{On Theoretical Properties of Sum-Product Networks}

Abstract

Sum-product networks (SPNs) are a promising avenue for probabilistic modeling and have been successfully applied to various tasks. However, some theoretic properties about SPNs are not yet well understood. In this paper we fill some gaps in the theoretic foundation of SPNs. First, we show that the weights of any complete and consistent SPN can be transformed into locally normalized weights without changing the SPN distribu-tion. Second, we show that consistent SPNs cannot model distributions significantly (ex-ponentially) more compactly than decompos-able SPNs. As a third contribution, we ex-tend the inference mechanisms known for SPNs with finite states to generalized SPNs with arbitrary input distributions.