{"type":"ScholarlyArticle","title":"Order Statistics for Probabilistic Graphical Models","authors":[{"name":"David Smith","slug":"david-smith","given":"David","family":"Smith","affiliation":"The University of Texas at Dallas"},{"name":"Sara Rouhani","slug":"sara-rouhani","given":"Sara","family":"Rouhani","affiliation":"The University of Texas at Dallas"},{"name":"Vibhav Gogate","slug":"vibhav-gogate","given":"Vibhav","family":"Gogate","affiliation":"The University of Texas at Dallas"}],"abstract":"We consider the problem of computing r-th order statistics, namely finding an assignment having rank r in a probabilistic graphical model. We show that the problem is NP-hard even when the graphical model has no edges (zero-treewidth models) via a reduction from the partition problem. We use this reduction, specifically a pseudo-polynomial time algorithm for number partitioning to yield a pseudo-polynomial time approximation algorithm for solving the r-th order statistics problem in zero- treewidth models. We then extend this algorithm to arbitrary graphical models by generalizing it to tree decompositions, and demonstrate via experimental evaluation on various datasets that our proposed algorithm is more accurate than sampling algorithms.","doi":"10.24963/ijcai.2017/645","url":"https://ijcai.org/proceedings/2017/645","pdf":"https://ijcai.org/proceedings/2017/0645.pdf","markdown":"https://ijcai.org/proceedings/2017/645.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/645","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Uncertainty in AI","track":"Main track","number":645,"pages":{"first":4625,"last":4631},"keywords":["Uncertainty in AI: Approximate Probabilistic Inference","Uncertainty in AI: Graphical Models"],"videos":[],"references":[{"position":1,"raw":"[Chow and Liu, 1968] C. K. Chow and C. N Liu. Approx- imating Discrete Probability Distributions with Depen- dence Trees. IEEE Transactions on Information Theory, 14:462-467, 1968.","title":"Approximating Discrete Probability Distributions with Dependence Trees","authors":"C K Chow, C N Liu","year":"1968","venue":"IEEE Transactions on Information Theory","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Darwiche, 2009] Adnan Darwiche. Modeling and Reason- ing with Bayesian Networks. Cambridge University Press, 2009.","title":"Modeling and Reasoning with Bayesian Networks","authors":"Adnan Darwiche","year":"2009","venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Dechter, 1999] Rina Dechter. Bucket elimination: A uni- fying framework for reasoning. Artificial Intelligence, 113:41-85, 1999.","title":"Bucket elimination: A unifying framework for reasoning","authors":"Rina Dechter","year":"1999","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Ermon et al., 2013] Stefano Ermon, Carla P. Gomes, Ashish Sabharwal, and Bart Selman. Taming the curse of dimen- sionality: Discrete integration by hashing and optimiza- tion. In Proceedings of the 30th International Conference on International Conference on Machine Learning -Vol- ume 28, ICML'13, pages II-334-II-342. JMLR.org, 2013.","title":"Taming the curse of dimen-sionality: Discrete integration by hashing and optimization","authors":"Stefano Ermon, Carla P Gomes, Ashish Sabharwal, Bart Selman","year":"2013","venue":"Proceedings of the 30th International Conference on International Conference on Machine Learning -Volume 28, ICML'13","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Flerova et al., 2016] Natalia Flerova, Radu Marinescu, and Rina Dechter. Searching for the m best solutions in graph- ical models. Journal of Artificial Intelligence Research, 55:889-952, 2016.","title":"Searching for the m best solutions in graphical models","authors":"Natalia Flerova, Radu Marinescu, Rina Dechter","year":"2016","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Fromer and Globerson, 2009] Menachem Fromer and Amir Globerson. An lp view of the m-best map problem. In NIPS, volume 22, pages 567-575, 2009.","title":"An lp view of the m-best map problem","authors":"Globerson Fromer, Menachem Fromer, Amir Globerson","year":"2009","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Gens and Domingos, 2013] Robert Gens and Pedro M Domingos. Learning the structure of sum-product net- works. In ICML (3), pages 873-880, 2013.","title":"Learning the structure of sum-product networks","authors":"Robert Gens, Pedro M Domingos","year":"2013","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Hayes, 2002] Brian Hayes. Computing science: The easiest hard problem. American Scientist, 90(2):113-117, 2002.","title":"Computing science: The easiest hard problem","authors":"Brian Hayes","year":"2002","venue":"American Scientist","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Jordan et al., 1999] Michael Jordan, Zoubin Ghahramani, Tommi Jaakkola, and Lawrence Saul. An Introduction to Variational Methods for Graphical Models. Machine Learning, 37(2):183-233, 1999.","title":"An Introduction to Variational Methods for Graphical Models","authors":"Michael Jordan, Zoubin Ghahramani, Tommi Jaakkola, Lawrence Saul","year":"1999","venue":"Machine Learning","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Kulesza et al., 2015] Todd Kulesza, Margaret Burnett, Weng-Keen Wong, and Simone Stumpf. Principles of explanatory debugging to personalize interactive machine learning. In Proceedings of the 20th International Con- ference on Intelligent User Interfaces, pages 126-137. ACM, 2015.","title":"Principles of explanatory debugging to personalize interactive machine learning","authors":"Todd Kulesza, Margaret Burnett, Weng-Keen Wong, Simone Stumpf","year":"2015","venue":"Proceedings of the 20th International Conference on Intelligent User Interfaces","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Kwisthout, 2008] Johan Kwisthout. Complexity results for enumerating mpe and partial map. In European Workshop on Probabilistic Graphical Models, 2008.","title":"Complexity results for enumerating mpe and partial map","authors":"Johan Kwisthout","year":"2008","venue":"European Workshop on Probabilistic Graphical Models","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Lawler, 1972] Eugene L Lawler. A procedure for comput- ing the k best solutions to discrete optimization problems and its application to the shortest path problem. Manage- ment science, 18(7):401-405, 1972.","title":"A procedure for computing the k best solutions to discrete optimization problems and its application to the shortest path problem","authors":"Eugene L Lawler","year":"1972","venue":"Management science","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Lowd and Davis, 2010] Daniel Lowd and Jesse Davis. Learning markov network structure with decision trees. In Data Mining (ICDM), 2010 IEEE 10th International Con- ference on, pages 334-343. IEEE, 2010.","title":"Learning markov network structure with decision trees","authors":"Davis ; Lowd, Daniel Lowd, Jesse Davis","year":"2010","venue":"IEEE 10th International Conference on","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Pearl, 1988] Judea Pearl. Probabilistic Reasoning in Intel- ligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco, CA, 1988.","title":"Judea Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference","authors":"Pearl","year":"1988","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Rahman and Gogate, 2016] Tahrima Rahman and Vibhav Gogate. Learning ensembles of cutset networks. In AAAI conference on Artificial Intelligence, pages 3301-3307, 2016.","title":"Tahrima Rahman and Vibhav Gogate. Learning ensembles of cutset networks","authors":"Gogate Rahman","year":"2016","venue":"AAAI conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Yedidia et al., 2005] Judea Yedidia, William Freeman, and Yair Weiss. Constructing free-energy approximations and generalized Belief propagation algorithms. IEEE Transac- tions on Information Theory, 51(7):2282-2312, 2005.","title":"Constructing free-energy approximations and generalized Belief propagation algorithms","authors":"Yedidia","year":"2005","venue":"IEEE Transactions on Information Theory","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}