code: def between_group_generalized_entropy_error(
      y_true,
      y_pred,
      prot_attr=None,
      priv_group=None,
      alpha=2,
      pos_label=1,
  ):
      r"""Compute the between-group generalized entropy.
  
      Between-group generalized entropy index is proposed as a group
      fairness measure in [#speicher18]_ and is one of two terms that the
      generalized entropy index decomposes to.
  
      Args:
          y_true (pandas.Series): Ground truth (correct) target values.
          y_pred (array-like): Estimated targets as returned by a classifier.
          prot_attr (array-like, optional): Protected attribute(s). If ``None``,
              all protected attributes in y_true are used.
          priv_group (scalar, optional): The label of the privileged group. If
              provided, the index will be computed between only the privileged and
              unprivileged groups. Otherwise, the index will be computed between
              all groups defined by the prot_attr.
          alpha (scalar, optional): Parameter that regulates the weight given to
              distances between values at different parts of the distribution. A
              value of 0 is equivalent to the mean log deviation, 1 is the Theil
              index, and 2 is half the squared coefficient of variation.
          pos_label (scalar, optional): The label of the positive class.
  
      See also:
          :func:`generalized_entropy_index`
  
      References:
          .. [#speicher18] `T. Speicher, H. Heidari, N. Grgic-Hlaca,
             K. P. Gummadi, A. Singla, A. Weller, and M. B. Zafar, "A Unified
             Approach to Quantifying Algorithmic Unfairness: Measuring Individual
             and Group Unfairness via Inequality Indices," ACM SIGKDD
             International Conference on Knowledge Discovery and Data Mining,
             2018. <https://dl.acm.org/citation.cfm?id=3220046>`_
      """
      groups, _ = check_groups(y_true, prot_attr)
      b = np.empty_like(y_true, dtype="float")
      if priv_group is not None:
          groups = [1 if g == priv_group else 0 for g in groups]
      for g in np.unique(groups):
          b[groups == g] = (
              1
              + (y_pred[groups == g] == pos_label)
              - (y_true[groups == g] == pos_label)
          ).mean()
      return generalized_entropy_index(b, alpha=alpha)
  
imports: from itertools import permutations
  from typing import Union
  import warnings
  import numpy
  import pandas
  from scipy.special import rel_entr
  from sklearn.metrics import make_scorer, recall_score, precision_score
  from sklearn.metrics import multilabel_confusion_matrix
  from sklearn.metrics._classification import _prf_divide, _check_zero_division
  from sklearn.neighbors import NearestNeighbors
  from sklearn.utils import check_X_y
  from aif360.metrics import ot_metric
  from aif360.sklearn.utils import check_inputs, check_groups
  from aif360.detectors.mdss.ScoringFunctions import BerkJones, Bernoulli
  from aif360.detectors.mdss.MDSS import MDSS
label_desc: Use image node_id 31 for calling a global function with example usage: between_group_generalized_entropy_error(y_true, y_pred, prot_attr, priv_group, alpha, pos_label) and returns: generalized_entropy_index