code: def _laplace_vi_ape(
      model,
      design,
      observation_labels,
      target_labels,
      guide,
      loss,
      optim,
      num_steps,
      final_num_samples,
      y_dist=None,
  ):
      def posterior_entropy(y_dist, design):
          # Important that y_dist is sampled *within* the function
          y = pyro.sample("conditioning_y", y_dist)
          y_dict = {
              label: y[i, ...]
              for i, label in enumerate(observation_labels)
          }
          conditioned_model = pyro.condition(model, data=y_dict)
          # Here just using SVI to run the MAP optimization
          guide.train()
          svi = SVI(
              conditioned_model, guide=guide, loss=loss, optim=optim
          )
          with poutine.block():
              for _ in range(num_steps):
                  svi.step(design)
          # Recover the entropy
          with poutine.block():
              final_loss = loss(conditioned_model, guide, design)
              guide.finalize(final_loss, target_labels)
              entropy = mean_field_entropy(
                  guide, [design], whitelist=target_labels
              )
          return entropy
  
      if y_dist is None:
          y_dist = EmpiricalMarginal(
              Importance(model, num_samples=final_num_samples).run(
                  design
              ),
              sites=observation_labels,
          )
  
      # Calculate the expected posterior entropy under this distn of y
      loss_dist = EmpiricalMarginal(
          Search(posterior_entropy).run(y_dist, design)
      )
      ape = loss_dist.mean
  
      return ape
  
imports: import math
  import warnings
  import torch
  import pyro
  from pyro import poutine
  from pyro.contrib.oed.search import Search
  from pyro.contrib.util import lexpand
  from pyro.infer import SVI, EmpiricalMarginal, Importance
  from pyro.infer.autoguide.utils import mean_field_entropy
  from pyro.util import torch_isinf, torch_isnan
label_desc: Use image node_id 3 for calling a global function with example usage: _laplace_vi_ape(model, design, observation_labels, target_labels, guide, loss, optim, num_steps, final_num_samples, y_dist) and returns: ape, entropy