docstr: Computes the expected change in mean and variance at the representer 
  points (cf. Section 2.4 in the paper). 
  
  
  :param x: candidate for which to compute the expected change in the GP
  :type x: np.array(1, input_dim)
  
  :return: innovation of mean (without samples) and variance at the representer points
  :rtype: (np.array(num_repr_points, 1), np.array(num_repr_points, num_repr_points))
              
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code: def _innovations(self, x):
      """
      Computes the expected change in mean and variance at the representer
      points (cf. Section 2.4 in the paper).
  
  
      :param x: candidate for which to compute the expected change in the GP
      :type x: np.array(1, input_dim)
  
      :return: innovation of mean (without samples) and variance at the representer points
      :rtype: (np.array(num_repr_points, 1), np.array(num_repr_points, num_repr_points))
  
      """
  
      """
          The notation differs from the paper. The representer points
          play the role of x*, the test input x is X. The Omega term is applied
          in the calling function _compute_acq. Another difference is that we
          ignore the noise as in the original Matlab implementation:
          https://github.com/ProbabilisticNumerics/entropy-search/blob/master/matlab/GP_innovation_local.m
          """
  
      # Get the standard deviation at x without noise
      _, stdev_x = self.model.predict(x, with_noise=False)
  
      # Compute the variance between the test point x and the representer points
      sigma_x_rep = self.model.get_covariance_between_points(
          self.repr_points, x
      )
      dm_rep = sigma_x_rep / stdev_x
  
      # Compute the deterministic innovation for the variance
      dv_rep = -dm_rep.dot(dm_rep.T)
      return dm_rep, dv_rep
  
file_path: GPyOpt/GPyOpt/acquisitions/ES.py
imports: import scipy
  import numpy
  from .base import AcquisitionBase
  from .EI import AcquisitionEI
  from ..util import epmgp
  from ..models.gpmodel import GPModel
label_desc: Use image node_id 7 for calling the AcquisitionEntropySearch obj's underlying member method code with example usage: obj._innovations(x) and returns: dm_rep,  dv_rep