Computable Bernstein Certificates for Cross-Fitted Clipped Covariance Estimation

TL;DR

This paper introduces a data-driven, robust covariance estimator that uses computable Bernstein certificates and cross-fitting to adaptively handle heavy tails and outliers, with theoretical guarantees and practical effectiveness.

Contribution

It proposes a fully computable Bernstein-type deviation certificate for cross-fitted clipped covariance estimation, enabling adaptive, robust covariance estimation under heavy tails and outliers.

Findings

Stable performance on contaminated benchmarks

Competitive accuracy across different regimes

Effective adaptation to intrinsic complexity measures

Abstract

We study operator-norm covariance estimation from heavy-tailed samples that may include a small fraction of arbitrary outliers. A simple and widely used safeguard is \emph{Euclidean norm clipping}, but its accuracy depends critically on an unknown clipping level. We propose a cross-fitted clipped covariance estimator equipped with \emph{fully computable} Bernstein-type deviation certificates, enabling principled data-driven tuning via a selector (\emph{MinUpper}) that balances certified stochastic error and a robust hold-out proxy for clipping bias. The resulting procedure adapts to intrinsic complexity measures such as effective rank under mild tail regularity and retains meaningful guarantees under only finite fourth moments. Experiments on contaminated spiked-covariance benchmarks illustrate stable performance and competitive accuracy across regimes.