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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...
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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...
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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 ...
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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 (...
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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...
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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...
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05/13/2022
LASSO reloaded: a variational analysis perspective with applications to compressed sensing
This paper provides a variational analysis of the unconstrained formulat...
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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...
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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...
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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...
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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...
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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...
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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...
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03/13/2020
Compressive Isogeometric Analysis
This work is motivated by the difficulty in assembling the Galerkin matr...
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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...
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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...
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06/11/2018