Simone Brugiapaglia | DeepAI

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∙ 06/30/2023

Generalization Limits of Graph Neural Networks in Identity Effects Learning

Graph Neural Networks (GNNs) have emerged as a powerful tool for data-dr...

0 Giuseppe Alessio D'Inverno, et al. ∙

∙ 03/27/2023

Square Root LASSO: Well-posedness, Lipschitz stability and the tuning trade off

This paper studies well-posedness and parameter sensitivity of the Squar...

0 Aaron Berk, et al. ∙

∙ 03/01/2023

The greedy side of the LASSO: New algorithms for weighted sparse recovery via loss function-based orthogonal matching pursuit

We propose a class of greedy algorithms for weighted sparse recovery by ...

0 Sina Mohammad-Taheri, et al. ∙

∙ 11/22/2022

Near-optimal learning of Banach-valued, high-dimensional functions via deep neural networks

The past decade has seen increasing interest in applying Deep Learning (...

0 Ben Adcock, et al. ∙

∙ 08/18/2022

Is Monte Carlo a bad sampling strategy for learning smooth functions in high dimensions?

This paper concerns the approximation of smooth, high-dimensional functi...

0 Ben Adcock, et al. ∙

∙ 07/19/2022

A coherence parameter characterizing generative compressed sensing with Fourier measurements

In Bora et al. (2017), a mathematical framework was developed for compre...

0 Aaron Berk, et al. ∙

∙ 05/13/2022

LASSO reloaded: a variational analysis perspective with applications to compressed sensing

This paper provides a variational analysis of the unconstrained formulat...

0 Aaron Berk, et al. ∙

∙ 03/25/2022

On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples

Sparse polynomial approximation has become indispensable for approximati...

0 Ben Adcock, et al. ∙

∙ 10/28/2021

Iterative and greedy algorithms for the sparsity in levels model in compressed sensing

Motivated by the question of optimal functional approximation via compre...

0 Ben Adcock, et al. ∙

∙ 12/11/2020

Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data

The accurate approximation of scalar-valued functions from sample points...

0 Ben Adcock, et al. ∙

∙ 06/23/2020

The benefits of acting locally: Reconstruction algorithms for sparse in levels signals with stable and robust recovery guarantees

The sparsity in levels model recently inspired a new generation of effec...

0 Ben Adcock, et al. ∙

∙ 05/14/2020

Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs

We study sparse recovery with structured random measurement matrices hav...

0 Simone Brugiapaglia, et al. ∙

∙ 05/09/2020

Generalizing Outside the Training Set: When Can Neural Networks Learn Identity Effects?

Often in language and other areas of cognition, whether two components o...

0 Simone Brugiapaglia, et al. ∙

∙ 03/13/2020

Compressive Isogeometric Analysis

This work is motivated by the difficulty in assembling the Galerkin matr...

0 Simone Brugiapaglia, et al. ∙

∙ 05/24/2019

Do log factors matter? On optimal wavelet approximation and the foundations of compressed sensing

A signature result in compressed sensing is that Gaussian random samplin...

0 Ben Adcock, et al. ∙

∙ 10/25/2018

Sparse approximation of multivariate functions from small datasets via weighted orthogonal matching pursuit

We show the potential of greedy recovery strategies for the sparse appro...

0 Ben Adcock, et al. ∙

∙ 06/11/2018

On oracle-type local recovery guarantees in compressed sensing

We present improved sampling complexity bounds for stable and robust spa...

0 Ben Adcock, et al. ∙

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