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分类、聚类与回归的评价指标

article 2025/1/7 17:09:28

在cross_validate或cross_val_score中，参数scoring，与分类、聚类和回归算法的评价指标有关。

3.4.3. The scoring parameter: defining model evaluation rules

For the most common use cases, you can designate a scorer object with the scoring parameter via a string name; the table below shows all possible values. All scorer objects follow the convention that higher return values are better than lower return values. Thus metrics which measure the distance between the model and the data, like metrics.mean_squared_error, are available as ‘neg_mean_squared_error’ which return the negated value of the metric
对于最常见的用例，您可以通过字符串名称使用 scoring 参数指定一个评分对象；下表显示了所有可能的值。所有评分对象都遵循这样的约定：返回值越高越好。因此，像 metrics.mean_squared_error 这样衡量模型与数据之间距离的指标，会以 ‘neg_mean_squared_error’ 的形式提供，返回该指标的负值。

1、分类

字符串	函数	公式
`accuracy`	metrics.accuracy_score	$accuracy(y,\hat{y}) = \frac{1}{n}\sum\limits_{i=0}^{n-1}1(\hat{y}_i=y_i)$
`balanced_accuracy`	metrics.balanced_accuracy_score	$balanced-accuracy=\frac{1}{2}(\frac{TP}{TP+FN}+\frac{TN}{TN+FP})$
`top_k_accuracy`	metrics.top_k_accuracy_score	$top-k\ \ accuracy(y,\hat{y}) = \frac{1}{n}\sum\limits_{i=0}^{n-1}\sum\limits_{j=1}^{k}1(\hat{f}_{i,j}=y_i)$
`average_precision`	metrics.average_precision_score	$\sum_{n}(R_n-R_{n-1})P_n$
`neg_brier_score`	metrics.brier_score_loss	$\frac{1}{n}\sum\limits_{i=0}^{n-1}(y_i-p_i)^2=\frac{1}{n}\sum\limits_{i=0}^{n-1}(y_i-predict\_{proba}(y=1))^2$
`f1`	metrics.f1_score	$F1=\frac{2\times TP}{2\times TP+FP+FN}$ (average{‘micro’, ‘macro’, ‘samples’, ‘weighted’} or None, default=’macro’)
`neg_log_loss`	metrics.log_loss	$L_{log}(y,p)=-logPr(y\|p)=-(ylog(p)+(1-y)log(1-p))$ $L_{log}(Y,P)=-logPr(Y\|P)=-\frac{1}{N}\sum\limits_{i=0}^{N-1}\sum\limits_{k=0}^{K-1}y_{i,k}logp_{i,k}$
`precision`	metrics.precision_score	$P=\frac{TP}{TP+FP}$
`recall`	metrics.recall_score	$R=\frac{TP}{TP+FN}$
`jaccard`	metrics.jaccard_score	$J(y,\hat{y})=\frac{y\bigcap\hat{y}}{y\bigcup\hat{y}}$
`roc_auc`	metrics.roc_auc_score	Compute Area Under the Receiver Operating Characteristic Curve (ROC AUC) from prediction scores （average{‘micro’, ‘macro’, ‘samples’, ‘weighted’} or None, default=’macro’）
`d2_log_loss_score`	metrics.d2_log_loss_score	$D^2(y,\hat{y})=1-\frac{dev(y,\hat{y})}{dev(y,y_{null})}$

