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Robust Training in High Dimensions via Block Coordinate Geometric Median Descent
arXiv - CS - Distributed, Parallel, and Cluster Computing Pub Date : 2021-06-16 , DOI: arxiv-2106.08882
Anish Acharya, Abolfazl Hashemi, Prateek Jain, Sujay Sanghavi, Inderjit S. Dhillon, Ufuk Topcu

Geometric median (\textsc{Gm}) is a classical method in statistics for achieving a robust estimation of the uncorrupted data; under gross corruption, it achieves the optimal breakdown point of 0.5. However, its computational complexity makes it infeasible for robustifying stochastic gradient descent (SGD) for high-dimensional optimization problems. In this paper, we show that by applying \textsc{Gm} to only a judiciously chosen block of coordinates at a time and using a memory mechanism, one can retain the breakdown point of 0.5 for smooth non-convex problems, with non-asymptotic convergence rates comparable to the SGD with \textsc{Gm}.

中文翻译:

通过块坐标几何中值下降在高维上进行鲁棒训练

几何中值 (\textsc{Gm}) 是统计学中的一种经典方法,用于实现对未损坏数据的稳健估计;在严重腐败下,它达到了 0.5 的最佳分解点。然而,它的计算复杂性使得它对于高维优化问题的随机梯度下降 (SGD) 进行鲁棒化是不可行的。在本文中,我们表明,通过一次仅将 \textsc{Gm} 应用于一个明智选择的坐标块并使用一种记忆机制,对于平滑非凸问题,可以保留 0.5 的分解点,具有非渐近性收敛速度与具有 \textsc{Gm} 的 SGD 相当。
更新日期:2021-06-17
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