TY - GEN

T1 - Robust Mean Estimation in High Dimensions

T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022

AU - Deshmukh, Aditya

AU - Liu, Jing

AU - Veeravalli, Venugopal V.

N1 - Publisher Copyright:
© 2022 IEEE.

PY - 2022

Y1 - 2022

N2 - The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is formulated as the minimization of the ℓ0-'norm' of an outlier indicator vector, under a second moment constraint on the datapoints. The ℓ0-'norm' is then relaxed to the ℓp-norm (0 < p ≤ 1) in the objective, and it is shown that the global minima for each of these objectives are order-optimal and have optimal breakdown point for the robust mean estimation problem. Furthermore, a computationally tractable iterative ℓp-minimization and hard thresholding algorithm is proposed that outputs an order-optimal robust estimate of the population mean. The proposed algorithm (with breakdown point ≈0.3) does not require prior knowledge of the fraction of outliers, in contrast with most existing algorithms, and for p = 1 it has near-linear time complexity. Both synthetic and real data experiments demonstrate that the proposed algorithm outperforms state-of-the-art robust mean estimation methods.

AB - The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is formulated as the minimization of the ℓ0-'norm' of an outlier indicator vector, under a second moment constraint on the datapoints. The ℓ0-'norm' is then relaxed to the ℓp-norm (0 < p ≤ 1) in the objective, and it is shown that the global minima for each of these objectives are order-optimal and have optimal breakdown point for the robust mean estimation problem. Furthermore, a computationally tractable iterative ℓp-minimization and hard thresholding algorithm is proposed that outputs an order-optimal robust estimate of the population mean. The proposed algorithm (with breakdown point ≈0.3) does not require prior knowledge of the fraction of outliers, in contrast with most existing algorithms, and for p = 1 it has near-linear time complexity. Both synthetic and real data experiments demonstrate that the proposed algorithm outperforms state-of-the-art robust mean estimation methods.

KW - Global outlier pursuit

KW - High-dimensional statistics

KW - Robust estimation

KW - linear time complexity algorithm

UR - http://www.scopus.com/inward/record.url?scp=85136247115&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85136247115&partnerID=8YFLogxK

U2 - 10.1109/ISIT50566.2022.9834585

DO - 10.1109/ISIT50566.2022.9834585

M3 - Conference contribution

AN - SCOPUS:85136247115

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1115

EP - 1120

BT - 2022 IEEE International Symposium on Information Theory, ISIT 2022

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 26 June 2022 through 1 July 2022

ER -