Fixing an error in Caponnetto and de Vito (2007)
Danica J. Sutherland

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.
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Stochastic Gradient Optimization Techniques · Matrix Theory and Algorithms
