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Overall Objectives
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Bibliography
Overall Objectives
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Bibliography


Section: New Results

Optimal rates for spectral algorithms with least-squares regression over Hilbert spaces

In [12], we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral-regularized algorithms, including ridge regression, principal component analysis, and gradient methods. We prove optimal, high-probability convergence results in terms of variants of norms for the studied algorithms, considering a capacity assumption on the hypothesis space and a general source condition on the target function. Consequently, we obtain almost sure convergence results with optimal rates. Our results improve and generalize previous results, filling a theoretical gap for the non-attainable cases.