{"type":"ScholarlyArticle","title":"Weighted Model Integration with Orthogonal Transformations","authors":[{"name":"David Merrell","slug":"david-merrell","given":"David","family":"Merrell","affiliation":"University of Wisconsin-Madison Department of Computer Sciences"},{"name":"Aws Albarghouthi","slug":"aws-albarghouthi","given":"Aws","family":"Albarghouthi","affiliation":"University of Wisconsin-Madison Department of Computer Sciences"},{"name":"Loris D'Antoni","slug":"loris-d-antoni","given":"Loris","family":"D'Antoni","affiliation":"University of Wisconsin-Madison Department of Computer Sciences"}],"abstract":"Weighted model counting and integration (WMC/WMI) are natural problems to which we can reduce many probabilistic inference tasks, e.g., in Bayesian networks, Markov networks, and probabilistic programs. Typically, we are given a first-order formula, where each satisfying assignment is associated with a weight---e.g., a probability of occurrence---and our goal is to compute the total weight of the formula. In this paper, we target exact inference techniques for WMI that leverage the power of satisfiability modulo theories (SMT) solvers to decompose a first-order formula in linear real arithmetic into a set of hyperrectangular regions whose weight is easy to compute. We demonstrate the challenges of hyperrectangular decomposition and present a novel technique that utilizes orthogonal transformations to transform formulas in order to enable efficient inference. Our evaluation demonstrates our technique's ability to improve the time required to achieve exact probability bounds.","doi":"10.24963/ijcai.2017/643","url":"https://ijcai.org/proceedings/2017/643","pdf":"https://ijcai.org/proceedings/2017/0643.pdf","markdown":"https://ijcai.org/proceedings/2017/643.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/643","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":643,"pages":{"first":4610,"last":4616},"keywords":["Combinatorial & Heuristic Search: Combinatorial search/optimisation","Uncertainty in AI: Exact Probabilistic Inference","Multidisciplinary Topics and Applications: Validation and Verification"],"videos":[],"references":[{"position":1,"raw":"[Albarghouthi et al., 2016] Aws Albarghouthi, Loris D'Antoni, Samuel Drews, and Aditya Nori. 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