Fixing an error in Caponnetto and de Vito (2007)

TL;DR

This paper identifies and corrects an error in the proof of a seminal work on kernel ridge regression, confirming that the main results remain valid after correction.

Contribution

It corrects a bound on effective dimensionality in Caponnetto and de Vito's 2007 paper, ensuring the validity of their minimax-optimal rates.

Findings

Corrected the bound on effective dimensionality

Confirmed the main theorem remains valid

Ensured the robustness of prior minimax rates

Abstract

The seminal paper of Caponnetto and de Vito (2007) provides minimax-optimal rates for kernel ridge regression in a very general setting. Its proof, however, contains an error in its bound on the effective dimensionality. In this note, we explain the mistake, provide a correct bound, and show that the main theorem remains true.