code: def lfire_eig(
      model,
      design,
      observation_labels,
      target_labels,
      num_y_samples,
      num_theta_samples,
      num_steps,
      classifier,
      optim,
      return_history=False,
      final_design=None,
      final_num_samples=None,
  ):
      """Estimates the EIG using the method of Likelihood-Free Inference by Ratio Estimation (LFIRE) as in [1].
      LFIRE is run separately for several samples of :math:`\\theta`.
  
      [1] Kleinegesse, Steven, and Michael Gutmann. "Efficient Bayesian Experimental Design for Implicit Models."
      arXiv preprint arXiv:1810.09912 (2018).
  
      :param function model: A pyro model accepting `design` as only argument.
      :param torch.Tensor design: Tensor representation of design
      :param list observation_labels: A subset of the sample sites
          present in `model`. These sites are regarded as future observations
          and other sites are regarded as latent variables over which a
          posterior is to be inferred.
      :param list target_labels: A subset of the sample sites over which the posterior
          entropy is to be measured.
      :param int num_y_samples: Number of samples to take in :math:`y` for each :math:`\\theta`.
      :param: int num_theta_samples: Number of initial samples in :math:`\\theta` to take. The likelihood ratio
                                     is estimated by LFIRE for each sample.
      :param int num_steps: Number of optimization steps.
      :param function classifier: a Pytorch or Pyro classifier used to distinguish between samples of :math:`y` under
                                  :math:`p(y|d)` and samples under :math:`p(y|\\theta,d)` for some :math:`\\theta`.
      :param pyro.optim.Optim optim: Optimiser to use.
      :param bool return_history: If `True`, also returns a tensor giving the loss function
          at each step of the optimization.
      :param torch.Tensor final_design: The final design tensor to evaluate at. If `None`, uses
          `design`.
      :param int final_num_samples: The number of samples to use at the final evaluation, If `None,
          uses `num_samples`.
      :return: EIG estimate, optionally includes full optimization history
      :rtype: torch.Tensor or tuple
      """
      if isinstance(observation_labels, str):
          observation_labels = [observation_labels]
      if isinstance(target_labels, str):
          target_labels = [target_labels]
  
      # Take N samples of the model
      expanded_design = lexpand(design, num_theta_samples)
      trace = poutine.trace(model).get_trace(expanded_design)
  
      theta_dict = {l: trace.nodes[l]["value"] for l in target_labels}
      cond_model = pyro.condition(model, data=theta_dict)
  
      loss = _lfire_loss(
          model,
          cond_model,
          classifier,
          observation_labels,
          target_labels,
      )
      out = opt_eig_ape_loss(
          expanded_design,
          loss,
          num_y_samples,
          num_steps,
          optim,
          return_history,
          final_design,
          final_num_samples,
      )
      if return_history:
          return out[0], out[1].sum(0) / num_theta_samples
      else:
          return out.sum(0) / num_theta_samples
  
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 12 for calling a global function with example usage: lfire_eig(model, design, observation_labels, target_labels, num_y_samples, num_theta_samples, num_steps, classifier, optim, return_history, final_design, final_num_samples) and returns: out,  unknown, unknown