Quadratization and Roof Duality of Markov Logic Networks

Abstract

This article discusses the quadratization of Markov Logic Networks, which enables efficient approximate MAP computation by means of maximum flows. The procedure relies on a pseudo-Boolean representation of the model, and allows handling models of any order. The employed pseudo-Boolean representation can be used to identify problems that are guaranteed to be solvable in low polynomial-time. Results on common benchmark problems show that the proposed approach finds optimal assignments for most variables in excellent computational time and approximate solutions that match the quality of ILPbased solvers.

Xeggora: Exploiting Immune-to-Evidence Symmetries with Full Aggregation in Statistical Relational Models

“…Finally, a single approach that deals with long formulas, follows the idea of pairwise MLNs (Fierens et al, 2013), performing inference through quadratization for pseudo-Boolean functions by the means of first-order slack predicates (de Nijs, Landsiedel, Wollherr, & Buss, 2016). It produces a new model with quadratic parfactors, at the cost of additional optimization over slack variables and the benefit of better bounds and more persistencies.…”