Recent Advances in Algorithmic High-Dimensional Robust Statistics

TL;DR

This survey reviews recent progress in developing efficient algorithms for high-dimensional robust statistics, focusing on robust mean estimation and broader tasks, highlighting core ideas, techniques, and future directions.

Contribution

It provides a comprehensive overview of recent algorithmic advances in high-dimensional robust statistics, emphasizing new methods for robust mean estimation and related tasks.

Findings

Introduction of core ideas and techniques in robust estimation

Overview of efficient algorithms for high-dimensional tasks

Discussion of future research directions

Abstract

Learning in the presence of outliers is a fundamental problem in statistics. Until recently, all known efficient unsupervised learning algorithms were very sensitive to outliers in high dimensions. In particular, even for the task of robust mean estimation under natural distributional assumptions, no efficient algorithm was known. Recent work in theoretical computer science gave the first efficient robust estimators for a number of fundamental statistical tasks, including mean and covariance estimation. Since then, there has been a flurry of research activity on algorithmic high-dimensional robust estimation in a range of settings. In this survey article, we introduce the core ideas and algorithmic techniques in the emerging area of algorithmic high-dimensional robust statistics with a focus on robust mean estimation. We also provide an overview of the approaches that have led to computationally efficient robust estimators for a range of broader statistical tasks and discuss new directions and opportunities for future work.