code: def model_4(
      sequences, lengths, args, batch_size=None, include_prior=True
  ):
      with ignore_jit_warnings():
          num_sequences, max_length, data_dim = map(
              int, sequences.shape
          )
          assert lengths.shape == (num_sequences,)
          assert lengths.max() <= max_length
      hidden_dim = int(args.hidden_dim**0.5)  # split between w and x
      with handlers.mask(mask=include_prior):
          probs_w = pyro.sample(
              "probs_w",
              dist.Dirichlet(
                  0.9 * torch.eye(hidden_dim) + 0.1
              ).to_event(1),
          )
          probs_x = pyro.sample(
              "probs_x",
              dist.Dirichlet(0.9 * torch.eye(hidden_dim) + 0.1)
              .expand_by([hidden_dim])
              .to_event(2),
          )
          probs_y = pyro.sample(
              "probs_y",
              dist.Beta(0.1, 0.9)
              .expand([hidden_dim, hidden_dim, data_dim])
              .to_event(3),
          )
      tones_plate = pyro.plate("tones", data_dim, dim=-1)
      with pyro.plate(
          "sequences", num_sequences, batch_size, dim=-2
      ) as batch:
          lengths = lengths[batch]
          # Note the broadcasting tricks here: we declare a hidden torch.arange and
          # ensure that w and x are always tensors so we can unsqueeze them below,
          # thus ensuring that the x sample sites have correct distribution shape.
          w = x = torch.tensor(0, dtype=torch.long)
          for t in pyro.markov(
              range(max_length if args.jit else lengths.max())
          ):
              with handlers.mask(mask=(t < lengths).unsqueeze(-1)):
                  w = pyro.sample(
                      "w_{}".format(t),
                      dist.Categorical(probs_w[w]),
                      infer={"enumerate": "parallel"},
                  )
                  x = pyro.sample(
                      "x_{}".format(t),
                      dist.Categorical(Vindex(probs_x)[w, x]),
                      infer={"enumerate": "parallel"},
                  )
                  with tones_plate as tones:
                      pyro.sample(
                          "y_{}".format(t),
                          dist.Bernoulli(probs_y[w, x, tones]),
                          obs=sequences[batch, t],
                      )
  
imports: import argparse
  import functools
  import logging
  import sys
  import torch
  import torch.nn
  from torch.distributions import constraints
  from pyro.contrib.examples import polyphonic_data_loader
  from pyro.infer.autoguide import AutoDelta
  from pyro.ops.indexing import Vindex
  from pyro.util import ignore_jit_warnings
  from pyroapi import distributions
  from pyroapi import handlers, infer, optim, pyro, pyro_backend
label_desc: Use image node_id 5 for calling a global function with example usage: model_4(sequences, lengths, args, batch_size, include_prior) without return types