{"type":"ScholarlyArticle","title":"Efficient Symbolic Integration for Probabilistic Inference","authors":[{"name":"Samuel Kolb","slug":"samuel-kolb","given":"Samuel","family":"Kolb","affiliation":"a KU Leuven"},{"name":"Martin Mladenov","slug":"martin-mladenov","given":"Martin","family":"Mladenov","affiliation":"b Google Research"},{"name":"Scott Sanner","slug":"scott-sanner","given":"Scott","family":"Sanner","affiliation":"c University of Toronto"},{"name":"Vaishak Belle","slug":"vaishak-belle","given":"Vaishak","family":"Belle","affiliation":"d University of Edinburgh; e Alan Turing Institute f TU Darmstadt ,"},{"name":"Kristian Kersting","slug":"kristian-kersting","given":"Kristian","family":"Kersting","affiliation":""}],"abstract":"Weighted model integration (WMI) extends  weighted model counting (WMC) to the integration of functions over mixed discrete-continuous probability spaces. It has shown tremendous promise for solving inference problems in graphical models and probabilistic programs. Yet, state-of-the-art tools for WMI are generally limited either by the range of amenable theories, or in terms of performance. To address both limitations, we propose the use of extended algebraic decision diagrams (XADDs) as a compilation language for WMI.\r\nAside from tackling typical WMI problems, XADDs also enable partial WMI yielding parametrized solutions. To overcome the main roadblock of XADDs -- the computational cost of integration -- we formulate a novel and powerful exact symbolic dynamic programming (SDP) algorithm that seamlessly handles Boolean, integer-valued and real variables, and is able to effectively cache partial computations, unlike its predecessor. Our empirical results demonstrate that these contributions can lead to a significant computational reduction \r\nover existing probabilistic inference algorithms.","doi":"10.24963/ijcai.2018/698","url":"https://ijcai.org/proceedings/2018/698","pdf":"https://ijcai.org/proceedings/2018/0698.pdf","markdown":"https://ijcai.org/proceedings/2018/698.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/698","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Uncertainty in AI","track":"Main track","number":698,"pages":{"first":5031,"last":5037},"keywords":["Uncertainty in AI: Exact Probabilistic Inference","Uncertainty in AI: Uncertainty Representations"],"videos":[],"references":[{"position":1,"raw":"[Albarghouthi et al., 2017] Aws Albarghouthi, Loris D'Antoni, Samuel Drews, and Aditya V. Nori. Quantifying program bias. CoRR, abs/1702.05437, 2017.","title":"Quantifying program bias","authors":"Albarghouthi","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bacchus et al., 2009] Fahiem Bacchus, Shannon Dalmao, and Toni- ann Pitassi. Solving #sat and bayesian inference with backtracking search. JAIR, 34:391-442, 2009.","title":"Fahiem Bacchus, Shannon Dalmao, and Toniann Pitassi. Solving #sat and bayesian inference with backtracking search","authors":"Bacchus","year":"2009","venue":"JAIR","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Belle et al., 2015] Vaishak Belle, Andrea Passerini, and Guy Van den Broeck. Probabilistic inference in hybrid domains by weighted model integration. In Proc. of IJCAI, pages 2770-2776, 2015.","title":"Probabilistic inference in hybrid domains by weighted model integration","authors":"Belle","year":"2015","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2015/392"},{"position":4,"raw":"[Belle et al., 2016] Vaishak Belle, Guy Van den Broeck, and Andrea Passerini. Component caching in hybrid domains with piecewise polynomial densities. In Proc. of AAAI, pages 3369-3375, 2016.","title":"Component caching in hybrid domains with piecewise polynomial densities","authors":"Belle","year":"2016","venue":"Proc. of AAAI","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Belle, 2017] Vaishak Belle. Weighted model counting with function symbols. In Proc. of UAI, 2017.","title":"Vaishak Belle. Weighted model counting with function symbols","authors":"Belle","year":"2017","venue":"Proc. of UAI","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Braz et al., 2016] Rodrigo de Salvo Braz, Ciaran O'Reilly, Vibhav Gogate, and Rina Dechter. Probabilistic inference modulo theories. In Proc. of IJCAI, pages 3591-3599, 2016.","title":"Probabilistic inference modulo theories","authors":"Rodrigo De, Salvo Braz, O' Ciaran, Vibhav Reilly, Rina Gogate, Dechter","year":"2016","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/506"},{"position":7,"raw":"[Chaki et al., 2009] Sagar Chaki, Arie Gurfinkel, and Ofer Strich- man. Decision diagrams for linear arithmetic. In Proceedings of the Conference on Formal Methods in Computer-Aided Design (FMCAD), pages 53-60. IEEE, 2009.","title":"Decision diagrams for linear arithmetic","authors":"Sagar Chaki, Arie Gurfinkel, Ofer Strichman","year":"2009","venue":"Proceedings of the Conference on Formal Methods in Computer-Aided Design (FMCAD)","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Chavira and Darwiche, 2008] Mark Chavira and Adnan Darwiche. On probabilistic inference by weighted model counting. Artificial Intelligence, 172(6-7):772-799, 2008.","title":"On probabilistic inference by weighted model counting","authors":"Darwiche Chavira, Mark Chavira, Adnan Darwiche","year":"2008","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Chistikov et al., 2015] Dmitry Chistikov, Rayna Dimitrova, and Ru- pak Majumdar. Approximate counting in SMT and value esti- mation for probabilistic programs. In TACAS, pages 320-334. Springer, 2015.","title":"Approximate counting in SMT and value estimation for probabilistic programs","authors":"Dmitry Chistikov, Rayna Dimitrova, Rupak Majumdar","year":"2015","venue":"TACAS","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Choi et al., 2013] Arthur Choi, Doga Kisa, and Adnan Darwiche. Compiling probabilistic graphical models using sentential deci- sion diagrams. In Proceedings of 12th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncer- tainty (ECSQARU), pages 121-132. Springer, 2013.","title":"Compiling probabilistic graphical models using sentential decision diagrams","authors":"Arthur Choi, Doga Kisa, Adnan Darwiche","year":"2013","venue":"Proceedings of 12th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU)","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Domshlak and Hoffmann, 2007] Carmel Domshlak and Jörg Hoff- mann. Probabilistic planning via heuristic forward search and weighted model counting. Journal of Artificial Intelligence Re- search, 30:565-620, 2007.","title":"Carmel Domshlak and Jörg Hoffmann. Probabilistic planning via heuristic forward search and weighted model counting","authors":"Hoffmann Domshlak","year":"2007","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Fierens et al., 2013] Daan Fierens, Guy Van den Broeck, Joris Renkens, Dimitar Shterionov, Bernd Gutmann, Ingo Thon, Gerda Janssens, and Luc De Raedt. Inference and learning in probabilis- tic logic programs using weighted Boolean formulas. Journal of Theory and Practice of Logic Programming, 15:358-401, 2013.","title":"Inference and learning in probabilistic logic programs using weighted Boolean formulas","authors":"Daan Fierens, Guy Van Den, Joris Broeck, Dimitar Renkens, Bernd Shterionov, Ingo Gutmann, Gerda Thon, Luc Janssens, Raedt De","year":"2013","venue":"Journal of Theory and Practice of Logic Programming","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Gario and Micheli, 2015] Marco Gario and Andrea Micheli. Pysmt: a solver-agnostic library for fast prototyping of smt-based algo- rithms. In Proceedings of the 13th International Workshop on Satisfiability Modulo Theories (SMT), pages 373-384, 2015.","title":"Pysmt: a solver-agnostic library for fast prototyping of smt-based algorithms","authors":"Micheli Gario, Marco Gario, Andrea Micheli","year":"2015","venue":"Proceedings of the 13th International Workshop on Satisfiability Modulo Theories (SMT)","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Meurer et al., 2017] Aaron Meurer et al. Sympy: symbolic comput- ing in python. PeerJ Computer Science, 3:e103, January 2017.","title":"Sympy: symbolic computing in python","authors":"Meurer","year":"2017","venue":"PeerJ Computer Science","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Morettin et al., 2017] Paolo Morettin, Andrea Passerini, and Roberto Sebastiani. Efficient weighted model integration via smt- based predicate abstraction. In Proc. of IJCAI, pages 720-728, 2017.","title":"Efficient weighted model integration via smtbased predicate abstraction","authors":"Paolo Morettin, Andrea Passerini, Roberto Sebastiani","year":"2017","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Sanner and Abbasnejad, 2012] Scott Sanner and Ehsan Abbasne- jad. Symbolic variable elimination for discrete and continuous graphical models. In Proc. of AAAI, pages 1954-1960, 2012.","title":"Symbolic variable elimination for discrete and continuous graphical models","authors":"Scott Sanner, Ehsan Abbasnejad","year":"2012","venue":"Proc. of AAAI","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Sanner et al., 2011] S. Sanner, K. V. Delgado, and L. Nunes de Bar- ros. Symbolic dynamic programming for discrete and continuous state MDPs. In Proc. of UAI, pages 643-652, 2011.","title":"Symbolic dynamic programming for discrete and continuous state MDPs","authors":"S Sanner, K V Delgado, L Nunes De Barros","year":"2011","venue":"Proc. of UAI","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Suciu et al., 2011] Dan Suciu, Dan Olteanu, Christopher Ré, and Christoph Koch. Probabilistic databases. Synthesis Lectures on Data Management, 3(2):1-180, 2011.","title":"Probabilistic databases","authors":"Dan Suciu, Dan Olteanu, Christopher Ré, Christoph Koch","year":"2011","venue":"Synthesis Lectures on Data Management","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}