Exponentiated strongly Rayleigh distributions
© 2018 Curran Associates Inc..All rights reserved. Strongly Rayleigh (SR) measures are discrete probability distributions over the subsets of a ground set. They enjoy strong negative dependence properties, as a result of which they assign higher probability to subsets of diverse elements. We introdu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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2021
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| Online Access: | https://hdl.handle.net/1721.1/132305 |
| _version_ | 1826188432212230144 |
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| author | Mariet, Z Sra, S Jegelka, S |
| author_facet | Mariet, Z Sra, S Jegelka, S |
| author_sort | Mariet, Z |
| collection | MIT |
| description | © 2018 Curran Associates Inc..All rights reserved. Strongly Rayleigh (SR) measures are discrete probability distributions over the subsets of a ground set. They enjoy strong negative dependence properties, as a result of which they assign higher probability to subsets of diverse elements. We introduce in this paper Exponentiated Strongly Rayleigh (ESR) measures, which sharpen (or smoothen) the negative dependence property of SR measures via a single parameter (the exponent) that can be intuitively understood as an inverse temperature. We develop efficient MCMC procedures for approximate sampling from ESRs, and obtain explicit mixing time bounds for two concrete instances: exponentiated versions of Determinantal Point Processes and Dual Volume Sampling. We illustrate some of the potential of ESRs, by applying them to a few machine learning problems; empirical results confirm that beyond their theoretical appeal, ESR-based models hold significant promise for these tasks. |
| first_indexed | 2024-09-23T07:59:15Z |
| format | Article |
| id | mit-1721.1/132305 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T07:59:15Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | mit-1721.1/1323052021-09-21T04:09:15Z Exponentiated strongly Rayleigh distributions Mariet, Z Sra, S Jegelka, S © 2018 Curran Associates Inc..All rights reserved. Strongly Rayleigh (SR) measures are discrete probability distributions over the subsets of a ground set. They enjoy strong negative dependence properties, as a result of which they assign higher probability to subsets of diverse elements. We introduce in this paper Exponentiated Strongly Rayleigh (ESR) measures, which sharpen (or smoothen) the negative dependence property of SR measures via a single parameter (the exponent) that can be intuitively understood as an inverse temperature. We develop efficient MCMC procedures for approximate sampling from ESRs, and obtain explicit mixing time bounds for two concrete instances: exponentiated versions of Determinantal Point Processes and Dual Volume Sampling. We illustrate some of the potential of ESRs, by applying them to a few machine learning problems; empirical results confirm that beyond their theoretical appeal, ESR-based models hold significant promise for these tasks. 2021-09-20T18:21:46Z 2021-09-20T18:21:46Z 2020-12-21T19:19:51Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/132305 en https://papers.nips.cc/paper/2018/hash/1c6a0198177bfcc9bd93f6aab94aad3c-Abstract.html Advances in Neural Information Processing Systems Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Neural Information Processing Systems (NIPS) |
| spellingShingle | Mariet, Z Sra, S Jegelka, S Exponentiated strongly Rayleigh distributions |
| title | Exponentiated strongly Rayleigh distributions |
| title_full | Exponentiated strongly Rayleigh distributions |
| title_fullStr | Exponentiated strongly Rayleigh distributions |
| title_full_unstemmed | Exponentiated strongly Rayleigh distributions |
| title_short | Exponentiated strongly Rayleigh distributions |
| title_sort | exponentiated strongly rayleigh distributions |
| url | https://hdl.handle.net/1721.1/132305 |
| work_keys_str_mv | AT marietz exponentiatedstronglyrayleighdistributions AT sras exponentiatedstronglyrayleighdistributions AT jegelkas exponentiatedstronglyrayleighdistributions |