Sequential Monte Carlo methods for graphical models

Inference in probabilistic graphical models (PGMs) does typically not allow for analytical solutions, confining us to various approximative methods. We propose a sequential Monte Carlo (SMC) algorithm for inference in general PGMs. Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a monotonically increasing sequence of probability spaces. By targeting these auxiliary distributions using purpose built SMC samplers we are able to approximate the full joint distribution defined by the graphical model. Our SMC sampler also provides an unbiased estimate of the partition function (normalization constant) and we show how it can be used within a particle Markov chain Monte Carlo framework. This allows for better approximations of the marginals and for unknown parameters to be estimated. The proposed inference algorithms can deal with an arbitrary graph structure and the domain of the random variables in the graph can be discrete or continuous.