Active learning of self-concordant like multi-index functions

Ilija Bogunovic, Volkan Cevher, Jarvis Haupt, Jonathan Scarlett

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

We study the problem of actively learning a multi-index function of the form f(x) = g0(A0x) from its point evaluations, where A0k×d with k 蠑 d. We build on the assumptions and techniques of an existing approach based on low-rank matrix recovery (Tyagi and Cevher, 2012). Specifically, by introducing an additional self-concordant like assumption on g0 and adapting the sampling scheme and its analysis accordingly, we provide a bound on the sampling complexity with a weaker dependence on d in the presence of additive Gaussian sampling noise. For example, under natural assumptions on certain other parameters, the dependence decreases from O(d3/2) to O(d).

Original languageEnglish (US)
Title of host publication2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2189-2193
Number of pages5
ISBN (Electronic)9781467369978
DOIs
StatePublished - Aug 4 2015
Event40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Brisbane, Australia
Duration: Apr 19 2014Apr 24 2014

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2015-August
ISSN (Print)1520-6149

Other

Other40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
CountryAustralia
CityBrisbane
Period4/19/144/24/14

Keywords

  • Dantzig selector
  • Function learning
  • low-rank matrix recovery
  • multi-index functions

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