Message Passing Stein Variational Gradient Descent

TL;DR

This paper identifies a particle collapse issue in Stein variational gradient descent (SVGD) in high dimensions and introduces Message Passing SVGD (MP-SVGD), which leverages graphical model structures to improve inference quality and efficiency.

Contribution

The paper proposes MP-SVGD, a novel method that uses graphical model structures to mitigate particle collapse in high-dimensional SVGD, enhancing inference performance.

Findings

MP-SVGD prevents particle collapse in high dimensions.

MP-SVGD outperforms traditional SVGD in particle efficiency.

MP-SVGD offers better approximation flexibility on graphical models.

Abstract

Stein variational gradient descent (SVGD) is a recently proposed particle-based Bayesian inference method, which has attracted a lot of interest due to its remarkable approximation ability and particle efficiency compared to traditional variational inference and Markov Chain Monte Carlo methods. However, we observed that particles of SVGD tend to collapse to modes of the target distribution, and this particle degeneracy phenomenon becomes more severe with higher dimensions. Our theoretical analysis finds out that there exists a negative correlation between the dimensionality and the repulsive force of SVGD which should be blamed for this phenomenon. We propose Message Passing SVGD (MP-SVGD) to solve this problem. By leveraging the conditional independence structure of probabilistic graphical models (PGMs), MP-SVGD converts the original high-dimensional global inference problem into a set of local ones over the Markov blanket with lower dimensions. Experimental results show its advantages of preventing vanishing repulsive force in high-dimensional space over SVGD, and its particle efficiency and approximation flexibility over other inference methods on graphical models.