{"type":"ScholarlyArticle","title":"Bayesian Dynamic Mode Decomposition","authors":[{"name":"Naoya Takeishi","slug":"naoya-takeishi","given":"Naoya","family":"Takeishi","affiliation":"RIKEN Center for Advanced Intelligence Project"},{"name":"Yoshinobu Kawahara","slug":"yoshinobu-kawahara","given":"Yoshinobu","family":"Kawahara","affiliation":"† Department of Aeronautics and Astronautics , The University of Tokyo"},{"name":"Yasuo Tabei","slug":"yasuo-tabei","given":"Yasuo","family":"Tabei","affiliation":"‡ The Institute of Scientific and Industrial Research , Osaka University"},{"name":"Takehisa Yairi","slug":"takehisa-yairi","given":"Takehisa","family":"Yairi","affiliation":"RIKEN Center for Advanced Intelligence Project"}],"abstract":"Dynamic mode decomposition (DMD) is a data-driven method for calculating a modal representation of a nonlinear dynamical system, and it has been utilized in various fields of science and engineering. In this paper, we propose Bayesian DMD, which provides a principled way to transfer the advantages of the Bayesian formulation into DMD. To this end, we first develop a probabilistic model corresponding to DMD, and then, provide the Gibbs sampler for the posterior inference in Bayesian DMD. Moreover, as a specific example, we discuss the case of using a sparsity-promoting prior for an automatic determination of the number of dynamic modes. We investigate the empirical performance of Bayesian DMD using synthetic and real-world datasets.","doi":"10.24963/ijcai.2017/392","url":"https://ijcai.org/proceedings/2017/392","pdf":"https://ijcai.org/proceedings/2017/0392.pdf","markdown":"https://ijcai.org/proceedings/2017/392.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/392","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, IIIA-CSIC","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning S-Z","track":"Main track","number":392,"pages":{"first":2814,"last":2821},"keywords":["Machine Learning: Time-series/Data Streams","Uncertainty in AI: Uncertainty in AI","Machine Learning: Unsupervised Learning"],"videos":[],"references":[{"position":1,"raw":"[Arbabi and Mezić, 2016] Hassan Arbabi and Igor Mezić. 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