class_docstr: Gaussian Process probability of improvement acquisition function.
  
  Computes the analytic sequential probability of improvement for a Gaussian
  process model relative to observed data.
  
  Requires that `predictive_distribution` has `mean` and `stddev` methods.
  
  #### Examples
  
  Build and evaluate a GP Probability of Improvement acquisition function.
  
  ```python
  import numpy as np
  import tensorflow_probability as tfp
  
  tfd = tfp.distributions
  tfpk = tfp.math.psd_kernels
  tfp_acq = tfp.experimental.bayesopt.acquisition
  
  # Sample 10 4-dimensional index points and associated observations.
  index_points = np.random.uniform(size=[10, 4])
  observations = np.random.uniform(size=[10])
  
  # Build a GP regression model.
  dist = tfd.GaussianProcessRegressionModel(
      kernel=tfpk.ExponentiatedQuadratic(),
      observation_index_points=index_points,
      observations=observations)
  
  gp_poi = tfp_acq.GaussianProcessProbabilityOfImprovement(
      predictive_distribution=dist,
      observations=observations)
  
  # Evaluate the acquisition function at a set of predictive index points.
  pred_index_points = np.random.uniform(size=[6, 4])
  acq_fn_vals = gp_poi(pred_index_points)  # Has shape [6].
  ```
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docstr: Computes analytic GP probability of improvement.
  
  Args:
    **kwargs: Keyword args passed on to the `mean` and `stddev` methods of
      `predictive_distribution`.
  
  Returns:
    Probability of improvement at index points implied by
    `predictive_distribution` (or overridden in `**kwargs`).
docstr_tok: ["Computes","analytic","GP","probability","of","improvement",".","Args",":","*","*","kwargs",":","Keyword","args","passed","on","to","the","`","mean","`","and","`","stddev","`","methods","of","`","predictive_distribution","`",".","Returns",":","Probability","of","improvement","at","index","points","implied","by","`","predictive_distribution","`","(","or","overridden","in","`","*","*","kwargs","`",")","."]
code: def __call__(self, **kwargs):
      """Computes analytic GP probability of improvement.
  
      Args:
        **kwargs: Keyword args passed on to the `mean` and `stddev` methods of
          `predictive_distribution`.
  
      Returns:
        Probability of improvement at index points implied by
        `predictive_distribution` (or overridden in `**kwargs`).
      """
      stddev = self.predictive_distribution.stddev(**kwargs)
      mean = self.predictive_distribution.mean(**kwargs)
      best_observed = tf.reduce_max(self.observations, axis=-1)
      return normal_probability_of_improvement(
          best_observed, mean, stddev
      )
  
file_path: probability/tensorflow_probability/python/experimental/bayesopt/acquisition/probability_of_improvement.py
imports: import tensorflow.compat.v2
  from tensorflow_probability.python.distributions import normal
  from tensorflow_probability.python.experimental.bayesopt.acquisition import acquisition_function
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import samplers
label_desc: Use image node_id 2 for calling the GaussianProcessProbabilityOfImprovement obj's underlying member method code with example usage: obj.__call__() and returns: normal_probability_of_improvement