论文标题
通过$ \ ell_0 $最小化在高维度中的强大平均估计
Robust Mean Estimation in High Dimensions via $\ell_0$ Minimization
论文作者
论文摘要
我们研究了高维度的鲁棒平均估计问题，其中$α<0.5 $的数据点可以被任意损坏。通过压缩感应，我们将鲁棒的平均估计问题提出，因为在第二刻（第二刻）限制下，在嵌入式数据点上，离群指标向量的$ \ ell_0 $ - “ norm”。我们证明，该目标的全球最低限度是适合鲁棒平均估计问题的最佳订单，我们提出了一个最小化目标的一般框架。我们进一步利用$ \ ell_1 $和$ \ ell_p $ $（0 <p <1）$，最小化压缩感应中的最小化技术，为$ \ ell_0 $最小化问题提供计算上可拖动的解决方案。合成和真实数据实验都表明，所提出的算法显着超过了最先进的鲁棒均值估计方法。
We study the robust mean estimation problem in high dimensions, where $α<0.5$ fraction of the data points can be arbitrarily corrupted. Motivated by compressive sensing, we formulate the robust mean estimation problem as the minimization of the $\ell_0$-`norm' of the outlier indicator vector, under second moment constraints on the inlier data points. We prove that the global minimum of this objective is order optimal for the robust mean estimation problem, and we propose a general framework for minimizing the objective. We further leverage the $\ell_1$ and $\ell_p$ $(0<p<1)$, minimization techniques in compressive sensing to provide computationally tractable solutions to the $\ell_0$ minimization problem. Both synthetic and real data experiments demonstrate that the proposed algorithms significantly outperform state-of-the-art robust mean estimation methods.
