This paper establishes the algorithmic principle of alternating projections onto incoherent low-rank subspaces (APIS) as a unifying principle for designing robust regression algorithms that offer consistent model recovery even when a significant fraction of training points are corrupted by an adaptive adversary. APIS offers the first algorithm for robust non-parametric (kernel) regression with an explicit breakdown point that works for general PSD kernels under minimal assumptions. APIS also offers, as straightforward corollaries, robust algorithms for a much wider variety of well-studied settings, including robust linear regression, robust sparse recovery, and robust Fourier transforms. Algorithms offered by APIS enjoy formal guarantees that are frequently sharper than (especially in non-parametric settings) or competitive to existing results in these settings. They are also straightforward to implement and outperform existing algorithms in several experimental settings.

本文建立了交替投影到非相干低秩子空间 ( APIS )的算法原理，作为设计鲁棒回归算法的统一原则，即使在很大一部分训练点被自适应对手破坏时，该算法也能提供一致的模型恢复。APIS提供了第一个稳健的非参数（核）回归算法，具有明确的分解点，在最小假设下适用于一般 PSD 核。作为直接推论，APIS还为更广泛的研究设置提供了稳健的算法，包括稳健的线性回归、稳健的稀疏恢复和稳健的傅立叶变换。APIS提供的算法享受通常比这些设置中的现有结果（尤其是在非参数设置中）或与现有结果更具竞争力的正式保证。它们在几个实验设置中也很容易实现和优于现有算法。