Polynomial time algorithms for dual volume sampling
Name
NIPS-2017-polynomial-time-algorithms-for-dual-volume-sampling-Paper.pdf
Description
Published version
Size
478.37 KB
Format
Unknown
Checksum (MD5)
dd4c32587995d7e394ea2a6a2558b657
Author(s)
Li, Chengtao
Jegelka, Stefanie Sabrina
Sra, Suvrit
Date Issued
2017
Journal
Advances in Neural Information Processing Systems
Version
Final published version
Abstract
© 2017 Neural information processing systems foundation. All rights reserved. We study dual volume sampling, a method for selecting k columns from an n × m short and wide matrix (n ≤ k ≤ m) such that the probability of selection is proportional to the volume spanned by the rows of the induced submatrix. This method was proposed by Avron and Boutsidis (2013), who showed it to be a promising method for column subset selection and its multiple applications. However, its wider adoption has been hampered by the lack of polynomial time sampling algorithms. We remove this hindrance by developing an exact (randomized) polynomial time sampling algorithm as well as its derandomization. Thereafter, we study dual volume sampling via the theory of real stable polynomials and prove that its distribution satisfies the "Strong Rayleigh" property. This result has numerous consequences, including a provably fast-mixing Markov chain sampler that makes dual volume sampling much more attractive to practitioners. This sampler is closely related to classical algorithms for popular experimental design methods that are to date lacking theoretical analysis but are known to empirically work well.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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