Semi-Empirical Objective Functions for Neural MCMC Proposal Optimization

Chris Cannella, Vahid Tarokh

Keywords: Markov Chain Monte Carlo, Neural MCMC, Generative Models, Deep Generative Models, Normalizing Flows

Abstract: Current objective functions used for training neural MCMC proposal distributions implicitly rely on architectural restrictions to yield sensible optimization results, which hampers the development of highly expressive neural MCMC proposal architectures. In this work, we introduce and demonstrate a semi-empirical procedure for determining approximate objective functions suitable for optimizing arbitrarily parameterized proposal distributions in MCMC methods. Our proposed Ab Initio objective functions consist of the weighted combination of functions following constraints on their global optima and transformation invariances that we argue should be upheld by general measures of MCMC efficiency for use in proposal optimization. Our experimental results demonstrate that Ab Initio objective functions maintain favorable performance and preferable optimization behavior compared to existing objective functions for neural MCMC optimization. We find that Ab Initio objective functions are sufficiently robust to enable the confident optimization of neural proposal distributions parameterized by deep generative networks extending beyond the regimes of traditional MCMC schemes.

One-sentence Summary: We introduce and demonstrate principled objective functions for optimizing MCMC proposal distributions paramterized by deep generative models.