33 citations · 141 across the 20 of their papers we have counts for
22 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…
Scale Invariant Interest Points with Shearlets
Miguel A. Duval-Poo, Nicoletta Noceti, Francesca Odone +1
Shearlets are a relatively new directional multi-scale framework for signal analysis, which have been shown effective to enhance signal discontinuities such as edges and corners at…
Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings
Giovanni S. Alberti, Stephan Dahlke, Filippo De Mari +2
The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had…
Continuous and discrete frames generated by the evolution flow of the Schrödinger equation
Giovanni S. Alberti, Stephan Dahlke, Filippo De Mari +2
We study a family of coherent states, called Schrödingerlets, both in the continuous and discrete setting. They are defined in terms of the Schrödinger equation of a free quantum p…
Different faces of the shearlet group
Stefan Dahlke, Filippo De Mari, Ernesto De Vito +3
Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrabl…
Geometric classification of semidirect products in the maximal parabolic subgroup of
Filippo De Mari, Ernesto De Vito, Stefano Vigogna
We classify up to conjugation by (more precisely, block diagonal symplectic matrices) all the semidirect products inside the maximal parabolic of…
Coorbit spaces with voice in a Fréchet space
Stephan Dahlke, Filippo De Mari, Ernesto De Vito +4
We set up a new general coorbit space theory for reproducing representations of a locally compact second countable group that are not necessarily irreducible nor integrable. Ou…
Reproducing subgroups of Sp(2,R). Part II: admissible vectors
Giovanni S. Alberti, Filippo De Mari, Ernesto De Vito +1
In part I we introduced the class of Lie subgroups of and obtained a classification up to conjugation (Theorem 1.1). Here, we determine for which of the…
Learning Sets with Separating Kernels
Ernesto De Vito, Lorenzo Rosasco, Alessandro Toigo
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from th…
An extension of Mercer theorem to vector-valued measurable kernels
Ernesto De Vito, Veronica Umanita`, Silvia Villa
We extend the classical Mercer theorem to reproducing kernel Hilbert spaces whose elements are functions from a measurable space into . Given a finite measure o…
A mock metaplectic representation
Filippo De Mari, Ernesto De Vito
We obtain necessary and sufficient conditions for the admissible vectors of a new unitary non irreducible representation . The group is an arbitrary semidirect product whose…
Reproducing subgroups of . Part I: algebraic classification
Giovanni S. Alberti, Luca Balletti, Filippo De Mari +1
We classify the connected Lie subgroups of the symplectic group whose elements are matrices in block lower triangular form. The classification is up to conjugati…
Quantum Homodyne Tomography as an Informationally Complete Positive Operator Valued Measure
P. Albini, E. De Vito, A. Toigo
We define a positive operator valued measure on describing the measurement of randomly sampled quadratures in quantum homodyne tomography, and we study its pro…
Positive operator valued measures covariant with respect to an irreducible representation
G. Cassinelli, E. De Vito, A. Toigo
Given an irreducible representation of a group G, we show that all the covariant positive operator valued measures based on G/Z, where Z is a central subgroup, are described by tra…
Teleportation of a state in view of the quantum theory of measurement
P. Busch, G. Cassinelli, E. De Vito +2
We give a description of the teleportation of an unknown quantum state which takes into account the action of the measuring device and manifestly avoids any reference to the postul…
Phase space observables and isotypic spaces
G. Cassinelli, E. De Vito, A. Levrero +1
We give necessary and sufficient conditions for the set of Neumark projections of a countable set of phase space observable to constitute a resolution of the identity, and we give…
Group Theoretical Quantum Tomography
G. Cassinelli, G. M. D'Ariano, E. De Vito +1
The paper is devoted to the mathematical foundation of the quantum tomography using the theory of square-integrable representations of unimodular Lie groups.