Exchangeability-Aware Sum-Product Networks

Sum-Product Networks (SPNs) are expressive probabilistic models that provide exact, tractable inference. They achieve this efficiency by making used of local independence. On the other hand, mixtures of exchangeable variable models (MEVMs) are a class of tractable probabilistic models that make use of exchangeability of random variables to render inference tractable. Exchangeability, which arises naturally in systems consisting of multiple, interrelated entities, has not been considered for efficient representation and inference in SPNs yet. The contribution of this paper is a novel probabilistic model which we call Exchangeability-Aware Sum-Product Networks (XSPNs). It contains both SPNs and MEVMs as special cases, and combines the ability of SPNs to efficiently learn deep probabilistic models with the ability of MEVMs to efficiently handle exchangeable random variables. We also introduce a structure learning algorithm for XSPNs and empirically show that they can be more accurate and efficient than conventional SPNs when the data contains repeated, interchangeable parts.