High-Dimensional Robust Mean Estimation via Outlier-Sparsity Minimization

Aditya Deshmukh, Jing Liu, Venugopal V. Veeravalli

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

Abstract

We study the robust mean estimation problem in high dimensions, where less than half of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, we formulate the robust mean estimation problem as the minimization of the 0-'norm' of an outlier indicator vector, under a second moment constraint on the datapoints. We further relax the 0-'norm' to the p-norm (0 < p ≤ 1) in the objective and prove that the global minima for each of these objectives are order-optimal for the robust mean estimation problem. Then we propose a computationally tractable iterative p-minimization and hard thresholding algorithm based on the proposed optimization problems. Empirical studies demonstrate that the proposed algorithm outperforms state-of-the-art robust mean estimation methods.

Original languageEnglish (US)
Title of host publication55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages1027-1031
Number of pages5
ISBN (Electronic)9781665458283
DOIs
StatePublished - 2021
Externally publishedYes
Event55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021 - Virtual, Pacific Grove, United States
Duration: Oct 31 2021Nov 3 2021

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
Volume2021-October
ISSN (Print)1058-6393

Conference

Conference55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021
Country/TerritoryUnited States
CityVirtual, Pacific Grove
Period10/31/2111/3/21

ASJC Scopus subject areas

  • Signal Processing
  • Computer Networks and Communications

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