Deterministic Langevin Monte Carlo with Normalizing Flows for Bayesian Inference

TL;DR

This paper introduces a deterministic Langevin Monte Carlo method utilizing Normalizing Flows to improve Bayesian inference efficiency, especially for complex, high-dimensional problems.

Contribution

It presents a novel deterministic approach replacing stochastic terms with NF-based density gradients, enhancing convergence and performance in Bayesian inference.

Findings

Method is competitive with state-of-the-art samplers

Uses NF preconditioning for faster convergence

Effective for high-dimensional, expensive likelihoods

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.