Expectation Particle Belief Propagation
This work addresses the computational bottleneck in probabilistic inference for continuous-state graphical models, offering a more efficient and robust solution for applications in fields like computer vision and signal processing, though it is incremental as it builds on existing particle and belief propagation methods.
The authors tackled the problem of performing Loopy Belief Propagation on continuous-state Markov Random Fields by proposing a particle-based algorithm that adaptively constructs proposal distributions using Expectation Propagation. The result is a method that provides more accurate marginal estimates than the Particle Belief Propagation algorithm at a fraction of the computational cost, with an accelerated version maintaining near-optimal performance.
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. The algorithm constructs adaptively efficient proposal distributions approximating the local beliefs at each note of the MRF. 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. We also propose an accelerated implementation with sub-quadratic computational complexity which still provides consistent estimates of the loopy BP marginal distributions and performs almost as well as the original procedure.