# Computable Bernstein Certificates for Cross-Fitted Clipped Covariance Estimation

arXiv: https://arxiv.org/abs/2602.14020 · HTML: https://mlsanity.com/paper/2602.14020/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 15 Feb 2026.

## Builds on (most cited first, 6 of 6)

- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Robust Covariance and Scatter Matrix Estimation under Huber's Contamination Model](https://mlsanity.com/paper/1506.00691/) (2015)
- [Faster Algorithms for High-Dimensional Robust Covariance Estimation](https://mlsanity.com/paper/1906.04661/) (2019)
- [User-Friendly Covariance Estimation for Heavy-Tailed Distributions](https://mlsanity.com/paper/1811.01520/) (2018)
- [Covariance Estimation: Optimal Dimension-free Guarantees for Adversarial Corruption and Heavy Tails](https://mlsanity.com/paper/2205.08494/) (2022)

## Abstract (arXiv)

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 Euclidean norm clipping, but its accuracy depends critically on an unknown clipping level. We propose a cross-fitted clipped covariance estimator equipped with fully computable Bernstein-type deviation certificates, enabling principled data-driven tuning via a selector (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.