Robust High-Dimensional Mean Estimation With Low Data Size, an Empirical Study

TL;DR

This paper empirically investigates high-dimensional mean estimation methods under low data size conditions, highlighting practical challenges and performance in real-world scenarios with corrupted data.

Contribution

It provides an extensive experimental comparison of robust mean estimation techniques in high-dimensional, low-data regimes, an area with limited practical evaluation.

Findings

Certain algorithms perform better with limited data

Trade-offs between robustness and data efficiency are observed

Empirical results challenge some theoretical assumptions

Abstract

Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for efficiently estimating the mean in high dimensions on corrupted data. While several algorithms have been proposed that achieve near-optimal error, they all rely on large data size requirements as a function of dimension. In this paper, we perform an extensive experimentation over various mean estimation techniques where data size might not meet this requirement due to the high-dimensional setting.