{"type":"ScholarlyArticle","title":"Stochastic Anytime Search for Bounding Marginal MAP","authors":[{"name":"Radu Marinescu","slug":"radu-marinescu","given":"Radu","family":"Marinescu","affiliation":"IBM Research"},{"name":"Rina Dechter","slug":"rina-dechter","given":"Rina","family":"Dechter","affiliation":"University of California , Irvine"},{"name":"Alexander Ihler","slug":"alexander-ihler","given":"Alexander","family":"Ihler","affiliation":"University of California , Irvine"}],"abstract":"The Marginal MAP inference task is known to be extremely hard particularly because the evaluation of each complete MAP assignment involves an exact likelihood computation (a combinatorial sum). For  this reason, most recent state-of-the-art solvers that focus on computing anytime upper and lower bounds on the optimal value are limited to solving instances with tractable conditioned summation  subproblems. In this paper, we develop new search-based bounding schemes for Marginal MAP that produce anytime upper and lower bounds without performing exact likelihood computations. The empirical evaluation demonstrates the effectiveness of our new methods against the current best-performing search-based bounds.","doi":"10.24963/ijcai.2018/704","url":"https://ijcai.org/proceedings/2018/704","pdf":"https://ijcai.org/proceedings/2018/0704.pdf","markdown":"https://ijcai.org/proceedings/2018/704.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/704","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":704,"pages":{"first":5074,"last":5081},"keywords":["Heuristic Search and Game Playing: Combinatorial Search and Optimisation","Heuristic Search and Game Playing: Heuristic Search","Uncertainty in AI: Graphical Models","Uncertainty in AI: Bayesian Networks","Uncertainty in AI: Approximate Probabilistic Inference"],"videos":[],"references":[{"position":1,"raw":"[Bidyuk et al., 2010] Bozhena Bidyuk, Rina Dechter, and Emma Rollon. Active tuples-based scheme for bounding posterior beliefs. J. Artif. Intell. Res., 39:335-371, 2010.","title":"Active tuples-based scheme for bounding posterior beliefs","authors":"Bidyuk","year":"2010","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bonet and Geffner, 2005] Blai Bonet and Hector Geffner. An algorithm better than AO*? In Proceedings of the 20th National Conference on Artificial Intelligence (AAAI), pages 1343-1347, 2005.","title":"An algorithm better than AO","authors":"Geffner Bonet, Blai Bonet, Hector Geffner","year":"2005","venue":"Proceedings of the 20th National Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bonet and Geffner, 2012] Blai Bonet and Hector Geffner. Action selection for MDPs: Anytime AO* versus UCT. In Proceedings of 26th AAAI Conference on Artificial Intel- ligence (AAAI), pages 1749-1755, 2012.","title":"Action selection for MDPs: Anytime AO* versus UCT","authors":"Geffner ; ] Blai Bonet, Hector Bonet, Geffner","year":"2012","venue":"Proceedings of 26th AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Dechter and Mateescu, 2007] Rina Dechter and Robert Ma- teescu. AND/OR search spaces for graphical models. Arti- ficial Intelligence, 171(2-3):73-106, 2007.","title":"Rina Dechter and Robert Mateescu. AND/OR search spaces for graphical models","authors":"Mateescu Dechter","year":"2007","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Dechter and Rish, 2003] Rina Dechter and Irina Rish. Mini- buckets: A general scheme of approximating inference. Journal of ACM, 50(2):107-153, 2003.","title":"Minibuckets: A general scheme of approximating inference","authors":"Rina Dechter, Irina Rish","year":"2003","venue":"Journal of ACM","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Dechter, 2013] Rina Dechter. Reasoning with Probabilistic and Deterministic Graphical Models: Exact Algorithms. Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan & Claypool Publishers, 2013.","title":"Reasoning with Probabilistic and Deterministic Graphical Models: Exact Algorithms","authors":"Rina Dechter","year":"2013","venue":"Synthesis Lectures on Artificial Intelligence and Machine Learning","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Kask and Dechter, 2001] Kalev Kask and Rina Dechter. A general scheme for automatic search heuristics from speci- fication dependencies. Artificial Intelligence, 129(1-2):91- 131, 2001.","title":"A general scheme for automatic search heuristics from specification dependencies","authors":"Kalev Kask, Rina Dechter","year":"2001","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Lee et al., 2016a] Junkyu Lee, Radu Marinescu, and Rina Dechter. Applying search based probabilistic inference algorithms to probabilistic conformant planning: Prelimi- nary results. In Proceedings of International Symposium on Artificial Intelligence and Mathematics (ISAIM), 2016.","title":"Applying search based probabilistic inference algorithms to probabilistic conformant planning: Preliminary results","authors":"Lee","year":"2016","venue":"Proceedings of International Symposium on Artificial Intelligence and Mathematics (ISAIM)","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Lee et al., 2016b] Junkyu Lee, Radu Marinescu, Rina Dechter, and Alexander Ihler. From exact to anytime so- lutions for marginal MAP. In 30th AAAI Conference on Artificial Intelligence (AAAI), pages 1749-1755, 2016.","title":"From exact to anytime solutions for marginal MAP","authors":"Lee","year":"2016","venue":"30th AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Liu and Ihler, 2011] Q. Liu and A. Ihler. Bounding the parti- tion function using Hölder's inequality. In Int'l Conference on Machine Learning (ICML), pages 849-856, 2011.","title":"Bounding the partition function using Hölder's inequality","authors":"Q Liu, A Ihler","year":"2011","venue":"Int'l Conference on Machine Learning (ICML)","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Liu et al., 2015] Qiang Liu, John Fisher, and Alexander Ihler. Probabilistic variational bounds for graphical models. In Advances in Neural Information Processing Systems (NIPS) 28, pages 1432-1440, 2015.","title":"Probabilistic variational bounds for graphical models","authors":"Qiang Liu, John Fisher, Alexander Ihler","year":"2015","venue":"Advances in Neural Information Processing Systems (NIPS)","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Lou et al., 2018] Qi Lou, Rina Dechter, and Alexander Ihler. Anytime anyspace AND/OR best-first search for bounding marginal MAP. In AAAI Conference on Artificial Intelli- gence (AAAI), pages 860-867, 2018.","title":"Anytime anyspace AND/OR best-first search for bounding marginal MAP","authors":"Lou","year":"2018","venue":"AAAI Conference on Artificial Intelligence (AAAI)","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Luby et al., 1993] Michael Luby, Alistair Sinclair, and David Zuckerman. Optimal speedup of Las Vegas algo- rithms. Information Processing Letters, 47(4):173-180, 1993.","title":"Optimal speedup of Las Vegas algorithms","authors":"Michael Luby, Alistair Sinclair, David Zuckerman","year":"1993","venue":"Information Processing Letters","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Marinescu et al., 2014] Radu Marinescu, Rina Dechter, and Alexander Ihler. AND/OR search for marginal MAP. In Uncertainty in Artificial Intelligence (UAI), pages 563-572, 2014.","title":"AND/OR search for marginal MAP","authors":"Radu Marinescu, Rina Dechter, Alexander Ihler","year":"2014","venue":"Uncertainty in Artificial Intelligence (UAI)","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Marinescu et al., 2017] Radu Marinescu, Junkyu Lee, Rina Dechter, and Alexander Ihler. Anytime best+depth-first search for bounding marginal MAP. In 31th AAAI Confer- ence on Artificial Intelligence, pages 1749-1755, 2017.","title":"Anytime best+depth-first search for bounding marginal MAP","authors":"Radu Marinescu, Junkyu Lee, Rina Dechter, Alexander Ihler","year":"2017","venue":"31th AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Maua and Campos, 2012] Denis Maua and Cassio De Cam- pos. Anytime marginal MAP inference. In International Conference on Machine Learning, pages 1471-1478, 2012.","title":"Denis Maua and Cassio De Campos","authors":"Campos Maua","year":"2012","venue":"International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Roth, 1996] Dan Roth. On the hardness of approximate reasoning. Artificial Intelligence, 82(1-2):273-302, 1996.","title":"On the hardness of approximate reasoning","authors":"Dan Roth","year":"1996","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}