# Generalization error bounds for kernel matrix completion and extrapolation

## TL;DR

This paper analyzes the generalization error bounds for kernel matrix completion methods that incorporate prior information via reproducing kernel Hilbert spaces, supported by numerical experiments.

## Contribution

It provides theoretical error bounds for kernel-based matrix completion and extrapolation methods, enhancing understanding of their reliability.

## Key findings

- Theoretical error bounds are derived for kernel matrix completion.
- Numerical tests confirm the accuracy of the theoretical bounds.
- Incorporating prior information improves matrix completion performance.

## 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.