Structured Stein Variational Inference for Continuous Graphical Models

We propose a novel distributed inference algorithm for continuous graphical models by extending Stein variational gradient descent (SVGD) to leverage the Markov dependency structure of the distribution of interest. The idea is to use a set of local kernel functions over the Markov blanket of each node, which alleviates the problem of the curse of high dimensionality and simultaneously yields a distributed algorithm for decentralized inference tasks. We justify our method with theoretical analysis and show that the use of local kernels can be viewed as a new type of localized approximation that matches the target distribution on the conditional distributions of each node over its Markov blanket. Our empirical results demonstrate that our method outperforms a variety of baselines including standard MCMC and particle message passing methods.