Abstract

Probabilistic graphical models (PGMs) are widely used to represent and to reason about underlying structure in high-dimensional probability distributions. We develop a framework for using sequential Monte Carlo (SMC) methods for inference and learning in general PGMs. Structural information from the PGM is used to find a collection of graph decompositions, which are then used as the basis for an SMC sampler.

In the first part of the talk we consider sequential decompositions, which results in that standard SMC techniques can be used. In the second part, we consider instead an auxiliary tree decomposition. Based on this we develop a new class of SMC samplers, Divide-and-Conquer SMC , in which we maintain multiple independent populations of weighted particles. These particle populations are propagated, merged, and resampled as the method progresses up the tree. We will see how this method naturally extends the standard chain-based SMC framework to a method that naturally runs on trees. We illustrate empirically that these approaches can outperform standard methods in terms of estimation accuracy. They also open up novel parallel implementation options and the possibility of concentrating the computational effort on the most challenging parts of the problem at hand.