Expectation Particle Belief Propagation

Neural Information Processing Systems

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.


Graphical model inference: Sequential Monte Carlo meets deterministic approximations

Neural Information Processing Systems

Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases that are hard to quantify. The latter enjoy asymptotic consistency, but can suffer from high computational costs. In this paper we present a way of bridging the gap between deterministic and stochastic inference. Specifically, we suggest an efficient sequential Monte Carlo (SMC) algorithm for PGMs which can leverage the output from deterministic inference methods. While generally applicable, we show explicitly how this can be done with loopy belief propagation, expectation propagation, and Laplace approximations. The resulting algorithm can be viewed as a post-correction of the biases associated with these methods and, indeed, numerical results show clear improvements over the baseline deterministic methods as well as over "plain" SMC.


Graphical model inference: Sequential Monte Carlo meets deterministic approximations

Neural Information Processing Systems

Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases that are hard to quantify. The latter enjoy asymptotic consistency, but can suffer from high computational costs. In this paper we present a way of bridging the gap between deterministic and stochastic inference. Specifically, we suggest an efficient sequential Monte Carlo (SMC) algorithm for PGMs which can leverage the output from deterministic inference methods. While generally applicable, we show explicitly how this can be done with loopy belief propagation, expectation propagation, and Laplace approximations. The resulting algorithm can be viewed as a post-correction of the biases associated with these methods and, indeed, numerical results show clear improvements over the baseline deterministic methods as well as over "plain" SMC.


Particle-based Variational Inference for Continuous Systems

Neural Information Processing Systems

Since the development of loopy belief propagation, there has been considerable work on advancing the state of the art for approximate inference over distributions defined on discrete random variables. Improvements include guarantees of convergence, approximations that are provably more accurate, and bounds on the results of exact inference. However, extending these methods to continuous-valued systems has lagged behind. While several methods have been developed to use belief propagation on systems with continuous values, they have not as yet incorporated the recent advances for discrete variables. In this context we extend a recently proposed particle-based belief propagation algorithm to provide a general framework for adapting discrete message-passing algorithms to perform inference in continuous systems. The resulting algorithms behave similarly to their purely discrete counterparts, extending the benefits of these more advanced inference techniques to the continuous domain.