text: import pytest
  import numpy as np
  
  from numpy.testing import assert_allclose
  
  from sklearn.compose import ColumnTransformer
  from sklearn.datasets import load_diabetes
  from sklearn.datasets import load_iris
  from sklearn.datasets import make_classification
  from sklearn.datasets import make_regression
  from sklearn.dummy import DummyClassifier
  from sklearn.ensemble import RandomForestRegressor
  from sklearn.ensemble import RandomForestClassifier
  from sklearn.linear_model import LinearRegression
  from sklearn.linear_model import LogisticRegression
  from sklearn.impute import SimpleImputer
  from sklearn.inspection import permutation_importance
  from sklearn.model_selection import train_test_split
  from sklearn.pipeline import make_pipeline
  from sklearn.preprocessing import KBinsDiscretizer
  from sklearn.preprocessing import OneHotEncoder
  from sklearn.preprocessing import StandardScaler
  from sklearn.preprocessing import scale
  from sklearn.utils import parallel_backend
  from sklearn.utils._testing import _convert_container
  
  
  
  @pytest.mark.parametrize("n_jobs", [1, 2])
  def test_permutation_importance_correlated_feature_regression(n_jobs):
      # Make sure that feature highly correlated to the target have a higher
      # importance
      rng = np.random.RandomState(42)
      n_repeats = 5
  
      X, y = load_diabetes(return_X_y=True)
      y_with_little_noise = (
          y + rng.normal(scale=0.001, size=y.shape[0])).reshape(-1, 1)
  
      X = np.hstack([X, y_with_little_noise])
  
      clf = RandomForestRegressor(n_estimators=10, random_state=42)
      clf.fit(X, y)
  
      result = permutation_importance(clf, X, y, n_repeats=n_repeats,
                                      random_state=rng, n_jobs=n_jobs)
  
      assert result.importances.shape == (X.shape[1], n_repeats)
  
      # the correlated feature with y was added as the last column and should
      # have the highest importance
      assert np.all(result.importances_mean[-1] >
                    result.importances_mean[:-1])
  
  
  @pytest.mark.parametrize("n_jobs", [1, 2])
  def test_permutation_importance_correlated_feature_regression_pandas(n_jobs):
      pd = pytest.importorskip("pandas")
  
      # Make sure that feature highly correlated to the target have a higher
      # importance
      rng = np.random.RandomState(42)
      n_repeats = 5
  
      dataset = load_iris()
      X, y = dataset.data, dataset.target
      y_with_little_noise = (
          y + rng.normal(scale=0.001, size=y.shape[0])).reshape(-1, 1)
  
      # Adds feature correlated with y as the last column
      X = pd.DataFrame(X, columns=dataset.feature_names)
      X['correlated_feature'] = y_with_little_noise
  
      clf = RandomForestClassifier(n_estimators=10, random_state=42)
      clf.fit(X, y)
  
      result = permutation_importance(clf, X, y, n_repeats=n_repeats,
                                      random_state=rng, n_jobs=n_jobs)
  
      assert result.importances.shape == (X.shape[1], n_repeats)
  
      # the correlated feature with y was added as the last column and should
      # have the highest importance
      assert np.all(result.importances_mean[-1] > result.importances_mean[:-1])
  
  
  @pytest.mark.parametrize("n_jobs", [1, 2])
  def test_robustness_to_high_cardinality_noisy_feature(n_jobs, seed=42):
      # Permutation variable importance should not be affected by the high
      # cardinality bias of traditional feature importances, especially when
      # computed on a held-out test set:
      rng = np.random.RandomState(seed)
      n_repeats = 5
      n_samples = 1000
      n_classes = 5
      n_informative_features = 2
      n_noise_features = 1
      n_features = n_informative_features + n_noise_features
  
      # Generate a multiclass classification dataset and a set of informative
      # binary features that can be used to predict some classes of y exactly
      # while leaving some classes unexplained to make the problem harder.
      classes = np.arange(n_classes)
      y = rng.choice(classes, size=n_samples)
      X = np.hstack([(y == c).reshape(-1, 1)
                     for c in classes[:n_informative_features]])
      X = X.astype(np.float32)
  
      # Not all target classes are explained by the binary class indicator
      # features:
      assert n_informative_features < n_classes
  
      # Add 10 other noisy features with high cardinality (numerical) values
      # that can be used to overfit the training data.
      X = np.concatenate([X, rng.randn(n_samples, n_noise_features)], axis=1)
      assert X.shape == (n_samples, n_features)
  
