Approximating the permanent by sampling from adaptive partitions

Jonathan Kuck, Tri Dao, Hamid Rezatofighi, Ashish Sabharwal, Stefano Ermon

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

Abstract

Computing the permanent of a non-negative matrix is a core problem with practical applications ranging from target tracking to statistical thermodynamics. However, this problem is also #P-complete, which leaves little hope for finding an exact solution that can be computed efficiently. While the problem admits a fully polynomial randomized approximation scheme, this method has seen little use because it is both inefficient in practice and difficult to implement. We present ADAPART, a simple and efficient method for drawing exact samples from an unnormalized distribution. Using ADAPART, we show how to construct tight bounds on the permanent which hold with high probability, with guaranteed polynomial runtime for dense matrices. We find that ADAPART can provide empirical speedups exceeding 30x over prior sampling methods on matrices that are challenging for variational based approaches. Finally, in the context of multi-target tracking, exact sampling from the distribution defined by the matrix permanent allows us to use the optimal proposal distribution during particle filtering. Using ADAPART, we show that this leads to improved tracking performance using an order of magnitude fewer samples.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 32 (NIPS 2019)
EditorsH. Wallach, H. Larochelle, A. Beygelzimer, F. d' Alché-Buc, E. Fox, R. Garnett
Place of PublicationSan Diego CA USA
PublisherNeural Information Processing Systems (NIPS)
Number of pages12
Publication statusPublished - 2019
Externally publishedYes
EventAdvances in Neural Information Processing Systems 2019 - Vancouver, Canada
Duration: 8 Dec 201914 Dec 2019
Conference number: 32nd
https://nips.cc/Conferences/2019 (Proceedings)
https://papers.nips.cc/book/advances-in-neural-information-processing-systems-32-2019 (Proceedings)

Publication series

NameAdvances in Neural Information Processing Systems
PublisherMorgan Kaufmann Publishers
Volume32
ISSN (Print)1049-5258

Conference

ConferenceAdvances in Neural Information Processing Systems 2019
Abbreviated titleNIPS 2019
CountryCanada
CityVancouver
Period8/12/1914/12/19
Internet address

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