Generalization Error Bounds for Kernel Matrix Completion and Extrapolation

Abstract

Prior information can be incorporated in matrix completion to improve estimation accuracy and extrapolate the missing entries. Reproducing kernel Hilbert spaces provide tools to leverage the said prior information, and derive more reliable algorithms. This paper analyzes the generalization error of such approaches, and presents numerical tests confirming the theoretical results.

Passive sampling in reproducing kernel Hilbert spaces using leverage scores

“…, and (11) shows that it can only be zero when f ∈ H s so that Pf = f . Therefore, in order to have zero error for any f ∈ H N , then…”

“…Furthermore, the impact of noisy samples is diminished. This paper addresses passive sampling for function approximation in a reproducing kernel Hilbert space (RKHS), with a focus on kernel ridge regression (KRR) [9]- [11]. To do so, a functional analysis is conducted which connects the concept of optimal sampling to the Nyström approximation [12] -a low-rank approximation to the kernel matrix built from a subset of its columns.…”