提出可计算的偏差证书，实现鲁棒协方差估计的自动调参。
Computable Bernstein Certificates for Cross-Fitted Clipped Covariance Estimation
- 通过交叉拟合与可计算的伯恩斯坦证书，实现自适应裁剪。
- 在仅四阶矩有限下仍保持有效保证，有效秩自适应。
- 适合含异常值的高维数据，尤其适用于稳健统计分析。
我们研究从重尾样本中进行算子范数协方差估计，样本中可能包含少量任意异常值。一种简单且广泛使用的防护方法是欧几里得范数裁剪，但其精度严重依赖于未知的裁剪阈值。本文提出一种交叉拟合的裁剪协方差估计器，配备完全可计算的伯恩斯坦型偏差证书，使基于选择器（MinUpper）的原理性数据驱动调参成为可能，该选择器平衡了经认证的随机误差与对裁剪偏差的稳健留出代理。所得方法在温和尾部正则性条件下自适应于有效秩等内在复杂度度量，并在仅需四阶矩有限时仍保持有意义的保证。在污染的尖峰协方差基准上的实验表明，该方法在不同场景下均表现出稳定性能和竞争力的准确性。
原文摘要 · Abstract (English)
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.
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