TY - GEN
T1 - High-Dimensional Robust Mean Estimation via Outlier-Sparsity Minimization
AU - Deshmukh, Aditya
AU - Liu, Jing
AU - Veeravalli, Venugopal V.
N1 - Funding Information:
*Equal contribution. This research was supported by the Army Research Laboratory under Cooperative Agreement W911NF-17-2-0196 (IOBT CRA), through the University of Illinois.
Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85127019226&partnerID=8YFLogxK
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U2 - 10.1109/IEEECONF53345.2021.9723212
DO - 10.1109/IEEECONF53345.2021.9723212
M3 - Conference contribution
AN - SCOPUS:85127019226
T3 - Conference Record - Asilomar Conference on Signals, Systems and Computers
SP - 1027
EP - 1031
BT - 55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021
A2 - Matthews, Michael B.
PB - IEEE Computer Society
T2 - 55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021
Y2 - 31 October 2021 through 3 November 2021
ER -