code: def log_prob(self, data):
      (
          trans_logits,
          trans_probs,
          trans_mvn,
          obs_mvn,
          x_trans_dist,
          y_dist,
      ) = self.get_tensors_and_dists()
  
      log_prob = funsor.Number(0.0)
  
      s_vars = {
          -1: funsor.Tensor(torch.tensor(0), dtype=self.num_components)
      }
      x_vars = {}
  
      for t, y in enumerate(data):
          # construct free variables for s_t and x_t
          s_vars[t] = funsor.Variable(
              f"s_{t}", funsor.Bint[self.num_components]
          )
          x_vars[t] = funsor.Variable(
              f"x_{t}", funsor.Reals[self.hidden_dim]
          )
  
          # incorporate the discrete switching dynamics
          log_prob += dist.Categorical(
              trans_probs(s=s_vars[t - 1]), value=s_vars[t]
          )
  
          # incorporate the prior term p(x_t | x_{t-1})
          if t == 0:
              log_prob += self.x_init_mvn(value=x_vars[t])
          else:
              log_prob += x_trans_dist(
                  s=s_vars[t], x=x_vars[t - 1], y=x_vars[t]
              )
  
          # do a moment-matching reduction. at this point log_prob depends on (moment_matching_lag + 1)-many
          # pairs of free variables.
          if t > self.moment_matching_lag - 1:
              log_prob = log_prob.reduce(
                  ops.logaddexp,
                  {
                      s_vars[t - self.moment_matching_lag],
                      x_vars[t - self.moment_matching_lag],
                  },
              )
  
          # incorporate the observation p(y_t | x_t, s_t)
          log_prob += y_dist(s=s_vars[t], x=x_vars[t], y=y)
  
      T = data.shape[0]
      # reduce any remaining free variables
      for t in range(self.moment_matching_lag):
          log_prob = log_prob.reduce(
              ops.logaddexp,
              {
                  s_vars[T - self.moment_matching_lag + t],
                  x_vars[T - self.moment_matching_lag + t],
              },
          )
  
      # assert that we've reduced all the free variables in log_prob
      assert not log_prob.inputs, "unexpected free variables remain"
  
      # return the PyTorch tensor behind log_prob (which we can directly differentiate)
      return log_prob.data
  
imports: import argparse
  import time
  from collections import OrderedDict
  from os.path import exists
  from urllib.request import urlopen
  import numpy
  import pyro
  import torch
  import torch.nn
  import funsor
  import funsor.ops
  import funsor.torch.distributions
  from funsor.pyro.convert import funsor_to_cat_and_mvn, funsor_to_mvn, matrix_and_mvn_to_funsor, mvn_to_funsor
label_desc: Use image node_id 3 for calling the SLDS obj's underlying member method code with example usage: obj.log_prob(data) and returns: log_prob