Expression Graphs - Unifying Factor Graphs and Sum-Product Networks

Factor graphs are a very general knowledge representation, subsuming many existing formalisms in AI. Sum-product networks are a more recent representation, inspired by studying cases where factor graphs are tractable. Factor graphs emphasize expressive power, while sum-product networks restrict expressiveness to get strong guarantees on speed of inference. A sum-product network is not simply a restricted factor graph, however. Although the inference algorithms for the two structures are very similar, translating a sum-product network into factor graph representation can result in an exponential slowdown. We propose a formalism which generalizes factor graphs and sum-product networks, such that inference is fast in cases whose structure is close to a sumproduct network.