6 papers
PIKS: Universal Physics-Informed Kernel Methods
Joachim Bona-Pellissier, Giacomo Meanti, Matteo Santacesaria +1
Physics-informed machine learning incorporates physical principles --often expressed via differential operators-- into data-driven models. While physics-informed neural networks (P…
Learning Multi-Index Models with Hyper-Kernel Ridge Regression
Shuo Huang, Hippolyte Labarrière, Ernesto De Vito +2
Deep neural networks excel in high-dimensional problems, outperforming models such as kernel methods, which suffer from the curse of dimensionality. However, the theoretical founda…
Learning functions, operators and dynamical systems with kernels
Lorenzo Rosasco
This expository article presents the approach to statistical machine learning based on reproducing kernel Hilbert spaces. The basic framework is introduced for scalar-valued learni…
Computational Efficiency under Covariate Shift in Kernel Ridge Regression
Andrea Della Vecchia, Arnaud Mavakala Watusadisi, Ernesto De Vito +1
This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised l…
Learning convolution operators on compact Abelian groups
Emilia Magnani, Ernesto De Vito, Philipp Hennig +1
We consider the problem of learning convolution operators associated to compact Abelian groups. We study a regularization-based approach and provide corresponding learning guarante…
Neural reproducing kernel Banach spaces and representer theorems for deep networks
Francesca Bartolucci, Ernesto De Vito, Lorenzo Rosasco +1
Characterizing the function spaces defined by neural networks helps understanding the corresponding learning models and their inductive bias. While in some limits neural networks c…