code: def model_6(
      sequences, lengths, args, batch_size=None, include_prior=False
  ):
      num_sequences, max_length, data_dim = sequences.shape
      assert lengths.shape == (num_sequences,)
      assert lengths.max() <= max_length
      hidden_dim = args.hidden_dim
  
      if not args.raftery_parameterization:
          # Explicitly parameterize the full tensor of transition probabilities, which
          # has hidden_dim cubed entries.
          probs_x = pyro.param(
              "probs_x",
              torch.rand(hidden_dim, hidden_dim, hidden_dim),
              constraint=constraints.simplex,
          )
      else:
          # Use the more parsimonious "Raftery" parameterization of
          # the tensor of transition probabilities. See reference:
          # Raftery, A. E. A model for high-order markov chains.
          # Journal of the Royal Statistical Society. 1985.
          probs_x1 = pyro.param(
              "probs_x1",
              torch.rand(hidden_dim, hidden_dim),
              constraint=constraints.simplex,
          )
          probs_x2 = pyro.param(
              "probs_x2",
              torch.rand(hidden_dim, hidden_dim),
              constraint=constraints.simplex,
          )
          mix_lambda = pyro.param(
              "mix_lambda",
              torch.tensor(0.5),
              constraint=constraints.unit_interval,
          )
          # we use broadcasting to combine two tensors of shape (hidden_dim, hidden_dim) and
          # (hidden_dim, 1, hidden_dim) to obtain a tensor of shape (hidden_dim, hidden_dim, hidden_dim)
          probs_x = mix_lambda * probs_x1 + (
              1.0 - mix_lambda
          ) * probs_x2.unsqueeze(-2)
  
      probs_y = pyro.param(
          "probs_y",
          torch.rand(hidden_dim, data_dim),
          constraint=constraints.unit_interval,
      )
      tones_plate = pyro.plate("tones", data_dim, dim=-1)
      with pyro.plate(
          "sequences", num_sequences, batch_size, dim=-2
      ) as batch:
          lengths = lengths[batch]
          x_curr, x_prev = torch.tensor(0), torch.tensor(0)
          # we need to pass the argument `history=2' to `pyro.markov()`
          # since our model is now 2-markov
          for t in pyro.markov(range(lengths.max()), history=2):
              with poutine.mask(mask=(t < lengths).unsqueeze(-1)):
                  probs_x_t = Vindex(probs_x)[x_prev, x_curr]
                  x_prev, x_curr = x_curr, pyro.sample(
                      "x_{}".format(t),
                      dist.Categorical(probs_x_t),
                      infer={"enumerate": "parallel"},
                  )
                  with tones_plate:
                      probs_y_t = probs_y[x_curr.squeeze(-1)]
                      pyro.sample(
                          "y_{}".format(t),
                          dist.Bernoulli(probs_y_t),
                          obs=sequences[batch, t],
                      )
  
imports: import argparse
  import logging
  import sys
  import torch
  import torch.nn
  from torch.distributions import constraints
  import pyro
  import pyro.contrib.examples.polyphonic_data_loader
  import pyro.distributions
  from pyro import poutine
  from pyro.infer import SVI, JitTraceEnum_ELBO, TraceEnum_ELBO, TraceTMC_ELBO
  from pyro.infer.autoguide import AutoDelta
  from pyro.ops.indexing import Vindex
  from pyro.optim import Adam
  from pyro.util import ignore_jit_warnings
label_desc: Use image node_id 7 for calling a global function with example usage: model_6(sequences, lengths, args, batch_size, include_prior) without return types