\[R^2\] [coefficient of determination] regression score function.
Best possible score is 1.0 and it can be negative [because the model can be arbitrarily worse]. In the general case when the true y is non-constant, a constant model that always predicts the average y disregarding the input features would get a \[R^2\] score of 0.0.
In the particular case when y_true
is constant, the \[R^2\] score is not finite: it is either NaN
[perfect predictions] or -Inf
[imperfect
predictions]. To prevent such non-finite numbers to pollute higher-level experiments such as a grid search cross-validation, by default these cases are replaced with 1.0 [perfect predictions] or 0.0 [imperfect predictions] respectively. You can set force_finite
to False
to prevent this fix from happening.
Note: when the prediction residuals have zero mean, the \[R^2\] score is identical to the
Explained Variance score
.
Read more in the User Guide.
Parameters:y_truearray-like of shape [n_samples,] or [n_samples, n_outputs]Ground truth [correct] target values.
Estimated target values.
sample_weightarray-like of shape [n_samples,], default=NoneSample weights.
multioutput{‘raw_values’, ‘uniform_average’, ‘variance_weighted’}, array-like of shape [n_outputs,] or None, default=’uniform_average’Defines aggregating of multiple output scores. Array-like value defines weights used to average scores. Default is “uniform_average”.
‘raw_values’ :Returns a full set of scores in case of multioutput input.
‘uniform_average’ :Scores of all outputs are averaged with uniform weight.
‘variance_weighted’ :Scores of all outputs are averaged, weighted by the variances of each individual output.
Changed in version 0.19: Default value of multioutput is ‘uniform_average’.
force_finitebool, default=TrueFlag indicating if NaN
and -Inf
scores resulting from constant data should be replaced with real numbers [1.0
if prediction is perfect, 0.0
otherwise]. Default is True
, a convenient setting for hyperparameters’ search procedures [e.g. grid search cross-validation].
New in version 1.1.
Returns:zfloat or ndarray of floatsThe \[R^2\] score or ndarray of scores if ‘multioutput’ is ‘raw_values’.
Notes
This is not a symmetric function.
Unlike most other scores, \[R^2\] score may be negative [it need not actually be the square of a quantity R].
This metric is not well-defined for single samples and will return a NaN value if n_samples is less than two.
References
Examples
>>> 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] 0.948... >>> 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'] 0.938... >>> y_true = [1, 2, 3] >>> y_pred = [1, 2, 3] >>> r2_score[y_true, y_pred] 1.0 >>> y_true = [1, 2, 3] >>> y_pred = [2, 2, 2] >>> r2_score[y_true, y_pred] 0.0 >>> y_true = [1, 2, 3] >>> y_pred = [3, 2, 1] >>> r2_score[y_true, y_pred] -3.0 >>> y_true = [-2, -2, -2] >>> y_pred = [-2, -2, -2] >>> r2_score[y_true, y_pred] 1.0 >>> r2_score[y_true, y_pred, force_finite=False] nan >>> y_true = [-2, -2, -2] >>> y_pred = [-2, -2, -2 + 1e-8] >>> r2_score[y_true, y_pred] 0.0 >>> r2_score[y_true, y_pred, force_finite=False] -inf