2 citations · 8 across the 16 of their papers we have counts for
19 papers
Fractal and Regular Geometry of Deep Neural Networks
Simmaco Di Lillo, Domenico Marinucci, Michele Salvi +1
We study the geometric properties of random neural networks by investigating the boundary volumes of their excursion sets for different activation functions, as the depth increases…
A Lipschitz spaces view of infinitely wide shallow neural networks
Francesca Bartolucci, Marcello Carioni, José A. Iglesias +3
We revisit the mean field parametrization of shallow neural networks, using signed measures on unbounded parameter spaces and duality pairings that take into account the regularity…
Spectral complexity of deep neural networks
Simmaco Di Lillo, Domenico Marinucci, Michele Salvi +1
It is well-known that randomly initialized, push-forward, fully-connected neural networks weakly converge to isotropic Gaussian processes, in the limit where the width of all layer…
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…
A Quantitative Functional Central Limit Theorem for Shallow Neural Networks
Valentina Cammarota, Domenico Marinucci, Michele Salvi +1
We prove a Quantitative Functional Central Limit Theorem for one-hidden-layer neural networks with generic activation function. The rates of convergence that we establish depend he…
How many samples are needed to leverage smoothness?
Vivien Cabannes, Stefano Vigogna
A core principle in statistical learning is that smoothness of target functions allows to break the curse of dimensionality. However, learning a smooth function seems to require en…
A Case of Exponential Convergence Rates for SVM
Vivien Cabannes, Stefano Vigogna
Classification is often the first problem described in introductory machine learning classes. Generalization guarantees of classification have historically been offered by Vapnik-C…
Multiclass learning with margin: exponential rates with no bias-variance trade-off
Stefano Vigogna, Giacomo Meanti, Ernesto De Vito +1
We study the behavior of error bounds for multiclass classification under suitable margin conditions. For a wide variety of methods we prove that the classification error under a h…
Understanding neural networks with reproducing kernel Banach spaces
Francesca Bartolucci, Ernesto De Vito, Lorenzo Rosasco +1
Characterizing the function spaces corresponding to neural networks can provide a way to understand their properties. In this paper we discuss how the theory of reproducing kernel…
ParK: Sound and Efficient Kernel Ridge Regression by Feature Space Partitions
Luigi Carratino, Stefano Vigogna, Daniele Calandriello +1
We introduce ParK, a new large-scale solver for kernel ridge regression. Our approach combines partitioning with random projections and iterative optimization to reduce space and t…
Multiscale regression on unknown manifolds
Wenjing Liao, Mauro Maggioni, Stefano Vigogna
We consider the regression problem of estimating functions on but supported on a -dimensional manifold with . Draw…
Construction and Monte Carlo estimation of wavelet frames generated by a reproducing kernel
Ernesto De Vito, Zeljko Kereta, Valeriya Naumova +2
We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproduc…
Estimating multi-index models with response-conditional least squares
Timo Klock, Alessandro Lanteri, Stefano Vigogna
The multi-index model is a simple yet powerful high-dimensional regression model which circumvents the curse of dimensionality assuming for s…
Conditional regression for single-index models
Alessandro Lanteri, Mauro Maggioni, Stefano Vigogna
The single-index model is a statistical model for intrinsic regression where responses are assumed to depend on a single yet unknown linear combination of the predictors, allowing…
Monte Carlo wavelets: a randomized approach to frame discretization
Zeljko Kereta, Stefano Vigogna, Valeriya Naumova +2
In this paper we propose and study a family of continuous wavelets on general domains, and a corresponding stochastic discretization that we call Monte Carlo wavelets. First, using…
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…
Intrinsic Localization of Anisotropic Frames II: -Molecules
Philipp Grohs, Stefano Vigogna
This article is a continuation of the recent paper [Grohs, Intrinsic localization of anisotropic frames, ACHA, 2013], where off-diagonal-decay properties (often referred to as 'loc…
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…