      # Split the dataset to be able to evaluate on a held-out test set. The
      # Test size should be large enough for importance measurements to be
      # stable:
      X_train, X_test, y_train, y_test = train_test_split(
          X, y, test_size=0.5, random_state=rng)
      clf = RandomForestClassifier(n_estimators=5, random_state=rng)
      clf.fit(X_train, y_train)
  
      # Variable importances computed by impurity decrease on the tree node
      # splits often use the noisy features in splits. This can give misleading
      # impression that high cardinality noisy variables are the most important:
      tree_importances = clf.feature_importances_
      informative_tree_importances = tree_importances[:n_informative_features]
      noisy_tree_importances = tree_importances[n_informative_features:]
      assert informative_tree_importances.max() < noisy_tree_importances.min()
  
      # Let's check that permutation-based feature importances do not have this
      # problem.
      r = permutation_importance(clf, X_test, y_test, n_repeats=n_repeats,
                                 random_state=rng, n_jobs=n_jobs)
  
      assert r.importances.shape == (X.shape[1], n_repeats)
  
      # Split the importances between informative and noisy features
      informative_importances = r.importances_mean[:n_informative_features]
      noisy_importances = r.importances_mean[n_informative_features:]
  
      # Because we do not have a binary variable explaining each target classes,
      # the RF model will have to use the random variable to make some
      # (overfitting) splits (as max_depth is not set). Therefore the noisy
      # variables will be non-zero but with small values oscillating around
      # zero:
      assert max(np.abs(noisy_importances)) > 1e-7
      assert noisy_importances.max() < 0.05
  
      # The binary features correlated with y should have a higher importance
      # than the high cardinality noisy features.
      # The maximum test accuracy is 2 / 5 == 0.4, each informative feature
      # contributing approximately a bit more than 0.2 of accuracy.
      assert informative_importances.min() > 0.15
  
  
  def test_permutation_importance_mixed_types():
      rng = np.random.RandomState(42)
      n_repeats = 4
  
      # Last column is correlated with y
      X = np.array([[1.0, 2.0, 3.0, np.nan], [2, 1, 2, 1]]).T
      y = np.array([0, 1, 0, 1])
  
      clf = make_pipeline(SimpleImputer(), LogisticRegression(solver='lbfgs'))
      clf.fit(X, y)
      result = permutation_importance(clf, X, y, n_repeats=n_repeats,
                                      random_state=rng)
  
      assert result.importances.shape == (X.shape[1], n_repeats)
  
      # the correlated feature with y is the last column and should
      # have the highest importance
      assert np.all(result.importances_mean[-1] > result.importances_mean[:-1])
  
      # use another random state
      rng = np.random.RandomState(0)
      result2 = permutation_importance(clf, X, y, n_repeats=n_repeats,
                                       random_state=rng)
      assert result2.importances.shape == (X.shape[1], n_repeats)
  
      assert not np.allclose(result.importances, result2.importances)
  
      # the correlated feature with y is the last column and should
      # have the highest importance
      assert np.all(result2.importances_mean[-1] > result2.importances_mean[:-1])
  
  
  def test_permutation_importance_mixed_types_pandas():
      pd = pytest.importorskip("pandas")
      rng = np.random.RandomState(42)
      n_repeats = 5
  
      # Last column is correlated with y
      X = pd.DataFrame({'col1': [1.0, 2.0, 3.0, np.nan],
                        'col2': ['a', 'b', 'a', 'b']})
      y = np.array([0, 1, 0, 1])
  
      num_preprocess = make_pipeline(SimpleImputer(), StandardScaler())
      preprocess = ColumnTransformer([
          ('num', num_preprocess, ['col1']),
          ('cat', OneHotEncoder(), ['col2'])
      ])
      clf = make_pipeline(preprocess, LogisticRegression(solver='lbfgs'))
      clf.fit(X, y)
  
      result = permutation_importance(clf, X, y, n_repeats=n_repeats,
                                      random_state=rng)
  
      assert result.importances.shape == (X.shape[1], n_repeats)
      # the correlated feature with y is the last column and should
      # have the highest importance
      assert np.all(result.importances_mean[-1] > result.importances_mean[:-1])
  
  
  def test_permutation_importance_linear_regresssion():
      X, y = make_regression(n_samples=500, n_features=10, random_state=0)
  
