code: def test_when_using_feature_relevance_distribution_with_entropy_set_function_then_returns_correct_results():
      X = np.random.uniform(0, 1, (3000, 5))
      Y = []
  
      for n in X:
          if n[0] + n[1] > 1:
              Y.append(0)
          else:
              Y.append(1)
  
      Y = np.array(Y).astype(str)
  
      classifier_mdl = create_logistic_regression_classifier()
      classifier_mdl.fit(X, Y)
  
      # H(P(Y)) -- Can be precomputed
      h_p_Y = estimate_entropy_of_probabilities(
          np.mean(
              classifier_mdl.predict_probabilities(X), axis=0
          ).reshape(1, -1)
      )
  
      # -(H(P(Y | do(x_S)) - H(P(Y))) = H(P(Y)) - H(P(Y | do(x_S))
      def my_entropy_feature_attribution_function(
          randomized_predictions: np.ndarray,
          baseline_predictions: np.ndarray,
      ) -> float:
          # H(P(Y | do(x_S)) = H(E[P(Y | x_S, X'_\S)])
  
          # E[P(Y | x_S, X'_\S)]
          p_y_do_xs = np.mean(randomized_predictions, axis=0).reshape(
              1, -1
          )
  
          # H(E[P(Y | x_S, X'_\S)])
          h_p_Y_do_xs = estimate_entropy_of_probabilities(p_y_do_xs)
  
          # Using H(P(Y)) based on the origina data, i.e. ignoring baseline_predictions.
          return h_p_Y - h_p_Y_do_xs
  
      feature_contributions = feature_relevance_distribution(
          classifier_mdl.predict_probabilities,
          X,
          my_entropy_feature_attribution_function,
      )
  
      # E[H(P(Y)) - H(P(Y | do(X_U))] = H(P(Y)) - E[H(P(Y | X))]
      expected_sum_shapley_values = (
          h_p_Y
          - estimate_entropy_of_probabilities(
              classifier_mdl.predict_probabilities(X)
          )
      )
  
      assert feature_contributions[0] == approx(
          expected_sum_shapley_values / 2, abs=0.075
      )
      assert feature_contributions[1] == approx(
          expected_sum_shapley_values / 2, abs=0.075
      )
      assert feature_contributions[2] == approx(0, abs=0.01)
      assert feature_contributions[3] == approx(0, abs=0.01)
      assert feature_contributions[4] == approx(0, abs=0.01)
  
      assert np.sum(feature_contributions) == approx(
          expected_sum_shapley_values, abs=0.04
      )
  
file_path: dowhy/tests/gcm/test_feature_relevance.py
imports: import networkx
  import numpy
  import pandas
  from flaky import flaky
  from pytest import approx
  from scipy import stats
  from dowhy.gcm import AdditiveNoiseModel, ClassifierFCM, ScipyDistribution, StructuralCausalModel, auto, confidence_intervals, fit
  from dowhy.gcm.feature_relevance import feature_relevance_distribution, feature_relevance_sample, parent_relevance
  from dowhy.gcm.ml import create_linear_regressor, create_logistic_regression_classifier
  from dowhy.gcm.shapley import ShapleyApproximationMethods, ShapleyConfig
  from dowhy.gcm.uncertainty import estimate_entropy_of_probabilities
  from dowhy.gcm.util.general import means_difference
label_desc: Use image node_id 6 for calling a global function with example usage: test_when_using_feature_relevance_distribution_with_entropy_set_function_then_returns_correct_results() and returns: unknown