Fixing an error in Caponnetto and de Vito (2007)
This correction addresses a foundational issue in statistical learning theory, ensuring the validity of widely cited results, but it is incremental as it fixes an error rather than introducing new methods.
The paper identifies and corrects an error in the proof of minimax-optimal rates for kernel ridge regression from Caponnetto and de Vito (2007), specifically in the bound on effective dimensionality, and demonstrates that the main theorem still holds.
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.