Seminar
Convex Validation of Regularized Minimum Hilbert Norm Problems
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Series
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Speaker(s)Paul Schneider (Università della Svizzera Italiana, Switzerland)
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FieldComplexity
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LocationTinbergen Institute, Roeterseiland Campus, E5.07
Amsterdam -
Date and time
September 10, 2026
12:00 - 13:00
AbstractWe study a unifying regularized minimum-Hilbert-norm problem in kernel learning for which we combine training and validation into a single convex optimization problem. For a fixed kernel, a surrogate
(FAV) upper-bounds the validation loss and yields the regularization parameter in closed form. Letting the kernel be free, we learn it jointly with its regularization, either by minimizing the original (exact) validation loss as a box-constrained quadratic program (LEV), or in closed form through an approximate upper bound (LAV). Specializing to kernel ridge regression, we establish consistency and asymptotic distributions. A large-scale nonparametric portfolio exercise using a standard data set establishes a formidable and reproducible benchmark for non-convex approaches such as neural nets.
(FAV) upper-bounds the validation loss and yields the regularization parameter in closed form. Letting the kernel be free, we learn it jointly with its regularization, either by minimizing the original (exact) validation loss as a box-constrained quadratic program (LEV), or in closed form through an approximate upper bound (LAV). Specializing to kernel ridge regression, we establish consistency and asymptotic distributions. A large-scale nonparametric portfolio exercise using a standard data set establishes a formidable and reproducible benchmark for non-convex approaches such as neural nets.