Generalization error bounds for kernel matrix completion and extrapolation
This work addresses matrix completion for data analysis, but it appears incremental as it builds on existing kernel methods.
The paper tackles the problem of improving matrix completion accuracy and extrapolation by incorporating prior information using reproducing kernel Hilbert spaces, and it presents theoretical generalization error bounds with numerical confirmation.
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.