Adaptive Monte Carlo augmented with normalizing flows.

SignificanceMonte Carlo methods, tools for sampling data from probability distributions, are widely used in the physical sciences, applied mathematics, and Bayesian statistics. Nevertheless, there are many situations in which it is computationally prohibitive to use Monte Carlo due to slow "mixing" between modes of a distribution unless hand-tuned algorithms are used to accelerate the scheme. Machine learning techniques based on generative models offer a compelling alternative to the challenge of designing efficient schemes for a specific system. Here, we formalize Monte Carlo augmented with normalizing flows and show that, with limited prior data and a physically inspired algorithm, we can substantially accelerate sampling with generative models.

Adaptation of the Independent Metropolis-Hastings Sampler with Normalizing Flow Proposals.

Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependent on properly tuned parameters, most of which are difficult if not impossible to know a priori for a given target distribution. Adaptive MCMC methods aim to address this by allowing the parameters to be updated during sampling based on previous samples from the chain at the expense of requiring a new theoretical analysis to ensure convergence. In this work we extend the convergence theory of adaptive MCMC methods to a new class of methods built on a powerful class of parametric density estimators known as normalizing flows. In particular, we consider an independent Metropolis-Hastings sampler where the proposal distribution is represented by a normalizing flow whose parameters are updated using stochastic gradient descent. We explore the practical performance of this procedure on both synthetic settings and in the analysis of a physical field system, and compare it against both adaptive and non-adaptive MCMC methods.