Sparse Recovery with Shuffled Labels: Statistical Limits and Practical Estimators

Hang Zhang, Ping Li

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

1 Scopus citations

Abstract

This paper considers the sparse recovery with ner-muted labels, i.e., \boldsymbol{y}={\Pi}^{\ast}\boldsymbol{X}{\beta}^{\ast}+\boldsymbol{w} where \boldsymbol{y} \in \mathbb{R}^{n}, \mathbf{\Pi} \in \mathbb{R}^{n \times n}, \boldsymbol{X} \in \mathbb{R}^{n \times p}, {\beta}^{\ast} \in \mathbb{R}^{p}, \boldsymbol{w} \in \mathbb{R}^{n} denote the sensing result, unknown permutation matrix, design matrix, k-sparse covariates, and additive noise, respectively. The investigation is performed from both the statistical and the computational perspectives. For the statistical aspect, we first establish the statistical lower bounds on the measurement number n and the signal-to-noise ratio (SNR) for the correct recovery of the permutation matrix and the support set \text{supp}({\beta}^{\ast}), more specifically n \gtrsim k \log p and \log (\text{SNR}) \gtrsim \log n+\frac{k \log p}{n}. Then we confirm the tightness of these bounds by giving an exhaustive-search based estimators with matching orders. For the computational aspect, we propose a computationally-efficient estimator, namely, M-Lasso to recover both the permutation matrix and the sparse covariates. Numerical experiments are provided to verify the correctness and efficiency of the proposed estimator.

Original languageEnglish (US)
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1760-1765
Number of pages6
ISBN (Electronic)9781538682098
DOIs
StatePublished - Jul 12 2021
Externally publishedYes
Event2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia
Duration: Jul 12 2021Jul 20 2021

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2021-July
ISSN (Print)2157-8095

Conference

Conference2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/TerritoryAustralia
CityVirtual, Melbourne
Period7/12/217/20/21

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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