Quarantine a hidden variable from inference

Misc.
1 
def model(x,y):
    beta0 = pyro.sample("beta0", dist.Normal(loc=0, scale=10.))
    z_loc, z_cov = f1(x, beta0)
    z = pyro.sample("latent", dist.MultivariateNormal(z_loc,covariance_matrix=z_cov))
    y_loc = f2(x,z)
    sigma = pyro.sample('sigma', dist.Exponential(rate=1/10))

    with pyro.plate("data", N):
        pyro.sample("obs", dist.Normal(y_loc, sigma), obs=y)
        
nuts_kernel = NUTS(model)
mcmc = MCMC(nuts_kernel, num_samples=3000)
mcmc.run(x, y)

This model aims to seek posterior of beta0 and sigma. In this model, f1 and f2 are known (deterministic) functions.
My question is about z. The “z=pyro.sample()” sentence will assume z has a prior which is a multi Gaussian, and this model will seek posterior of z, too. But in my case, z_loc and z_cov are deterministic given beta0, and I don’t want any inference on z; it should be a forward-pass instead. How can I deal with it?

2

not entirely clear what you mean but if you want the outputs of f1 to be used “deterministically” you presumably need to compute the integral

y_loc = \int dz f2(x,z) p(z | z_loc, z_cov)

although that’s probably hard unless f2 is simple.

3

Thanks for the reply. f2 is a neural network. I will need to integrate it numerically.

4

if z is low dimensional, e.g. 1-4 dimension, you can use gauss-hermite quadrature

if it’s higher dimensional it becomes much harder and you probably just need to explicitly do inference over z, which effectively does the integral via sampling

5

Unfortunately, the dimension of z is rather high (e.g. over 100). I am trying to by pass the inference over z because the computation time is much longer than I desire. May be I should firstly try to reduce the dimension of z.