Connections between sparse estimation and robust statistical learning

Efthymios Tsakonas, Joakim Jalden, Nicholas D. Sidiropoulos, Bjorn Ottersten

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

4 Scopus citations

Abstract

Recent literature on robust statistical inference suggests that promising outlier rejection schemes can be based on accounting explicitly for sparse gross errors in the modeling, and then relying on compressed sensing ideas to perform the outlier detection. In this paper, we consider two models for recovering a sparse signal from noisy measurements, possibly also contaminated with outliers. The models considered here are a linear regression model, and its natural one-bit counterpart where measurements are additionally quantized to a single bit. Our contributions can be summarized as follows: We start by providing conditions for identification and the Cramér-Rao Lower Bounds (CRLBs) for these two models. Then, focusing on the one-bit model, we derive conditions for consistency of the associated Maximum Likelihood estimator, and show the performance of relevant l1-based relaxation strategies by comparing against the theoretical CRLB.

Original languageEnglish (US)
Title of host publication2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings
Pages5489-5493
Number of pages5
DOIs
StatePublished - Oct 18 2013
Event2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Vancouver, BC, Canada
Duration: May 26 2013May 31 2013

Publication series

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

Other

Other2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013
CountryCanada
CityVancouver, BC
Period5/26/135/31/13

Keywords

  • Cramér-Rao lower bounds
  • Sparsity
  • outlier detection
  • robustness

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