{"type":"ScholarlyArticle","title":"Approximate Optimal Transport for Continuous Densities with Copulas","authors":[{"name":"Jinjin Chi","slug":"jinjin-chi","given":"Jinjin","family":"Chi","affiliation":"College of Computer Science and Technology , Jilin University , China; Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education , China"},{"name":"Jihong Ouyang","slug":"jihong-ouyang","given":"Jihong","family":"Ouyang","affiliation":"College of Computer Science and Technology , Jilin University , China; Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education , China"},{"name":"Ximing Li","slug":"ximing-li","given":"Ximing","family":"Li","affiliation":"College of Computer Science and Technology , Jilin University , China; Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education , China"},{"name":"Yang Wang","slug":"yang-wang","given":"Yang","family":"Wang","affiliation":"School of Computer Science and Information Engineering , Hefei University of Technology , China"},{"name":"Meng Wang","slug":"meng-wang","given":"Meng","family":"Wang","affiliation":"School of Computer Science and Information Engineering , Hefei University of Technology , China"}],"abstract":"Optimal Transport (OT) formulates a powerful framework by comparing probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it suffers from severe computational burden, due to the intractable objective with respect to the distributions of interest. Especially, there still exist very few attempts for continuous OT, i.e., OT for comparing\r\ncontinuous densities. To this end, we develop a novel continuous OT method, namely Copula OT (Cop-OT). The basic idea is to transform the primal objective of continuous OT into a tractable form with respect to the copula parameter, which can be efficiently solved by stochastic optimization with less time and memory requirements. Empirical results on real applications of image retrieval and synthetic data demonstrate that our Cop-OT can gain more accurate approximations to continuous OT values than the state-of-the-art baselines.","doi":"10.24963/ijcai.2019/300","url":"https://ijcai.org/proceedings/2019/300","pdf":"https://ijcai.org/proceedings/2019/0300.pdf","markdown":"https://ijcai.org/proceedings/2019/300.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/300","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Machine Learning A-L","track":"Main track","number":300,"pages":{"first":2165,"last":2171},"keywords":["Machine Learning: Probabilistic Machine Learning","Machine Learning: Learning Theory"],"videos":[],"references":[{"position":1,"raw":"[Arjovsky et al., 2017] Martin Arjovsky, Soumith Chintala, and Léon Bottou. 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