code: def test_threshold_optimizer_multiple_sensitive_features():
      # Create sensitive features so that the third column is the first two combined.
      # Also, the name a2 is long since that caused bug #728.
      # The bug caused the merged names to get cut off, resulting in multiple groups
      # getting merged internally. To avoid that this test case checks even internal
      # representations.
      X = pd.DataFrame(
          [
              [0, 4],
              [6, 2],
              [1, 3],
              [10, 5],
              [1, 7],
              [-2, 1],
              [3, 10],
              [14, 5],
              [1, 3],
              [1, 5],
              [1, 7],
              [-5, 9],
              [3, 13],
              [7, 1],
              [-8, 4],
              [9, 1],
          ]
      )
      y = pd.Series([0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0])
      a1 = "a"
      a2 = "a very very very very very very very long group name"
      a3 = "a group name with commas ,, in , it"
      a4 = "a group name with backslashes \\ in \\\\ it"
      A = pd.DataFrame(
          [
              [a1, a3, a1 + a3],
              [a1, a3, a1 + a3],
              [a2, a3, a2 + a3],
              [a2, a3, a2 + a3],
              [a2, a3, a2 + a3],
              [a2, a3, a2 + a3],
              [a2, a4, a2 + a4],
              [a2, a4, a2 + a4],
              [a2, a4, a2 + a4],
              [a2, a4, a2 + a4],
              [a2, a4, a2 + a4],
              [a2, a4, a2 + a4],
              [a2, a4, a2 + a4],
              [a2, a4, a2 + a4],
              [a1, a4, a1 + a4],
              [a1, a4, a1 + a4],
          ],
          columns=["SF1", "SF2", "SF1+2"],
      )
  
      estimator = LinearRegression()
      estimator.fit(X, y)
  
      postprocess_est_multi = ThresholdOptimizer(
          estimator=estimator,
          constraints="demographic_parity",
          objective="accuracy_score",
          prefit=True,
          predict_method="predict",
      )
      postprocess_est_combined = ThresholdOptimizer(
          estimator=estimator,
          constraints="demographic_parity",
          objective="accuracy_score",
          prefit=True,
          predict_method="predict",
      )
  
      postprocess_est_multi.fit(
          X, y, sensitive_features=A.loc[:, ["SF1", "SF2"]]
      )
      postprocess_est_combined.fit(
          X, y, sensitive_features=A.loc[:, "SF1+2"]
      )
  
      X_test = pd.concat(
          [
              pd.DataFrame(
                  [
                      [5, 4],
                      [7, 2],
                      [0, 3],
                      [1, 2],
                      [-2, 9],
                      [1, 1],
                      [0, 5],
                      [-3, 3],
                  ]
              ),
              X,
          ]
      )
      A_test = pd.concat(
          [
              pd.DataFrame(
                  [
                      [a1, a3, a1 + a3],
                      [a1, a3, a1 + a3],
                      [a2, a3, a2 + a3],
                      [a2, a3, a2 + a3],
                      [a2, a4, a2 + a4],
                      [a2, a4, a2 + a4],
                      [a1, a4, a1 + a4],
                      [a1, a4, a1 + a4],
                  ],
                  columns=["SF1", "SF2", "SF1+2"],
              ),
              A,
          ]
      )
      y_test = pd.concat([pd.Series([0, 1, 0, 1, 0, 1, 0, 1]), y])
  
      y_pred_multi = postprocess_est_multi.predict(
          X_test,
          sensitive_features=A_test.loc[:, ["SF1", "SF2"]],
          random_state=1,
      )
      y_pred_combined = postprocess_est_combined.predict(
          X_test,
          sensitive_features=A_test.loc[:, "SF1+2"],
          random_state=1,
      )
  
      metricframe_multi = MetricFrame(
          metrics=fairness_metrics,
          y_true=y_test,
          y_pred=y_pred_multi,
          sensitive_features=A_test.loc[:, ["SF1", "SF2"]],
      )
  
      metricframe_combined = MetricFrame(
          metrics=fairness_metrics,
          y_true=y_test,
          y_pred=y_pred_combined,
          sensitive_features=A_test.loc[:, "SF1+2"],
      )
  
      # multi - names after escaping
      a3_escaped = a3.replace(",", "\\,")
      a4_escaped = a4.replace("\\", "\\\\")
      a13 = f"{a1},{a3_escaped}"
      a14 = f"{a1},{a4_escaped}"
      a23 = f"{a2},{a3_escaped}"
      a24 = f"{a2},{a4_escaped}"
  
      assert (
          metricframe_combined.overall == metricframe_multi.overall
      ).all()
  
      assert (
          metricframe_combined.by_group.loc[a1 + a3]
          == metricframe_multi.by_group.loc[(a1, a3)]
      ).all()
      assert (
          metricframe_combined.by_group.loc[a2 + a3]
          == metricframe_multi.by_group.loc[(a2, a3)]
      ).all()
      assert (
          metricframe_combined.by_group.loc[a1 + a4]
          == metricframe_multi.by_group.loc[(a1, a4)]
      ).all()
      assert (
          metricframe_combined.by_group.loc[a2 + a4]
          == metricframe_multi.by_group.loc[(a2, a4)]
      ).all()
  
      # comparing string representations of interpolation dicts is sufficient
      assert str(
          postprocess_est_combined.interpolated_thresholder_.interpolation_dict[
              a1 + a3
          ]
      ) == str(
          postprocess_est_multi.interpolated_thresholder_.interpolation_dict[
              a13
          ]
      )
      assert str(
          postprocess_est_combined.interpolated_thresholder_.interpolation_dict[
              a1 + a4
          ]
      ) == str(
          postprocess_est_multi.interpolated_thresholder_.interpolation_dict[
              a14
          ]
      )
      assert str(
          postprocess_est_combined.interpolated_thresholder_.interpolation_dict[
              a2 + a3
          ]
      ) == str(
          postprocess_est_multi.interpolated_thresholder_.interpolation_dict[
              a23
          ]
      )
      assert str(
          postprocess_est_combined.interpolated_thresholder_.interpolation_dict[
              a2 + a4
          ]
      ) == str(
          postprocess_est_multi.interpolated_thresholder_.interpolation_dict[
              a24
          ]
      )
  
imports: import numpy
  import pandas
  from sklearn.linear_model import LinearRegression
  from sklearn.metrics import accuracy_score, balanced_accuracy_score
  from fairlearn.metrics import MetricFrame, false_negative_rate, false_positive_rate
  from fairlearn.postprocessing import ThresholdOptimizer
label_desc: Use image node_id 1 for calling a global function with example usage: test_threshold_optimizer_multiple_sensitive_features() without return types