Projected Latent Markov Chain Monte Carlo: Conditional Inference with Normalizing Flows

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 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. By providing experimental results for a variety of data sets, we demonstrate the practicality and effectiveness of PL-MCMC for missing data inference using normalizing flows.