Difference `pyro.param` vs `pyro.sample`

Misc.
#1

I wonder what is the difference between pyro.sample and pyro.param when declaring variables in my probabilistic model or the guide? E.g.,

def model(data):
    x = pyro.param("x", torch.zeros(A, B))
    ...

vs

def model(data):
    x = pyro.sample("x", dist.Normal(torch.zeros(A), torch.ones(B)))
    ...

If I understand it correctly, during SVI the variable s will be “learned” in both models. Moreover, I can use x to declare/specify other variables in my model. So the difference is not clear to me.

Thanks in advance!

#2

parameters corresponds to point estimates and sample statements correspond to latent variables. latent variables are governed by distributions and inference yields a distribution over the inferred values of the latent variable (not a point estimate).

in other words sample statements correspond to quantities with associated uncertainty while parameters have no uncertainty about them.

1 Like
#3

Thanks for the quick reply.
To clarify: assume I want to estimate x_i = A * z_i, where x is my input of dimension N x F (samples x features).
Hence, with latent dimension K:

  • A should be a parameter, because it is fixed across samples:
    A = pyro.param("A", torch.ones(F, K))

  • z_i is a latent variable and therefore needs to be sampled:
    z = pyro.sample("z", dist.Normal(torch.zeros(K,1), torch.ones(K,1)))

Is that correct?

#4

there is no notion of correctness here. there are all kinds of modeling assumptions you could make: A could be a parameter or it could be a latent variable, etc

1 Like
#5

Thanks, the original question is answered!