Compiling probabilistic graphical models using sentential decision diagrams

• Authors: Arthur Choi;Doga Kisa;Adnan Darwiche
• Venue: ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
• Year: 2013

Knowledge compilation is a powerful approach to exact inference in probabilistic graphical models, which is able to effectively exploit determinism and context-specific independence, allowing it to scale to highly connected models that are otherwise infeasible using more traditional methods (based on treewidth alone). Previous approaches were based on performing two steps: encode a model into CNF, then compile the CNF into an equivalent but more tractable representation (d-DNNF), where exact inference reduces to weighted model counting. In this paper, we investigate a bottom-up approach, that is enabled by a recently proposed representation, the Sentential Decision Diagram (SDD). We describe a novel and efficient way to encode the factors of a given model directly to SDDs, bypassing the CNF representation. To compile a given model, it now suffices to conjoin the SDD representations of its factors, using an apply operator, which d-DNNFs lack. Empirically, we find that our simpler approach to knowledge compilation is as effective as those based on d-DNNFs, and at times, orders-of-magnitude faster.