Evidence-based clustering for scalable inference in Markov logic

Abstract

Markov Logic is a powerful representation that unifies first-order logic and probabilistic graphical models. However, scaling-up inference in Markov Logic Networks (MLNs) is extremely challenging. Standard graphical model inference algorithms operate on the propositional Markov network obtained by grounding the MLN and do not scale well as the number of objects in the realworld domain increases. On the other hand, algorithms which perform inference directly at the first-order level, namely lifted inference algorithms, although more scalable than propositional algorithms, require the MLN to have specific symmetric structure. Worse still, evidence breaks symmetries, and the performance of lifted inference is the same as propositional inference (or sometimes worse, due to overhead). In this paper, we propose a general method for solving this "evidence" problem. The main idea in our method is to approximate the given MLN having, say, n objects by an MLN having k objects such that k < < n and the results obtained by running potentially much faster inference on the smaller MLN are as close as possible to the ones obtained by running inference on the larger MLN. We achieve this by finding clusters of "similar" groundings using standard clustering algorithms (e.g., K-means), and replacing all groundings in the cluster by their cluster center. To this end, we develop a novel distance (or similarity) function for measuring the similarity between two groundings, based on the evidence presented to the MLN. We evaluated our approach on many different benchmark MLNs utilizing various clustering and inference algorithms. Our experiments clearly show the generality and scalability of our approach. © 2014 Springer-Verlag.