Message Passing Stein Variational Gradient Descent
This addresses a scalability issue in Bayesian inference for high-dimensional probabilistic models, though it is incremental as it builds on SVGD.
The paper tackles particle degeneracy in Stein variational gradient descent (SVGD) in high dimensions by proposing Message Passing SVGD (MP-SVGD), which leverages probabilistic graphical models to convert high-dimensional inference into local problems, resulting in improved repulsive force and particle efficiency.
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.