2、聚类

字符串	函数	公式
`mutual_info_score`	metrics.mutual_info_score	$\sum\limits_{i=0}^{\|U\|}\sum\limits_{j=0}^{\|V\|}\frac{U_i\bigcap V_j}{N}log\frac{N\|U_i\bigcap V_j\|}{\mid U_i\mid\mid V_j \mid}$
`adjusted_mutual_info_score`	metrics.adjusted_mutual_info_score	$\frac{MI(U,V)-E(MI(U,V))}{avg(H(U),H(V))-E(MI(U,V))}$
`normalized_mutual_info_score`	metrics.normalized_mutual_info_score	$\frac{2\times I(U;V)}{H(U)+H(V)}$
`rand_score`	metrics.rand_score	$\frac{a+b}{C_n^2}$ a表示在实际和聚类结果中都是同类别的样本点对数 b表示实际和聚类结果中都不是同类别的样本点对数
`adjusted_rand_score`	metrics.adjusted_rand_score	$\frac{RI-E(RI)}{max(RI)-E(RI)}$
`completeness_score`	metrics.completeness_score	$\frac{H(K\|C)}{H(K)}$
`homogeneity_score`	metrics.homogeneity_score	$\frac{H(C\|K)}{H(C)}$
`v_measure_score`	metrics.v_measure_score	$v=\frac{(1+\beta)\times homogeneity\times completeness}{\beta\times homogeneity+completeness}$
`fowlkes_mallows_score`	metrics.fowlkes_mallows_score	$FMI=\frac{TP}{\sqrt{(TP+FP)\times(TP+FN)} }$

3、回归

字符串	函数	公式
`explained_variance`	metrics.explained_variance_score	$explained\_variance(y,\hat{y})=1-\frac {Var\{y-\hat{y}\}}{Var\{y\}}$
`neg_max_error`	metrics.max_error	$MaxError(y,\hat{y})=max(\mid y_i-\hat{y_i}\mid)$
`neg_mean_absolute_error`	metrics.mean_absolute_error	$MAE(y,\hat{y})=\frac{1}{n}\sum\limits_{i=0}^{n-1}\mid y_i-\hat{y_i}\mid$
`neg_mean_squared_error`	metrics.mean_squared_error	$MSE(y,\hat{y})=\frac{1}{n}\sum\limits_{i=0}^{n-1}( y_i-\hat{y_i})^2$
`neg_root_mean_squared_error`	metrics.root_mean_squared_error	$RMSE(y,\hat{y})=\sqrt{\frac{1}{n}\sum\limits_{i=0}^{n-1}( y_i-\hat{y_i})^2}$
`neg_root_mean_squared_log_error`	metrics.root_mean_squared_log_error	$MSLE(y,\hat{y})=\frac{1}{n}\sum\limits_{i=0}^{n-1}( log_e(1+y_i)-log_e(1+\hat y_i))^2$
`neg_median_absolute_error`	metrics.median_absolute_error	$MadAE(y,\hat{y})=median(\mid y_1-\hat y_1\mid,...,\mid y_n-\hat y_n\mid)$
`r2`	metrics.r2_score	$R^2(y,\hat{y})=1-\frac{\sum\limits_{i=1}^{n}(y_i-\hat y_i)^2}{\sum\limits_{i=1}^{n}(y_i-\overline y_i)^2}$
`neg_mean_poisson_deviance` `neg_mean_gamma_deviance`	metrics.mean_poisson_deviance metrics.mean_gamma_deviance	$D(y,\hat{y})=\frac{1}{n}\sum\limits_{i=0}^{n-1}\begin{cases}( y_i-\hat{y_i})^2,& \text{for p=0(Normal)}\\2(y_ilog(y_i/\hat y_i)+\hat y_i-y_i),& \text{for p=1(Poisson)}\\2(log(\hat y_i/y_i)+y_i/\hat y_i-1),& \text{for p=2(Gamma)}\\2(\frac{max(y_i,0)^{2-p}}{(1-p)(2-p)}-\frac{y_i\hat y_i^{1-p}}{1-p}+\frac{\hat y_i^{2-p}}{2-p}),& \text{for p=2(otherwise)}\end{cases}$
`neg_mean_absolute_percentage_error`	metrics.mean_absolute_percentage_error	$MAPE(y,\hat{y})=\frac{1}{n}\sum\limits_{i=0}^{n-1}\frac{\mid y_i-\hat y_i\mid}{max(\epsilon,\mid y_i\mid)}$
`d2_absolute_error_score`	metrics.d2_absolute_error_score	$D^2(y,\hat{y})=1-\frac{\sum\limits_{i=1}^{n}\mid y_i-\hat y_i\mid}{\sum\limits_{i=1}^{n}\mid y_i-\overline y_i\mid}$