I have a high dimensional bayesian numpyro model, where I have two sets of parameters I’m trying to estimate “x” and “z”. Each are vectors of the same length ~10,000. I’m fitting using NUTS and MCMC.
I know that “x” and “z” are highly correlated, but only for matching pairs. That is, I know that x_1 is correlated with z_1, and x_2 with z_2, but not x_1 with z_2 or x_2 with z_1. Put another way, I know x_i is correlated with z_j for i==j only.
Because the dimensionality is so high, if I just specify
dense_mass = [("x","z")] crashes due to insufficient memory.
So my question is, how do I tell NUTS to estimate only the matching pairs from “x” and “z” in the mass matrix?
Here is a basic version of my model:
def model(a,b,y): x = numpyro.sample("x",dist.Normal(0,1).expand()) z = numpyro.sample("z",dist.Normal(0,1).expand()) lambda_ = jnp.exp(x*a+z*b) + 1e-16 numpyro.sample('T',dist.Poisson(lambda_),obs=y)