D2 Absolute Error Score

d2-absolute-error-score

Metric d2_absolute_error_score from scikit-learn (sklearn.metrics.d2_absolute_error_score)

When to invoke this skill

The user has predictions + ground truth and asks to evaluate with d2_absolute_error_score, or mentions sklearn.metrics.d2_absolute_error_score directly, or wants the standard scikit-learn implementation.

Reference signature

from sklearn.metrics import d2_absolute_error_score

# d2_absolute_error_score(y_true, y_pred, *, sample_weight=None, multioutput='uniform_average')

Library docstring

:math:`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 :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.

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 an absolute error deviance
    or ndarray of scores if 'multioutput' is '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 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 

Quick recipe

import sklearn.metrics as _m
score = _m.d2_absolute_error_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).