Weakly submodular maximization beyond cardinality constraints: Doc randomization help greedy?

Lin Chen, Moran Feldman, Amin Karbasi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Submodular functions are a broad class of set functions that naturally arise in many machine learning applications. Due to their combinatorial structures, there has been a myriad of algorithms for maximizing such functions under various constraints. Unfortunately, once a function deviates from submodularity (even slightly), the known algorithms may perform arbitrarily poorly. Amending this issue, by obtaining approximation results for functions obeying properties that generalize submodularity, has been the focus of several recent works. One such class, known as weakly submodular functions, has received a lot of recent attention from the machine learning community due to its strong connections to restricted strong convexity and sparse reconstruction. In this paper, we prove that a randomized version of the greedy algorithm achieves an approximation ratio of (1 + I/7)-2 for weakly submodular maximization subject to a general matroid constraint, where 7 is a parameter measuring the distance from submodularity. To the best of our knowledge, this is the first algorithm with a non-trivial approximation guarantee for this constrained optimization problem. Moreover, our experimental results show that our proposed algorithm performs well in a variety of real-world problems, including regression, video summarization, splice site detection, and black-box interpretation.

Original languageEnglish
Title of host publication35th International Conference on Machine Learning, ICML 2018
EditorsJennifer Dy, Andreas Krause
PublisherInternational Machine Learning Society (IMLS)
Pages1252-1265
Number of pages14
ISBN (Electronic)9781510867963
StatePublished - 2018
Externally publishedYes
Event35th International Conference on Machine Learning, ICML 2018 - Stockholm, Sweden
Duration: 10 Jul 201815 Jul 2018

Publication series

Name35th International Conference on Machine Learning, ICML 2018
Volume2

Conference

Conference35th International Conference on Machine Learning, ICML 2018
Country/TerritorySweden
CityStockholm
Period10/07/1815/07/18

Bibliographical note

Funding Information:
MF was supported by Israel Science Foundation (ISF) grant number 1357/16 and AK was supported by AFOSR YIP (FA9550-18-1-0160

Publisher Copyright:
© 2018 by the Authors. All rights reserved.

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Human-Computer Interaction
  • Software

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