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# `sklearn.metrics`.d2_pinball_score

sklearn.metrics.d2_pinball_score(y_true, y_pred, *, sample_weight=None, alpha=0.5, multioutput='uniform_average')

  \(D^2\) 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_true array-like of shape (n_samples,) or (n_samples, n_outputs)

      Ground truth (correct) target values.

    y_pred array-like of shape (n_samples,) or (n_samples, n_outputs)

      Estimated target values.

    sample_weight array-like of shape (n_samples,), default=None

      Sample weights.

    alpha float, 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 to `d2_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:
    score float 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]

  Eq. (7) of Koenker, Roger; Machado, José A. F. (1999). “Goodness of Fit and Related Inference Processes for Quantile Regression”

  [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