Deterministic Langevin Monte Carlo with Normalizing Flows for Bayesian Inference

Richard D.P. Grumitt, Biwei Dai, Uros Seljak

Keywords: probabilistic methods, Bayesian Inference, Normalizing Flows

TL;DR: Deterministic Langevin Monte Carlo with Normalizing Flows for Bayesian Inference achieves state of the art performance on many challenging high dimensional examples, often at orders of magnitude lower computational cost.

Abstract: We propose a general purpose Bayesian inference algorithm for expensive likelihoods, replacing the stochastic term in the Langevin equation with a deterministic density gradient term. The particle density is evaluated from the current particle positions using a Normalizing Flow (NF), which is differentiable and has good generalization properties in high dimensions. We take advantage of NF preconditioning and NF based Metropolis-Hastings updates for a faster convergence. We show on various examples that the method is competitive against state of the art sampling methods.