Flexible modeling of diversity with strongly log-concave distributions
Name
NeurIPS-2019-flexible-modeling-of-diversity-with-strongly-log-concave-distributions-Paper.pdf
Description
Published version
Size
345.62 KB
Format
Unknown
Checksum (MD5)
afbef307888b137db47b0748397712e6
Author(s)
Robinson, Joshua
Sra, Suvrit
Jegelka, Stefanie Sabrina
Date Issued
2019
Journal
Advances in Neural Information Processing Systems
Version
Final published version
Abstract
© 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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
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.
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