Learning Compact Markov Logic Networks with Decision Trees

Abstract

Markov Logic Networks (MLNs) are a prominent model class that generalizes both first-order logic and undirected graphical models (Markov networks). The qualitative component of an MLN is a set of clauses and the quantitative component is a set of clause weights. Generative MLNs model the joint distribution of relationships and attributes. A state-of-the-art structure learning method is the moralization approach: learn a 1st-order Bayes net, then convert it to conjunctive MLN clauses. The moralization approach takes advantage of the high-quality inference algorithms for MLNs and their ability to handle cyclic dependencies. A weakness of the moralization approach is that it leads to an unnecessarily large number of clauses. In this paper we show that using decision trees to represent conditional probabilities in the Bayes net is an effective remedy that leads to much more compact MLN structures. The accuracy of predictions is competitive with the unpruned model and in many cases superior.