Group-level support recovery guarantees for group lasso estimator

Mojtaba Kadkhodaie Elyaderani, Swayambhoo Jain, Jeffrey Druce, Stefano Gonella, Jarvis Haupt

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

5 Scopus citations

Abstract

This paper considers the problem of estimating an unknown high dimensional signal from (typically low-dimensional) noisy linear measurements, where the desired unknown signal is assumed to possess a group-sparse structure, i.e. given a (pre-defined) partition of its entries into groups, only a small number of such groups are non-zero. Assuming the unknown group-sparse signal is generated according to a certain statistical model, we provide guarantees under which it can be efficiently estimated via solving the well-known group Lasso problem. In particular, we demonstrate that the set of indices for non-zero groups of the signal (called the group-level support of the signal) can be exactly recovered by solving the proposed group Lasso problem provided that its constituent non-zero groups are small in number and possess enough energy. Our guarantees rely on the well-conditioning of measurement matrix, which is expressed in terms of the block coherence parameter and can be efficiently computed. Our results are non-asymptotic in nature and therefore applicable to practical scenarios.

Original languageEnglish (US)
Title of host publication2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4366-4370
Number of pages5
ISBN (Electronic)9781509041176
DOIs
StatePublished - Jun 16 2017
Event2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States
Duration: Mar 5 2017Mar 9 2017

Publication series

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

Other

Other2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
CountryUnited States
CityNew Orleans
Period3/5/173/9/17

Keywords

  • Group sparsity
  • group Lasso
  • primal-dual witness
  • structured support recovery

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