What is it doing in the HMM tutorial?

Tutorials
1

I’m reading the HMM tutorial from here: Example: Hidden Markov Models — Pyro Tutorials 1.8.4 documentation

def model_0(sequences, lengths, args, batch_size=None, include_prior=True):
    assert not torch._C._get_tracing_state()
    num_sequences, max_length, data_dim = sequences.shape
    with poutine.mask(mask=include_prior):
        # Our prior on transition probabilities will be:
        # stay in the same state with 90% probability; uniformly jump to another
        # state with 10% probability.
        probs_x = pyro.sample(
            "probs_x",
            dist.Dirichlet(0.9 * torch.eye(args.hidden_dim) + 0.1).to_event(1),
        )
        # We put a weak prior on the conditional probability of a tone sounding.
        # We know that on average about 4 of 88 tones are active, so we'll set a
        # rough weak prior of 10% of the notes being active at any one time.
        probs_y = pyro.sample(
            "probs_y",
            dist.Beta(0.1, 0.9).expand([args.hidden_dim, data_dim]).to_event(2),
        )
    # In this first model we'll sequentially iterate over sequences in a
    # minibatch; this will make it easy to reason about tensor shapes.
    tones_plate = pyro.plate("tones", data_dim, dim=-1)
    for i in pyro.plate("sequences", len(sequences), batch_size):
      length = lengths[i]
      sequence = sequences[i, :length]
      x = 0
      for t in pyro.markov(range(length)):
          # On the next line, we'll overwrite the value of x with an updated
          # value. If we wanted to record all x values, we could instead
          # write x[t] = pyro.sample(...x[t-1]...).
          x = pyro.sample(
              "x_{}_{}".format(i, t),
              dist.Categorical(probs_x[x]),
              infer={"enumerate": "parallel"},
          )
          with tones_plate:
              pyro.sample(
                  "y_{}_{}".format(i, t),
                  dist.Bernoulli(probs_y[x.squeeze(-1)]),
                  obs=sequence[t],
              )

I have question about this part:

tones_plate = pyro.plate("tones", data_dim, dim=-1)
for i in pyro.plate("sequences", len(sequences), batch_size):
       length = lengths[i]
       sequence = sequences[i, :length]
       x = 0
       for t in pyro.markov(range(length)):
            # On the next line, we'll overwrite the value of x with an updated
            # value. If we wanted to record all x values, we could instead
            # write x[t] = pyro.sample(...x[t-1]...).
            x = pyro.sample(
                "x_{}_{}".format(i, t),
                dist.Categorical(probs_x[x]),
                infer={"enumerate": "parallel"},
            )
            with tones_plate:
                pyro.sample(
                    "y_{}_{}".format(i, t),
                    dist.Bernoulli(probs_y[x.squeeze(-1)]),
                    obs=sequence[t],
                )

Is it saying that for each batch, the model takes previous length[I] observations and fit to it?
X is set to 0 for each iteration. Is it saying that the initial state is always set to 0?

2

In the outer loop, each sequence is indepently fit, so no i depends on a previous i. In the inner loop, each step t is dependent on the previous step t-1, initialized to x=0. So yes, for each sequence, the initial state is set to 0.