Learning Relational Sum-Product Networks

Aniruddh Nath, Pedro M. Domingos

Abstract: Sum-product networks (SPNs) are a recently-proposed deep architecture that guarantees tractable inference, even on certain high-treewidth models. SPNs are a propositional architecture, treating the instances as independent and identically distributed. In this paper, we introduce Relational SumProduct Networks (RSPNs), a new tractable first-order probabilistic architecture. RSPNs generalize SPNs by modeling a set of instances jointly, allowing them to influence each other's probability distributions, as well as modeling probabilities of relations between objects. We also present LearnR-SPN, the first algorithm for learning high-treewidth tractable statistical relational models. LearnRSPN is a recursive top-down structure learning algorithm for RSPNs, based on Gens and Domingos' LearnSPN algorithm for propositional SPN learning. We evaluate the algorithm on three datasets; the RSPN learning algorithm outperforms Markov Logic Networks in both running time and predictive accuracy.