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# `sklearn.metrics`.d2_tweedie_score

sklearn.metrics.d2_tweedie_score(y_true, y_pred, *, sample_weight=None, power=0)

  D^2 regression score function, fraction of Tweedie deviance 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 mean 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 1.0.

  Parameters:
    y_true array-like of shape (n_samples,)

      Ground truth (correct) target values.

    y_pred array-like of shape (n_samples,)

      Estimated target values.

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

      Sample weights.

    power float, default=0

      Tweedie power parameter. Either power <= 0 or power >= 1.

      The higher `p` the less weight is given to extreme deviations between true and predicted targets.

      - power < 0: Extreme stable distribution. Requires: y_pred > 0.

      - power = 0 : Normal distribution, output corresponds to r2_score. y_true and y_pred can be any real numbers.

      - power = 1 : Poisson distribution. Requires: y_true >= 0 and y_pred > 0.

      - 1 < p < 2 : Compound Poisson distribution. Requires: y_true >= 0 and y_pred > 0.

      - power = 2 : Gamma distribution. Requires: y_true > 0 and y_pred > 0.

      - power = 3 : Inverse Gaussian distribution. Requires: y_true > 0 and y_pred > 0.

      - otherwise : Positive stable distribution. Requires: y_true > 0 and y_pred > 0.

  Returns:
    z float or ndarray of floats

      The D^2 score.

  Notes

  This is not a symmetric function.

  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_tweedie_score
      >>> y_true = [0.5, 1, 2.5, 7]
      >>> y_pred = [1, 1, 5, 3.5]
      >>> d2_tweedie_score(y_true, y_pred)
      0.285...
      >>> d2_tweedie_score(y_true, y_pred, power=1)
      0.487...
      >>> d2_tweedie_score(y_true, y_pred, power=2)
      0.630...
      >>> d2_tweedie_score(y_true, y_true, power=2)
      1.0