论文标题
协方差估计：对对抗性腐败和重型尾巴的最佳无维度保证
Covariance Estimation: Optimal Dimension-free Guarantees for Adversarial Corruption and Heavy Tails
论文作者
论文摘要
We provide an estimator of the covariance matrix that achieves the optimal rate of convergence (up to constant factors) in the operator norm under two standard notions of data contamination: We allow the adversary to corrupt an $η$-fraction of the sample arbitrarily, while the distribution of the remaining data points only satisfies that the $L_{p}$-marginal moment with some $p \ge 4$ is equivalent to the corresponding $ l_2 $ - 麦格纳时刻。尽管只需要几点时刻，但我们的估计器还是达到相同的尾巴估计，就好像基础分布是高斯。作为我们分析的一部分，我们证明了政权$ p> 4 $中的无维度的bai-yin型定理。
We provide an estimator of the covariance matrix that achieves the optimal rate of convergence (up to constant factors) in the operator norm under two standard notions of data contamination: We allow the adversary to corrupt an $η$-fraction of the sample arbitrarily, while the distribution of the remaining data points only satisfies that the $L_{p}$-marginal moment with some $p \ge 4$ is equivalent to the corresponding $L_2$-marginal moment. Despite requiring the existence of only a few moments, our estimator achieves the same tail estimates as if the underlying distribution were Gaussian. As a part of our analysis, we prove a dimension-free Bai-Yin type theorem in the regime $p > 4$.
