Fast mixing Markov chains for strongly rayleigh measures, DPPs, and constrained sampling
Name
NIPS-2016-fast-mixing-markov-chains-for-strongly-rayleigh-measures-dpps-and-constrained-sampling-Paper.pdf
Description
Published version
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609.57 KB
Format
Adobe PDF
Checksum (MD5)
f11ffe281ef05dd593f948bc93558502
Author(s)
Li, Chengtao
Jegelka, Stefanie Sabrina
Sra, Suvrit
Date Issued
December 2016
Journal
Advances in Neural Information Processing Systems
Publisher
Morgan Kaufmann Publishers
Citation
Li, Chengtao, Stefanie Jegelka and Suvrit Sra. “Fast mixing Markov chains for strongly rayleigh measures, DPPs, and constrained sampling.” Advances in Neural Information Processing Systems, 29 (December 2016) © 2016 The Author(s)
Version
Final published version
Abstract
We study probability measures induced by set functions with constraints. Such measures arise in a variety of real-world settings, where prior knowledge, resource limitations, or other pragmatic considerations impose constraints. We consider the task of rapidly sampling from such constrained measures, and develop fast Markov chain samplers for them. Our first main result is for MCMC sampling from Strongly Rayleigh (SR) measures, for which we present sharp polynomial bounds on the mixing time. As a corollary, this result yields a fast mixing sampler for Determinantal Point Processes (DPPs), yielding (to our knowledge) the first provably fast MCMC sampler for DPPs since their inception over four decades ago. Beyond SR measures, we develop MCMC samplers for probabilistic models with hard constraints and identify sufficient conditions under which their chains mix rapidly. We illustrate our claims by empirically verifying the dependence of mixing times on the key factors governing our theoretical bounds.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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