Expectation Particle Belief Propagation

We propose an original particle-based implementation of the Loopy Belief Propagation (LPB) algorithm for pairwise Markov Random Fields (MRF) on a continuous state space. This is achieved by considering proposal distributions in the exponential family whose parameters are updated iterately in an Expectation Propagation (EP) framework. The proposed particle scheme provides consistent estimation of the LBP marginals as the number of particles increases. We demonstrate that it provides more accurate results than the Particle Belief Propagation (PBP) algorithm of Ihler and McAllester (2009) at a fraction of the computational cost and is additionally more robust empirically. The computational complexity of our algorithm at each iteration is quadratic in the number of particles.