D2 Pinball Score

d2-pinball-score

Metric d2_pinball_score from scikit-learn (sklearn.metrics.d2_pinball_score)

When to invoke this skill

The user has predictions + ground truth and asks to evaluate with d2_pinball_score, or mentions sklearn.metrics.d2_pinball_score directly, or wants the standard scikit-learn implementation.

Reference signature

from sklearn.metrics import d2_pinball_score

# d2_pinball_score(y_true, y_pred, *, sample_weight=None, alpha=0.5, multioutput='uniform_average')

Library docstring

:math:`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 :math:`D^2` score of 0.0.

Read more in the :ref:`User Guide <d2_score>`.

.. versionadded:: 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 :math:`D^2` score with a pinball deviance
    or ndarray of scores if `multioutput='raw_values'`.

Notes
-----
Like :math:`R^2`, :math:`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.

This metric is not a built-in :ref:`string name scorer
<scoring_string_names>` to use along with tools such as
:class:`~sklearn.model_selection.GridSearchCV` or
:class:`~sklearn.model_selection.RandomizedSearchCV`.
Instead, you can :ref:`create a scorer object <scoring_adapt_metric>` using
:func:`~sklearn.metrics.make_scorer`, with any desired parameter settings.
See the `Examples` section for details.

 References
----------
.. [1] Eq. (7) of `Ko

Quick recipe

import sklearn.metrics as _m
score = _m.d2_pinball_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).