论文标题
通过稳定性和次高斯的稳健估计值
Outlier Robust Mean Estimation with Subgaussian Rates via Stability
论文作者
论文摘要
我们研究了有限的协方差假设下的鲁棒高维平均估计的问题，并且在有限的低度力矩假设下更广泛地研究。我们考虑了来自最近的强大统计文献中的标准稳定性条件，并证明，除了指数较小的故障概率外，还存在满足此条件的大部分插入物。作为推论，因此，许多最近开发的用于鲁棒平均估计的算法，包括迭代过滤和非凸梯度下降，给出了（接近）subgaussian速率的最佳误差估计器。对这些算法的先前分析给出了显着的次优率。作为我们方法的必然性，我们在有限的协方差假设下获得了强烈污染模型中的第一个计算有效算法，用于subgaussian速率的次数率。
We study the problem of outlier robust high-dimensional mean estimation under a finite covariance assumption, and more broadly under finite low-degree moment assumptions. We consider a standard stability condition from the recent robust statistics literature and prove that, except with exponentially small failure probability, there exists a large fraction of the inliers satisfying this condition. As a corollary, it follows that a number of recently developed algorithms for robust mean estimation, including iterative filtering and non-convex gradient descent, give optimal error estimators with (near-)subgaussian rates. Previous analyses of these algorithms gave significantly suboptimal rates. As a corollary of our approach, we obtain the first computationally efficient algorithm with subgaussian rate for outlier-robust mean estimation in the strong contamination model under a finite covariance assumption.
