Flexible modeling of diversity with strongly log-concave distributions
© 2019 Neural information processing systems foundation. All rights reserved. Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-kno...
| 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/1721.1/132308 |
| _version_ | 1826198896395681792 |
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| author | Robinson, J Sra, S Jegelka, S |
| author_facet | Robinson, J Sra, S Jegelka, S |
| author_sort | Robinson, J |
| collection | MIT |
| description | © 2019 Neural information processing systems foundation. All rights reserved. Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal point process. While SR distributions offer elegant models of diversity, they lack an easy control over how they express diversity. We propose SLC as the right extension of SR that enables easier, more intuitive control over diversity, illustrating this via examples of practical importance. We develop two fundamental tools needed to apply SLC distributions to learning and inference: sampling and mode finding. For sampling we develop an MCMC sampler and give theoretical mixing time bounds. For mode finding, we establish a weak log-submodularity property for SLC functions and derive optimization guarantees for a distorted greedy algorithm. |
| first_indexed | 2024-09-23T11:11:39Z |
| format | Article |
| id | mit-1721.1/132308 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:11:39Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | mit-1721.1/1323082021-09-21T03:44:13Z Flexible modeling of diversity with strongly log-concave distributions Robinson, J Sra, S Jegelka, S © 2019 Neural information processing systems foundation. All rights reserved. Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal point process. While SR distributions offer elegant models of diversity, they lack an easy control over how they express diversity. We propose SLC as the right extension of SR that enables easier, more intuitive control over diversity, illustrating this via examples of practical importance. We develop two fundamental tools needed to apply SLC distributions to learning and inference: sampling and mode finding. For sampling we develop an MCMC sampler and give theoretical mixing time bounds. For mode finding, we establish a weak log-submodularity property for SLC functions and derive optimization guarantees for a distorted greedy algorithm. 2021-09-20T18:21:46Z 2021-09-20T18:21:46Z 2020-12-21T19:31:04Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/132308 en 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 | Robinson, J Sra, S Jegelka, S Flexible modeling of diversity with strongly log-concave distributions |
| title | Flexible modeling of diversity with strongly log-concave distributions |
| title_full | Flexible modeling of diversity with strongly log-concave distributions |
| title_fullStr | Flexible modeling of diversity with strongly log-concave distributions |
| title_full_unstemmed | Flexible modeling of diversity with strongly log-concave distributions |
| title_short | Flexible modeling of diversity with strongly log-concave distributions |
| title_sort | flexible modeling of diversity with strongly log concave distributions |
| url | https://hdl.handle.net/1721.1/132308 |
| work_keys_str_mv | AT robinsonj flexiblemodelingofdiversitywithstronglylogconcavedistributions AT sras flexiblemodelingofdiversitywithstronglylogconcavedistributions AT jegelkas flexiblemodelingofdiversitywithstronglylogconcavedistributions |