code: def testMulticlassClassificationLikelihood(self):
      kernel = tfpk.ExponentiatedQuadratic()
      num_predictive_points = 10
      num_inducing_points = 5
      num_observations = 15
      num_classes = 10
  
      # To handle the multiclass classification task, we just need to make sure we
      # model a batch of `num_classes` independent GPs, whose values are the
      # logits of a Categorical distribution over observations.
      vgp = variational_gaussian_process.VariationalGaussianProcess(
          kernel=kernel,
          index_points=np.random.uniform(
              size=(num_predictive_points, 1)
          ),
          # Batch inducing points of size `num_classes`.
          inducing_index_points=np.random.uniform(
              size=(num_classes, num_inducing_points, 1)
          ),
          # Variational inducing observations posterior normal with mean zero and
          # identity scale. These are also in batches of size `num_classes`.
          variational_inducing_observations_loc=np.zeros(
              (num_classes, num_inducing_points), dtype=np.float64
          ),
          variational_inducing_observations_scale=(
              np.ones((num_classes, 1, 1))
              * np.eye(num_inducing_points, dtype=np.float64)
          ),
          # No observation noise
          observation_noise_variance=0.0,
      )
  
      def log_likelihood_fn(observations, gp_events):
          # The shape of `gp_events` will be of the form
          #   [num_classes, quadrature_size, num_obserations]
          #
          # We want a batch of `Independent(Categorical)` distributions with
          #
          #   independent_categorical.batch_shape = [quadrature_size]
          #   independent_categorical.event_shape = [num_observations]
          #
          # and number of categories equal to `num_classes`. So we need to permute
          # the shape of  `gp_events` from the above to
          #
          #   [quadrature_size, num_observations, num_classes].
          logits = tf.transpose(gp_events, [1, 2, 0])
          independent_categorical = independent.Independent(
              categorical.Categorical(logits=logits),
              # Reinterpret `num_observations` as part of the event shape.
              reinterpreted_batch_ndims=1,
          )
          return independent_categorical.log_prob(observations)
  
      observations = np.random.randint(
          num_classes, size=num_observations
      )
      observation_index_points = np.random.uniform(
          size=(num_observations, 1)
      )
  
      # We really just check that this goes through without any shape errors.
      # TODO(b/127523126): Add more principled tests that this actually computes
      # what we expect it to (manual experimentation and testing has been done and
      # convincing results observed, but no clear strategy for automated tests
      # jumps out as terribly obvious).
      vgp.surrogate_posterior_expected_log_likelihood(
          observations,
          observation_index_points=observation_index_points,
          log_likelihood_fn=log_likelihood_fn,
          quadrature_size=20,
      )
  
imports: from absl.testing import parameterized
  import numpy
  import tensorflow.compat.v1
  import tensorflow.compat.v2
  from tensorflow_probability.python.distributions import bernoulli
  from tensorflow_probability.python.distributions import categorical
  from tensorflow_probability.python.distributions import independent
  from tensorflow_probability.python.distributions import variational_gaussian_process
  from tensorflow_probability.python.internal import tensorshape_util
  from tensorflow_probability.python.internal import test_util
  from tensorflow_probability.python.math.psd_kernels import exponentiated_quadratic
label_desc: Use image node_id 6 for calling the VariationalGaussianProcessTest obj's underlying member method code with example usage: obj.testMulticlassClassificationLikelihood() and returns: independent_categorical