code: def simplified_kolmogorov_smirnov_test(
      neighbor_histogram: npt.NDArray[np.float64],
      non_neighbor_histogram: npt.NDArray[np.float64],
  ) -> float:
      """Computes the Kolmogorov-Smirnov statistic between two groups of data.
      The statistic is the largest difference between the empirical cumulative
      distribution functions (ECDFs) of the two groups.
  
      Parameters
      ----------
      neighbor_histogram :
         Histogram data for the nearest neighbor group.
  
      non_neighbor_histogram :
          Histogram data for the non-neighbor group.
  
      Returns
      -------
      statistic :
          The KS statistic between the two ECDFs.
  
      Note
      ----
      - Both input arrays should have the same length.
      - The input arrays are histograms, which means they contain the count
        or frequency of values in each group. The data in the histograms
        should be normalized so that they sum to one.
  
      To calculate the KS statistic, the function first calculates the ECDFs
      for both input arrays, which are step functions that show the cumulative
      sum of the data up to each point. The function then calculates the
      largest absolute difference between the two ECDFs.
      """
  
      neighbor_cdf = np.cumsum(neighbor_histogram)
      non_neighbor_cdf = np.cumsum(non_neighbor_histogram)
  
      statistic = np.max(np.abs(neighbor_cdf - non_neighbor_cdf))
      return statistic
  
imports: from __future__ import annotations
  from typing import TYPE_CHECKING, Any, ClassVar, Dict, Optional, Union, cast
  import warnings
  import itertools
  from scipy.stats import gaussian_kde
  import numpy
  import pandas
  from scipy.sparse import csr_matrix
  from sklearn.neighbors import NearestNeighbors
  from sklearn.exceptions import NotFittedError
  from sklearn.utils.validation import check_is_fitted
  from cleanlab.datalab.internal.issue_manager import IssueManager
label_desc: Use image node_id 1 for calling a global function with example usage: simplified_kolmogorov_smirnov_test(neighbor_histogram, non_neighbor_histogram) and returns: statistic