Robust High-Dimensional Statistics
Robust High-Dimensional Statistics
复制标题
稳健的高维统计
DOI：
10.1017/9781108637435.023
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
D. Kane
中科院分区：
文献类型：
--
作者：
Ilias Diakonikolas;D. Kane
存在离群值时的学习是统计学中的一个基本问题。直到最近，所有已知的高效无监督学习算法都对高维离群值非常敏感。特别是，即使对于自然分布假设下的鲁棒均值估计任务，也没有已知的有效算法。最近的一系列工作为许多基本统计任务（包括均值和协方差估计）提供了第一个高效的鲁棒估计器。本章介绍了算法高维稳健统计的新兴领域的核心思想和技术，重点是稳健均值估计。
Learning in the presence of outliers is a fundamental problem in statistics. Until recently, all known efficient unsupervised learning algorithms were very sensitive to outliers in high dimensions. In particular, even for the task of robust mean estimation under natural distributional assumptions, no efficient algorithm was known. A recent line of work gave the first efficient robust estimators for a number of fundamental statistical tasks, including mean and covariance estimation. This chapter introduces the core ideas and techniques in the emerging area of algorithmic high-dimensional robust statistics with a focus on robust mean estimation.