7 papers
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…
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…
Continuous Wavelet Frames on the Sphere: The Group-Theoretic Approach Revisited
S. Dahlke, F. De Mari, E. De Vito +5
In \cite{AV99}, Antoine and Vandergheynst propose a group-theoretic approach to continuous wavelet frames on the sphere. The frame is constructed from a single so-called admissible…
The Nyström method for convex loss functions
Andrea Della Vecchia, Ernesto De Vito, Jaouad Mourtada +1
We investigate an extension of classical empirical risk minimization, where the hypothesis space consists of a random subspace within a given Hilbert space. Specifically, we examin…
Interpolation and Learning with Scale Dependent Kernels
Nicolò Pagliana, Alessandro Rudi, Ernesto De Vito +1
We study the learning properties of nonparametric ridge-less least squares. In particular, we consider the common case of estimators defined by scale dependent kernels, and focus o…
A Machine Learning Approach to Optimal Tikhonov Regularisation I: Affine Manifolds
Ernesto De Vito, Massimo Fornasier, Valeriya Naumova
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficu…