Robust non-parametric regression via incoherent subspace projections

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.