`sklearn.metrics`.r2_score¶

sklearn.metrics.r2_score(y_true, y_pred, *, sample_weight=None, multioutput='uniform_average', force_finite=True)[source]¶

\(R^2\) (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.

y_predarray-like of shape (n_samples,) or (n_samples, n_outputs)

Estimated target values.

sample_weightarray-like of shape (n_samples,), default=None

Sample 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=True

Flag 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 floats: The \(R^2\) 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

[1]

Wikipedia entry on the Coefficient of determination

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

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