code: def smoothed_base_rate(
      y_true,
      y_pred=None,
      *,
      concentration=1.0,
      pos_label=1,
      sample_weight=None,
  ):
      r"""Compute the smoothed base rate,
      :math:`\frac{P + \alpha}{P + N + |R_Y|\alpha}`.
  
      Args:
          y_true (array-like): Ground truth (correct) target values.
          y_pred (array-like, optional): Estimated targets. Ignored.
          concentration (scalar): Dirichlet smoothing concentration parameter
              :math:`|R_Y|\alpha` (must be non-negative).
          pos_label (scalar, optional): The label of the positive class.
          sample_weight (array-like, optional): Sample weights.
  
      Returns:
          float: Smoothed base rate.
      """
      if concentration < 0:
          raise ValueError(
              "Concentration parameter must be non-negative."
          )
      num_classes = len(np.unique(y_true))
      idx = y_true == pos_label
      avg, tot = np.average(idx, weights=sample_weight, returned=True)
      return (avg * tot + concentration / num_classes) / (
          tot + concentration
      )
  
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 12 for calling a global function with example usage: smoothed_base_rate(y_true, y_pred) and returns: unknown