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