code: 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
      )
  
imports: from itertools import product
  import numpy
  import pytest
  from numpy.testing import assert_allclose
  from scipy import optimize
  from scipy.special import factorial, xlogy
  from sklearn.dummy import DummyRegressor
  from sklearn.exceptions import UndefinedMetricWarning
  from sklearn.metrics import d2_absolute_error_score, d2_pinball_score, d2_tweedie_score, explained_variance_score, make_scorer, max_error, mean_absolute_error, mean_absolute_percentage_error, mean_pinball_loss, mean_squared_error, mean_squared_log_error, mean_tweedie_deviance, median_absolute_error, r2_score, root_mean_squared_error, root_mean_squared_log_error
  from sklearn.metrics._regression import _check_reg_targets
  from sklearn.model_selection import GridSearchCV
  from sklearn.utils._testing import assert_almost_equal, assert_array_almost_equal, assert_array_equal
label_desc: Use image node_id 14 for calling a global function with example usage: test_pinball_loss_relation_with_mae() without return types