A Unified Particle-Optimization Framework for Scalable Bayesian Sampling

TL;DR

This paper introduces a unified particle-optimization framework based on Wasserstein gradient flows that connects and enhances scalable Bayesian sampling methods like SG-MCMC and SVGD, improving efficiency and effectiveness.

Contribution

The paper proposes a novel particle-optimization framework that unifies SG-MCMC and SVGD, enabling new algorithms and better understanding of their relationship.

Findings

Framework effectively unifies SG-MCMC and SVGD.

Experimental results show improved sampling efficiency.

Demonstrates scalability on deep neural networks.

Abstract

There has been recent interest in developing scalable Bayesian sampling methods such as stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) for big-data analysis. A standard SG-MCMC algorithm simulates samples from a discrete-time Markov chain to approximate a target distribution, thus samples could be highly correlated, an undesired property for SG-MCMC. In contrary, SVGD directly optimizes a set of particles to approximate a target distribution, and thus is able to obtain good approximations with relatively much fewer samples. In this paper, we propose a principle particle-optimization framework based on Wasserstein gradient flows to unify SG-MCMC and SVGD, and to allow new algorithms to be developed. Our framework interprets SG-MCMC as particle optimization on the space of probability measures, revealing a strong connection between SG-MCMC and SVGD. The key component of our framework is several particle-approximate techniques to efficiently solve the original partial differential equations on the space of probability measures. Extensive experiments on both synthetic data and deep neural networks demonstrate the effectiveness and efficiency of our framework for scalable Bayesian sampling.