High-Dimensional Robust Mean Estimation via Outlier-Sparsity Minimization
High-Dimensional Robust Mean Estimation via Outlier-Sparsity Minimization
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DOI：
10.1109/ieeeconf53345.2021.9723212
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
Aditya Deshmukh;Jing Liu;V. Veeravalli
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文献类型：
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作者：
Aditya Deshmukh;Jing Liu;V. Veeravalli
我们研究了高维中的稳健均值估计问题，其中只有不到一半的数据点可以被任意破坏。在压缩感知的启发下，我们将稳健均值估计问题描述为在数据点的二次矩约束下，离群点指示向量的ℓ0‘范数’的最小化。我们进一步将目标中的ℓ0-‘范数’放宽为ℓp-范数(0<；p-≤1)，并证明了对于稳健均值估计问题，每个目标的全局极小值是阶最优的。然后，基于所提出的优化问题，提出了一种易于计算的迭代ℓp-最小化和硬阈值算法。实验结果表明，该算法的性能优于现有的稳健均值估计方法。
We study the robust mean estimation problem in high dimensions, where less than half of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, we formulate the robust mean estimation problem as the minimization of the ℓ0-‘norm’ of an outlier indicator vector, under a second moment constraint on the datapoints. We further relax the ℓ0-‘norm’ to the ℓp-norm (0 < p ≤ 1) in the objective and prove that the global minima for each of these objectives are order-optimal for the robust mean estimation problem. Then we propose a computationally tractable iterative ℓp-minimization and hard thresholding algorithm based on the proposed optimization problems. Empirical studies demonstrate that the proposed algorithm outperforms state-of-the-art robust mean estimation methods.