code: def indiv_smooth(a0, a, e, x):
      alph = indiv_filter(a0, a, e, x)
      beta = torch.zeros(alph.shape)
      beta[-1, :] = 1.0
      for t in range(alph.shape[0] - 1, 0, -1):
          for i in range(a0.shape[0]):
              for j in range(a0.shape[0]):
                  vec = beta[t, j] * a[i, j]
                  if torch.sum(x[t, :]) > 0.5:
                      vec = vec * torch.dot(x[t, :], e[j, :])
                  beta[t - 1, i] += vec
      smooth = torch.exp(alph) * beta
      smooth = smooth / torch.sum(smooth, -1, True)
      return torch.log(smooth)
  
file_path: pyro/tests/contrib/mue/test_missingdatahmm.py
imports: import pytest
  import torch
  from pyro.contrib.mue.missingdatahmm import MissingDataDiscreteHMM
  from pyro.distributions import Categorical, DiscreteHMM
label_desc: Use image node_id 6 for calling a global function with example usage: indiv_smooth(a0, a, e, x) and returns: torch