Projected Latent Markov Chain Monte Carlo: Conditional Sampling of Normalizing Flows
This addresses conditional sampling for normalizing flows, enabling training from incomplete data, but appears incremental as it builds on existing MCMC and normalizing flow methods.
The paper tackles the problem of sampling from high-dimensional conditional distributions learned by normalizing flows, introducing Projected Latent Markov Chain Monte Carlo (PL-MCMC) and proving it asymptotically samples from exact conditional distributions, enabling Monte Carlo Expectation Maximization training from incomplete data with demonstrated efficacy in missing data tasks.
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.