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# `sklearn.metrics`.d2_absolute_error_score

sklearn.metrics.d2_absolute_error_score(y_true, y_pred, *, sample_weight=None, multioutput='uniform_average')

  \(D^2\) regression score function, fraction of absolute error 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 median 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.

    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 an absolute error deviance or ndarray of scores if ‘multioutput’ is ‘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 single samples and will return a NaN value if n_samples is less than two.

  References

  [1]

  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_absolute_error_score
      >>> y_true = [3, -0.5, 2, 7]
      >>> y_pred = [2.5, 0.0, 2, 8]
      >>> d2_absolute_error_score(y_true, y_pred)
      0.764...
      >>> y_true = [[0.5, 1], [-1, 1], [7, -6]]
      >>> y_pred = [[0, 2], [-1, 2], [8, -5]]
      >>> d2_absolute_error_score(y_true, y_pred, multioutput='uniform_average')
      0.691...
      >>> d2_absolute_error_score(y_true, y_pred, multioutput='raw_values')
      array([0.8125    , 0.57142857])
      >>> y_true = [1, 2, 3]
      >>> y_pred = [1, 2, 3]
      >>> d2_absolute_error_score(y_true, y_pred)
      1.0
      >>> y_true = [1, 2, 3]
      >>> y_pred = [2, 2, 2]
      >>> d2_absolute_error_score(y_true, y_pred)
      0.0
      >>> y_true = [1, 2, 3]
      >>> y_pred = [3, 2, 1]
      >>> d2_absolute_error_score(y_true, y_pred)
      -1.0