Robust Low-Complexity Randomized Methods for Locating Outliers in Large Matrices

TL;DR

This paper introduces a randomized two-step framework for accurately identifying outlier columns in large, noisy, or incomplete matrices, with proven theoretical guarantees and demonstrated computational efficiency.

Contribution

It proposes a novel randomized inference method with theoretical sample complexity bounds for outlier detection in large matrices.

Findings

The method accurately locates outliers with high probability.

The approach is computationally efficient for large-scale data.

Theoretical bounds are validated through numerical experiments.

Abstract

This paper examines the problem of locating outlier columns in a large, otherwise low-rank matrix, in settings where {}{the data} are noisy, or where the overall matrix has missing elements. We propose a randomized two-step inference framework, and establish sufficient conditions on the required sample complexities under which these methods succeed (with high probability) in accurately locating the outliers for each task. Comprehensive numerical experimental results are provided to verify the theoretical bounds and demonstrate the computational efficiency of the proposed algorithm.