DOC Mention factor x2 between MAE and mean pinball loss (scikit-learn…

…#23651)

doc/modules/model_evaluation.rst

@@ -2562,7 +2562,7 @@ performance of `quantile regression
 
  \text{pinball}(y, \hat{y}) = \frac{1}{n_{\text{samples}}} \sum_{i=0}^{n_{\text{samples}}-1} \alpha \max(y_i - \hat{y}_i, 0) + (1 - \alpha) \max(\hat{y}_i - y_i, 0)
 
-The pinball loss is equivalent to :func:`mean_absolute_error` when the quantile
+The value of pinball loss is equivalent to half of :func:`mean_absolute_error` when the quantile
 parameter ``alpha`` is set to 0.5.
 
 

sklearn/metrics/tests/test_regression.py

@@ -613,3 +613,15 @@ def test_dummy_quantile_parameter_tuning():
  ).fit(X, y)
 
  assert grid_search.best_params_["quantile"] == pytest.approx(alpha)
+
+
+def test_pinball_loss_relation_with_mae():
+ # Test that mean_pinball loss with alpha=0.5 if half of mean absolute error
+ rng = np.random.RandomState(714)
+ n = 100
+ y_true = rng.normal(size=n)
+ y_pred = y_true.copy() + rng.uniform(n)
+ assert (
+ mean_absolute_error(y_true, y_pred)
+ == mean_pinball_loss(y_true, y_pred, alpha=0.5) * 2
+ )