Does the value of the prior in the model matter?

1

I was going through the Dirichlet Process Mixture Models in Pyro — Pyro Tutorials 1.9.0 documentation, and realized that the dimensions of the parameters in the model and the guide do not match?

The parameter beta in the guide is drawn from Beta(torch.ones(T-1), kappa) where kappa is a T-1 dimensional tensor itself (which makes sense for the Dirichlet process).
However, in the model, beta is drawn from Beta(1, alpha) which will just return a single value.

How does this work?

2

in the model beta is in a plate that will effectively broadcast out the shape to be (T-1,)

3

Isn’t the beta in the plate even in the guide?
In model:

with pyro.plate("beta_plate", T-1):
        beta = pyro.sample("beta", Beta(1, alpha))

In guide:

with pyro.plate("beta_plate", T-1):
        q_beta = pyro.sample("beta", Beta(torch.ones(T-1), kappa))

Or are the two different?

4

i don’t understand your question. in the context of variational inference sample statements in the model define prior distributions. sample statements in the guide define approximate posterior distributions over the corresponding latent variable.

5

Sorry for the ambiguity.
What I meant was - the beta sample should have the same dimension in both model and guide, right?

6

both beta in the model and guide have shape (T-1,)