Robust Mean Estimation in High Dimensions via ℓ₀ Minimization

2020/08/21 by Jing Liu, Liu, Jing, Aditya Deshmukh +3
Engineering · Mathematics · #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Advanced Statistical Methods and Models

paper · pdf · doi:10.48550/arxiv.2008.09239

Abstract

We study the robust mean estimation problem in high dimensions, where α<0.5 fraction of the data points can be arbitrarily corrupted. Motivated by compressive sensing, we formulate the robust mean estimation problem as the minimization of the ℓ₀-`norm' of the outlier indicator vector, under second moment constraints on the inlier data points. We prove that the global minimum of this objective is order optimal for the robust mean estimation problem, and we propose a general framework for minimizing the objective. We further leverage the ℓ₁ and ℓ_p (0

Citations

• Robust Estimation of a Location Parameter

Related

• Robust Mean Estimation in High Dimensions: An Outlier Fraction Agnostic and Efficient Algorithm
• High-Dimensional Robust Mean Estimation via Gradient Descent
• Being Robust (in High Dimensions) Can Be Practical
• How Hard Is Robust Mean Estimation?
• Robust Mean Estimation on Highly Incomplete Data with Arbitrary Outliers