Lifted Probabilistic Inference by First-Order Knowledge Compilation Guy Van den Broeck, Nima Taghipour, Wannes Meert, Jesse Davis, Luc De Raedt Lifted Probabilistic Inference ● Probabilistic relational model, e.g. First-Order d-DNNF Circuits FO d-DNNF Circuit Compilation ● Logical variabiables have domains ● Propositional inference is hard! ● Exploit symmetries in logic ● Reason at first-order level → Lifted Inference! Variable Elimination Belief Propagation Knowledge Compilation Ground [Zhang94] [Pearl82] [Darwiche03] Lifted [Poole03] [Singla08] Our approach Why Knowledge Compilation? Compile probabilistic model once, then run polytime inference for multiple queries, evidence ● Factor Graph MLN Compilation Algorithm ● Weighted CNF d-DNNF Circuit Weighted Model Counting ● Bayesian Network 7 compilation rules applied recursively Weighted FO CNF FO d-DNNF Circuit Independent Partial Grounding Generate first-order operators in inner d-DNNF nodes Uses efficient logical data structures ● Exploits context-specific independences ● State of the art for exact inference in Bayesian networks and statistical relational learning, but used in many areas, not just probabilistic inference Atom Counting ● Unit Propagation Research Question Can we lift knowledge compilation to a first-order setting? First step taken: first-order d-DNNFs for ● weighted first-order model counting (WFOMC) ● lifted probabilistic inference Parfactor Graph MLN Weighted FO CNF FO d-DNNF Circuit Weighted FO CNF Weighted FO Model Counting FO d-DNNF Circuit Experiments & Conclusions Converting to Weighted FO CNF MLN Weighted FO Theory assign we ight to a tom Weighted FO CNF Principled logical approach to lifted inference ● First model theoretic approach to lifted probabilistic inference ● Uses concepts from logical inference: model counting, unit propagation, Shannon decomposition, etc. ●Exploits context-specific independences ●State of the art for exact lifted inference ● Lifts more models than C-FOVE ● TALK: tomorrow at 10:30 in UAI session WEBSITE: http://dtai.cs.kuleuven.be/ml/systems/wfomc