      X = scale(X)
      y = scale(y)
  
      lr = LinearRegression().fit(X, y)
  
      # this relationship can be computed in closed form
      expected_importances = 2 * lr.coef_**2
      results = permutation_importance(lr, X, y,
                                       n_repeats=50,
                                       scoring='neg_mean_squared_error')
      assert_allclose(expected_importances, results.importances_mean,
                      rtol=1e-1, atol=1e-6)
  
  
  def test_permutation_importance_equivalence_sequential_parallel():
      # regression test to make sure that sequential and parallel calls will
      # output the same results.
      X, y = make_regression(n_samples=500, n_features=10, random_state=0)
      lr = LinearRegression().fit(X, y)
  
      importance_sequential = permutation_importance(
          lr, X, y, n_repeats=5, random_state=0, n_jobs=1
      )
  
      # First check that the problem is structured enough and that the model is
      # complex enough to not yield trivial, constant importances:
      imp_min = importance_sequential['importances'].min()
      imp_max = importance_sequential['importances'].max()
      assert imp_max - imp_min > 0.3
  
      # The actually check that parallelism does not impact the results
      # either with shared memory (threading) or without isolated memory
      # via process-based parallelism using the default backend
      # ('loky' or 'multiprocessing') depending on the joblib version:
  
      # process-based parallelism (by default):
      importance_processes = permutation_importance(
          lr, X, y, n_repeats=5, random_state=0, n_jobs=2)
      assert_allclose(
          importance_processes['importances'],
          importance_sequential['importances']
      )
  
      # thread-based parallelism:
      with parallel_backend("threading"):
          importance_threading = permutation_importance(
              lr, X, y, n_repeats=5, random_state=0, n_jobs=2
          )
      assert_allclose(
          importance_threading['importances'],
          importance_sequential['importances']
      )
  
  
  @pytest.mark.parametrize("n_jobs", [None, 1, 2])
  def test_permutation_importance_equivalence_array_dataframe(n_jobs):
      # This test checks that the column shuffling logic has the same behavior
      # both a dataframe and a simple numpy array.
      pd = pytest.importorskip('pandas')
  
      # regression test to make sure that sequential and parallel calls will
      # output the same results.
      X, y = make_regression(n_samples=100, n_features=5, random_state=0)
      X_df = pd.DataFrame(X)
  
      # Add a categorical feature that is statistically linked to y:
      binner = KBinsDiscretizer(n_bins=3, encode="ordinal")
      cat_column = binner.fit_transform(y.reshape(-1, 1))
  
      # Concatenate the extra column to the numpy array: integers will be
      # cast to float values
      X = np.hstack([X, cat_column])
      assert X.dtype.kind == "f"
  
      # Insert extra column as a non-numpy-native dtype (while keeping backward
      # compat for old pandas versions):
      if hasattr(pd, "Categorical"):
          cat_column = pd.Categorical(cat_column.ravel())
      else:
          cat_column = cat_column.ravel()
      new_col_idx = len(X_df.columns)
      X_df[new_col_idx] = cat_column
      assert X_df[new_col_idx].dtype == cat_column.dtype
  
      # Stich an aribtrary index to the dataframe:
      X_df.index = np.arange(len(X_df)).astype(str)
  
      rf = RandomForestRegressor(n_estimators=5, max_depth=3, random_state=0)
      rf.fit(X, y)
  
      n_repeats = 3
      importance_array = permutation_importance(
          rf, X, y, n_repeats=n_repeats, random_state=0, n_jobs=n_jobs
      )
  
      # First check that the problem is structured enough and that the model is
      # complex enough to not yield trivial, constant importances:
      imp_min = importance_array['importances'].min()
      imp_max = importance_array['importances'].max()
      assert imp_max - imp_min > 0.3
  
      # Now check that importances computed on dataframe matche the values
      # of those computed on the array with the same data.
      importance_dataframe = permutation_importance(
          rf, X_df, y, n_repeats=n_repeats, random_state=0, n_jobs=n_jobs
      )
      assert_allclose(
          importance_array['importances'],
          importance_dataframe['importances']
      )
  
  
  @pytest.mark.parametrize("input_type", ["array", "dataframe"])
  def test_permutation_importance_large_memmaped_data(input_type):
      # Smoke, non-regression test for:
      # https://github.com/scikit-learn/scikit-learn/issues/15810
      n_samples, n_features = int(5e4), 4
      X, y = make_classification(n_samples=n_samples, n_features=n_features,
                                 random_state=0)
      assert X.nbytes > 1e6  # trigger joblib memmaping
  
