The Broader Landscape of Robustness in Algorithmic Statistics

TL;DR

This paper surveys recent advances in robust statistical algorithms, highlighting their connections across different robustness types like contamination, heavy tails, and privacy, with a focus on mean estimation.

Contribution

It unifies various robustness approaches under common algorithmic frameworks, revealing their shared underlying ideas and computational efficiencies.

Findings

Robust mean estimation algorithms are connected across different robustness settings.

Shared algorithmic principles enable efficient solutions for contamination, heavy tails, and privacy.

The survey clarifies conceptual links between diverse robustness methods.

Abstract

The last decade has seen a number of advances in computationally efficient algorithms for statistical methods subject to robustness constraints. An estimator may be robust in a number of different ways: to contamination of the dataset, to heavy-tailed data, or in the sense that it preserves privacy of the dataset. We survey recent results in these areas with a focus on the problem of mean estimation, drawing technical and conceptual connections between the various forms of robustness, showing that the same underlying algorithmic ideas lead to computationally efficient estimators in all these settings.