code: def black_box_variational_inference(logprob, D, num_samples):
      """Implements http://arxiv.org/abs/1401.0118, and uses the
      local reparameterization trick from http://arxiv.org/abs/1506.02557
      """
  
      def unpack_params(params):
          # Variational dist is a diagonal Gaussian.
          mean, log_std = params[:D], params[D:]
          return mean, log_std
  
      def gaussian_entropy(log_std):
          return 0.5 * D * (1.0 + np.log(2 * np.pi)) + np.sum(log_std)
  
      rs = npr.RandomState(0)
  
      def variational_objective(params, t):
          """Provides a stochastic estimate of the variational lower bound."""
          mean, log_std = unpack_params(params)
          samples = rs.randn(num_samples, D) * np.exp(log_std) + mean
          lower_bound = gaussian_entropy(log_std) + np.mean(
              logprob(samples, t)
          )
          return -lower_bound
  
      gradient = grad(variational_objective)
  
      return variational_objective, gradient, unpack_params
  
file_path: autograd/examples/black_box_svi.py
imports: from __future__ import absolute_import
  from __future__ import print_function
  import matplotlib.pyplot
  import autograd.numpy
  import autograd.numpy.random
  import autograd.scipy.stats.multivariate_normal
  import autograd.scipy.stats.norm
  from autograd import grad
  from autograd.misc.optimizers import adam
label_desc: Use image node_id 1 for calling a global function with example usage: black_box_variational_inference(logprob, D, num_samples) and returns: variational_objective,  gradient,  unpack_params, mean,  log_std, unknown, unknown