      X = _convert_container(X, input_type)
      clf = DummyClassifier(strategy='prior').fit(X, y)
  
      # Actual smoke test: should not raise any error:
      n_repeats = 5
      r = permutation_importance(clf, X, y, n_repeats=n_repeats, n_jobs=2)
  
      # Auxiliary check: DummyClassifier is feature independent:
      # permutating feature should not change the predictions
      expected_importances = np.zeros((n_features, n_repeats))
      assert_allclose(expected_importances, r.importances)
  
  
  def test_permutation_importance_sample_weight():
      # Creating data with 2 features and 1000 samples, where the target
      # variable is a linear combination of the two features, such that
      # in half of the samples the impact of feature 1 is twice the impact of
      # feature 2, and vice versa on the other half of the samples.
      rng = np.random.RandomState(1)
      n_samples = 1000
      n_features = 2
      n_half_samples = n_samples // 2
      x = rng.normal(0.0, 0.001, (n_samples, n_features))
      y = np.zeros(n_samples)
      y[:n_half_samples] = 2 * x[:n_half_samples, 0] + x[:n_half_samples, 1]
      y[n_half_samples:] = x[n_half_samples:, 0] + 2 * x[n_half_samples:, 1]
  
      # Fitting linear regression with perfect prediction
      lr = LinearRegression(fit_intercept=False)
      lr.fit(x, y)
  
      # When all samples are weighted with the same weights, the ratio of
      # the two features importance should equal to 1 on expectation (when using
      # mean absolutes error as the loss function).
      pi = permutation_importance(lr, x, y, random_state=1,
                                  scoring='neg_mean_absolute_error',
                                  n_repeats=200)
      x1_x2_imp_ratio_w_none = pi.importances_mean[0] / pi.importances_mean[1]
      assert x1_x2_imp_ratio_w_none == pytest.approx(1, 0.01)
  
      # When passing a vector of ones as the sample_weight, results should be
      # the same as in the case that sample_weight=None.
      w = np.ones(n_samples)
      pi = permutation_importance(lr, x, y, random_state=1,
                                  scoring='neg_mean_absolute_error',
                                  n_repeats=200, sample_weight=w)
      x1_x2_imp_ratio_w_ones = pi.importances_mean[0] / pi.importances_mean[1]
      assert x1_x2_imp_ratio_w_ones == pytest.approx(
          x1_x2_imp_ratio_w_none, 0.01)
  
      # When the ratio between the weights of the first half of the samples and
      # the second half of the samples approaches to infinity, the ratio of
      # the two features importance should equal to 2 on expectation (when using
      # mean absolutes error as the loss function).
      w = np.hstack([np.repeat(10.0 ** 10, n_half_samples),
                     np.repeat(1.0, n_half_samples)])
      lr.fit(x, y, w)
      pi = permutation_importance(lr, x, y, random_state=1,
                                  scoring='neg_mean_absolute_error',
                                  n_repeats=200,
                                  sample_weight=w)
      x1_x2_imp_ratio_w = pi.importances_mean[0] / pi.importances_mean[1]
      assert x1_x2_imp_ratio_w / x1_x2_imp_ratio_w_none == pytest.approx(2, 0.01)
  
  
  def test_permutation_importance_no_weights_scoring_function():
      # Creating a scorer function that does not takes sample_weight
      def my_scorer(estimator, X, y):
          return 1
  
      # Creating some data and estimator for the permutation test
      x = np.array([[1, 2], [3, 4]])
      y = np.array([1, 2])
      w = np.array([1, 1])
      lr = LinearRegression()
      lr.fit(x, y)
  
      # test that permutation_importance does not return error when
      # sample_weight is None
      try:
          permutation_importance(lr, x, y, random_state=1,
                                 scoring=my_scorer,
                                 n_repeats=1)
      except TypeError:
          pytest.fail("permutation_test raised an error when using a scorer "
                      "function that does not accept sample_weight even though "
                      "sample_weight was None")
  
      # test that permutation_importance raise exception when sample_weight is
      # not None
      with pytest.raises(TypeError):
          permutation_importance(lr, x, y, random_state=1,
                                 scoring=my_scorer,
                                 n_repeats=1,
                                 sample_weight=w)
  