d2_tweedie_score

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

\(D^2\) 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.

Added in version 1.0.

Parameters:

y_truearray-like of shape (n_samples,)

Ground truth (correct) target values.

y_predarray-like of shape (n_samples,)

Estimated target values.

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

Sample weights.

powerfloat, 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:

zfloat 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