code: def average_odds_error(
      y_true,
      y_pred,
      *,
      prot_attr=None,
      priv_group=None,
      pos_label=1,
      sample_weight=None,
  ):
      r"""A relaxed version of equality of odds.
  
      Returns the average of the absolute difference in FPR and TPR for the
      unprivileged and privileged groups:
  
      .. math::
  
          \dfrac{|FPR_{D = \text{unprivileged}} - FPR_{D = \text{privileged}}|
          + |TPR_{D = \text{unprivileged}} - TPR_{D = \text{privileged}}|}{2}
  
      A value of 0 indicates equality of odds.
  
      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, keyword-only): Protected attribute(s). If
              ``None``, all protected attributes in y_true are used.
          priv_group (scalar, optional): The label of the privileged group. If
              prot_attr is binary, this may be ``None``.
          pos_label (scalar, optional): The label of the positive class.
          sample_weight (array-like, optional): Sample weights.
  
      Returns:
          float: Average odds error.
      """
      if priv_group is None:
          priv_group = check_groups(
              y_true, prot_attr=prot_attr, ensure_binary=True
          )[0][0]
      fpr_diff = -difference(
          specificity_score,
          y_true,
          y_pred,
          prot_attr=prot_attr,
          priv_group=priv_group,
          pos_label=pos_label,
          sample_weight=sample_weight,
      )
      tpr_diff = difference(
          recall_score,
          y_true,
          y_pred,
          prot_attr=prot_attr,
          priv_group=priv_group,
          pos_label=pos_label,
          sample_weight=sample_weight,
      )
      return (abs(tpr_diff) + abs(fpr_diff)) / 2
  
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 21 for calling a global function with example usage: average_odds_error(y_true, y_pred) and returns: unknown