Projected Latent Markov Chain Monte Carlo: Conditional Sampling of Normalizing Flows

TL;DR

PL-MCMC is a novel method for accurately sampling from high-dimensional conditional distributions learned by normalizing flows, enabling improved training and inference with incomplete data.

Contribution

We introduce PL-MCMC, a new conditional sampling technique for normalizing flows, with proven asymptotic correctness and applications to MC-EM training from incomplete data.

Findings

PL-MCMC effectively samples from complex conditional distributions.

It improves normalizing flow training with incomplete data.

Experimental results show high accuracy in missing data tasks.

Abstract

We introduce Projected Latent Markov Chain Monte Carlo (PL-MCMC), a technique for sampling from the high-dimensional conditional distributions learned by a normalizing flow. We prove that a Metropolis-Hastings implementation of PL-MCMC asymptotically samples from the exact conditional distributions associated with a normalizing flow. As a conditional sampling method, PL-MCMC enables Monte Carlo Expectation Maximization (MC-EM) training of normalizing flows from incomplete data. Through experimental tests applying normalizing flows to missing data tasks for a variety of data sets, we demonstrate the efficacy of PL-MCMC for conditional sampling from normalizing flows.