D2 Tweedie Score

d2-tweedie-score

Metric d2_tweedie_score from scikit-learn (sklearn.metrics.d2_tweedie_score)

When to invoke this skill

The user has predictions + ground truth and asks to evaluate with d2_tweedie_score, or mentions sklearn.metrics.d2_tweedie_score directly, or wants the standard scikit-learn implementation.

Reference signature

from sklearn.metrics import d2_tweedie_score

# d2_tweedie_score(y_true, y_pred, *, sample_weight=None, power=0)

Library docstring

:math:`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 :ref:`User Guide <d2_score>`.

.. versionadded:: 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
    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_

Quick recipe

import sklearn.metrics as _m
score = _m.d2_tweedie_score(y_true, y_pred)

Don'ts

• Don't reimplement when the library version handles edge cases (NaN, ties, empty inputs) better than a hand-rolled formula.
• Always check the library version's argument order — sklearn is (y_true, y_pred) while torchmetrics is (preds, target).