sklearn.metrics
.d2_pinball_score¶
- sklearn.metrics.d2_pinball_score(y_true, y_pred, *, sample_weight=None, alpha=0.5, multioutput='uniform_average')[source]¶
\(D^2\) regression score function, fraction of pinball loss explained.
Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A model that always uses the empirical alpha-quantile of
y_true
as constant prediction, disregarding the input features, gets a \(D^2\) score of 0.0.Read more in the User Guide.
New in version 1.1.
- 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.
- alphafloat, default=0.5
Slope of the pinball deviance. It determines the quantile level alpha for which the pinball deviance and also D2 are optimal. The default
alpha=0.5
is equivalent tod2_absolute_error_score
.- multioutput{‘raw_values’, ‘uniform_average’} or array-like of shape (n_outputs,), default=’uniform_average’
Defines aggregating of multiple output values. Array-like value defines weights used to average scores.
- ‘raw_values’ :
Returns a full set of errors in case of multioutput input.
- ‘uniform_average’ :
Scores of all outputs are averaged with uniform weight.
- Returns:
- scorefloat or ndarray of floats
The \(D^2\) score with a pinball deviance or ndarray of scores if
multioutput='raw_values'
.
Notes
Like \(R^2\), \(D^2\) score may be negative (it need not actually be the square of a quantity D).
This metric is not well-defined for a single point and will return a NaN value if n_samples is less than two.
References
[1][2]Eq. (3.11) of Hastie, Trevor J., Robert Tibshirani and Martin J. Wainwright. “Statistical Learning with Sparsity: The Lasso and Generalizations.” (2015). https://hastie.su.domains/StatLearnSparsity/
Examples
>>> from sklearn.metrics import d2_pinball_score >>> y_true = [1, 2, 3] >>> y_pred = [1, 3, 3] >>> d2_pinball_score(y_true, y_pred) 0.5 >>> d2_pinball_score(y_true, y_pred, alpha=0.9) 0.772... >>> d2_pinball_score(y_true, y_pred, alpha=0.1) -1.045... >>> d2_pinball_score(y_true, y_true, alpha=0.1) 1.0