Hello,

I am fairly new to Pyro and SVI in general, so forgive me if what I describe does not make sense. But I was looking to implement a model that can basically work on an N x M matrix where there are N observations of M variables.

For each of the N observations, there are some latent parameters/distributions.

For each of the M variables, I want to effectively perform a bayesian regression to predict each variable independently, but given the same set of latent observations.

To put it in other words, I have N samples and I want to perform M independent regressions on them. But in this case both N and M are very large (N can be in the millions and M can be in the thousands), so I am wondering what the best way to structure this type of model.

I was considering training a single model on each of the M variables totally independently, but then I would lose out on the shared latent properties between them. So is there any other option?