Stein Self-Repulsive Dynamics: Benefits From Past Samples

TL;DR

This paper introduces Stein self-repulsive dynamics, a novel method that enhances sample diversity and efficiency in Langevin sampling by incorporating past sample information through Stein variational gradients, without biasing the target distribution.

Contribution

The paper presents a new Stein self-repulsive dynamics approach that reduces auto-correlation in Langevin sampling while maintaining correct asymptotic distribution, improving sample efficiency.

Findings

Significantly decreases auto-correlation in Langevin dynamics.

Increases effective sample size and sample efficiency.

Provides better uncertainty estimation than vanilla Langevin.

Abstract

We propose a new Stein self-repulsive dynamics for obtaining diversified samples from intractable un-normalized distributions. Our idea is to introduce Stein variational gradient as a repulsive force to push the samples of Langevin dynamics away from the past trajectories. This simple idea allows us to significantly decrease the auto-correlation in Langevin dynamics and hence increase the effective sample size. Importantly, as we establish in our theoretical analysis, the asymptotic stationary distribution remains correct even with the addition of the repulsive force, thanks to the special properties of the Stein variational gradient. We perform extensive empirical studies of our new algorithm, showing that our method yields much higher sample efficiency and better uncertainty estimation than vanilla Langevin dynamics.