sklearn 中的 r2_score

$R^2$不止一种定义方式，这里是scikit-learn中所使用的定义。

As such variance is dataset dependent, R² may not be meaningfully comparable across different datasets. Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R² score of 0.0.

As such variance is dataset dependent, R² may not be meaningfully comparable across different datasets. Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R² score of 0.0.

$$R^2(y,\hat{y})=1-\frac{{\sum }_{i=1}^n(y_i-{\hat{y}}_i{)}^2}{{\sum }_{i=1}^n(y_i-\bar{y}{)}^2}$$

$$\bar{y}=\frac{1}{n}\sum _{i=1}^n{y}_i$$

$$\sum _{i=1}^n(y_i-{\hat{y}}_i{)}^2=\sum _{i=1}^n{ϵ}_i^2$$

from sklearn.metrics import r2_score
y_true = [3, -0.5, 2, 7]
y_pred = [2.5, 0.0, 2, 8]
r2_score(y_true, y_pred)

y_true = [[0.5, 1], [-1, 1], [7, -6]]
y_pred = [[0, 2], [-1, 2], [8, -5]]
r2_score(y_true, y_pred, multioutput='variance_weighted')

y_true = [[0.5, 1], [-1, 1], [7, -6]]
y_pred = [[0, 2], [-1, 2], [8, -5]]
r2_score(y_true, y_pred, multioutput='uniform_average')

r2_score(y_true, y_pred, multioutput='raw_values')

r2_score(y_true, y_pred, multioutput=[0.3, 0.7])