Improving probabilistic inference in graphical models with determinism and cycles

Abstract

Many important real-world applications of machine learning, statistical physics, constraint programming and information theory can be formulated using graphical models that involve determinism and cycles. Accurate and efficient inference and training of such graphical models remains a key challenge. Markov logic networks (MLNs) have recently emerged as a popular framework for expressing a number of problems which exhibit these properties. While loopy belief propagation (LBP) can be an effective solution in some cases; unfortunately, when both determinism and cycles are present, LBP frequently fails to converge or converges to inaccurate results. As such, sampling based algorithms have been found to be more effective and are more popular for general inference tasks in MLNs. In this paper, we introduce Generalized arc-consistency Expectation Maximization MessagePassing (GEM-MP), a novel message-passing approach to inference in an extended factor graph that combines constraint programming techniques with variational methods. We focus our experiments on Markov logic and Ising models but the method is applicable to graphical models in general. In contrast to LBP, GEM-MP formulates the message-passing structure as steps of variational expectation maximization. Moreover, in the algorithm we leverage the local structures in the factor graph by using generalized arc consistency when performing a variational mean-field approximation. Thus each such update increases a lower bound on the model evidence. Our experiments on Ising grids, entity resolution and link prediction problems demonstrate the accuracy and convergence of GEM-MP over existing state-of-theart inference algorithms such as MC-SAT, LBP, and Gibbs sampling, as well as convergent Editor:

From Support Propagation to Belief Propagation in Constraint Programming

“…Previously introduced embp is guaranteed to converge to a local maximum but not necessarily to the exact marginals (Hsu et al, 2007). Ibrahim, Pal, and Pesant (2017) propose a variational message-passing algorithm based on Expectation Maximization in an effort to handle cycles, combined with some local consistency to better handle determinism in graphical models. In the context of deriving lower bounds on model counting for Boolean formulas, Kroc, Sabharwal, and Selman (2011) propose BPCount which repeatedly uses bp to identify "balanced" variables to branch on.…”