Model Reductions for Inference: Generality of Pairwise, Binary, and Planar Factor Graphs

Abstract

We offer a solution to the problem of efficiently translating algorithms between different types of discrete statistical model. We investigate the expressive power of three classes of model-those with binary variables, with pairwise factors, and with planar topology-as well as their four intersections. We formalize a notion of "simple reduction" for the problem of inferring marginal probabilities and consider whether it is possible to "simply reduce" marginal inference from general discrete factor graphs to factor graphs in each of these seven subclasses. We characterize the reducibility of each class, showing in particular that the class of binary pairwise factor graphs is able to simply reduce only positive models. We also exhibit a continuous "spectral reduction" based on polynomial interpolation, which overcomes this limitation. Experiments assess the performance of standard approximate inference algorithms on the outputs of our reductions.

Quadratization and Roof Duality of Markov Logic Networks

“…Because pseudoBoolean functions can be interpreted as factor graphs, such a transformation can be seen as a reduction of the MAP problem in a general binary factor graph to a MAP problem in a pairwise binary factor graph. A thorough study of reductions of inference problems in general factor graphs to more restricted factor graph models was presented by Eaton and Ghahramani (2013). Close to our work is also the idea of pairwise MLNs (Fierens et al, 2013), which relies on a transformation of logical formulas to compute a quadratic MLN that is equivalent to an original MLN of higher order.…”