0cthe larger the better\n* roc_curve(y_true, y_score, pos_label=None, sample_weight=None, drop_intermediate=True)\uff1b\u8ba1\u7b97ROC\u66f2\u7ebf\u7684\u6a2a\u7eb5\u5750\u6807\u503c\uff0cTPR\uff0cFPR<\/code><\/pre>\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
\n- TP\u2014\u2014\u5c06\u6b63\u7c7b\u9884\u6d4b\u4e3a\u6b63\u7c7b\u6570<\/li>\n
- FP\u2014\u2014\u5c06\u8d1f\u7c7b\u9884\u6d4b\u4e3a\u6b63\u7c7b\u6570<\/li>\n
- TN\u2014\u2014\u5c06\u8d1f\u7c7b\u9884\u6d4b\u4e3a\u8d1f\u7c7b\u6570<\/li>\n
- FN\u2014\u2014\u5c06\u6b63\u7c7b\u9884\u6d4b\u4e3a\u8d1f\u7c7b\u6570<\/li>\n<\/ul>\n
\n\n\n\u8bef\u5dee\u77e9\u9635<\/th>\n –<\/th>\n –<\/th>\n –<\/th>\n<\/tr>\n<\/thead>\n \n\n–<\/td>\n –<\/td>\n \u771f\u5b9e\u503c<\/td>\n \u771f\u5b9e\u503c<\/td>\n<\/tr>\n \n–<\/td>\n –<\/td>\n 1<\/td>\n 0<\/td>\n<\/tr>\n \n\u9884\u6d4b\u503c<\/td>\n 1<\/td>\n True Positive(TP)<\/td>\n False Positive(FP)<\/td>\n<\/tr>\n \n\u9884\u6d4b\u503c<\/td>\n 0<\/td>\n True Negative(TN)<\/td>\n False Negative(FN)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n1.3.1 \u51c6\u786e\u5ea6<\/h2>\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>\n1.3.2 \u67e5\u51c6\u7387<\/h2>\n
\u67e5\u51c6\u7387\uff08precision_score\uff09\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>\n1.3.3 \u67e5\u5168\u7387<\/h2>\n
\u67e5\u5168\u7387\uff08recall_score\u7b49\uff09\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>\n1.3.4 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\uff08f1_score\u7b49\uff09\u5b9a\u4e49\u4e3a
\n$$
\nF_1 = {\\frac{2P<\/em>R}{P+R}} = {\\frac{2TP}{2TP+FP+FN}} = {\\frac{2<\/em>TP}{\u6837\u4f8b\u603b\u6570+TP-TN}}
\n$$<\/p>\n $F\\beta$\u5b9a\u4e49\u4e3a\uff1a
\n$$
\nF<\/em>\\beta = {\\frac{(1+\\beta^2)P<\/em>R}{\\beta^2*P+R}}
\n$$<\/p>\n $F_\\beta$\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- \u5f53$\\beta<1$\u65f6\uff0c$P$\u7684\u6743\u91cd\u51cf\u5c0f\uff0c\u5373$R$\u67e5\u51c6\u7387\u66f4\u91cd\u8981<\/li>\n
- \u5f53$\\beta=1$\u65f6\uff0c$F_\\beta = F_1$<\/li>\n
- \u5f53$\\beta>1$\u65f6\uff0c$P$\u7684\u6743\u91cd\u589e\u5927\uff0c\u5373$P$\u67e5\u5168\u7387\u66f4\u91cd\u8981<\/li>\n<\/ol>\n
<\/p>
<\/div>\u67e5\u770b\u66f4\u591a<\/h2>\u8054\u7cfb\u7ba1\u7406\u5458\u5fae\u4fe1tutu19192010\uff0c\u6ce8\u518c\u8d26\u53f7<\/p>\n<\/div>
<\/div>