code: def _log_betabin(k, n, alpha, beta):
      import math
  
      try:
          const = (
              math.lgamma(alpha + beta)
              - math.lgamma(alpha)
              - math.lgamma(beta)
          )
      except:
          print("alpha = {}, beta = {}".format(alpha, beta))
      if isinstance(k, list) or isinstance(k, np.ndarray):
          if len(k) != len(n):
              print(
                  "length of k is %d and length of n is %d"
                  % (len(k), len(n))
              )
              raise ValueError
          lbeta = []
          for ki, ni in zip(k, n):
              lbeta.append(
                  math.lgamma(ki + alpha)
                  + math.lgamma(ni - ki + beta)
                  - math.lgamma(ni + alpha + beta)
                  + const
              )
          return np.array(lbeta)
      else:
          return (
              math.lgamma(k + alpha)
              + math.lgamma(n - k + beta)
              - math.lgamma(n + alpha + beta)
              + const
          )
  
imports: import itertools
  import operator
  import os
  import warnings
  from os.path import join
  from bisect import bisect_left
  from collections import defaultdict
  from copy import deepcopy
  from itertools import combinations
  from random import sample
  import numpy
  import pandas
  from mlxtend.frequent_patterns import fpgrowth
  from numpy.random import random
  from pandas import read_csv
  from scipy.sparse import csc_matrix
  from sklearn.base import BaseEstimator, ClassifierMixin
  from sklearn.ensemble import RandomForestClassifier
  from sklearn.utils.multiclass import check_classification_targets
  from sklearn.utils.validation import check_X_y, check_is_fitted
  from imodels.rule_set.rule_set import RuleSet
  from imodels.util.arguments import check_fit_arguments
label_desc: Use image node_id 4 for calling a global function with example usage: _log_betabin(k, n, alpha, beta) and returns: np, unknown