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06/01/2023
CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions
We introduce a general framework for active learning in regression probl...
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05/29/2023
Optimal approximation of infinite-dimensional holomorphic functions
Over the last decade, approximating functions in infinite dimensions fro...
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01/05/2023
Restarts subject to approximate sharpness: A parameter-free and optimal scheme for first-order methods
Sharpness is an almost generic assumption in continuous optimization tha...
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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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11/22/2022
Stable and accurate least squares radial basis function approximations on bounded domains
The computation of global radial basis function (RBF) approximations req...
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08/25/2022
CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning
The problem of approximating smooth, multivariate functions from sample ...
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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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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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03/02/2022
Stable, accurate and efficient deep neural networks for inverse problems with analysis-sparse models
Solving inverse problems is a fundamental component of science, engineer...
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02/04/2022
Towards optimal sampling for learning sparse approximation in high dimensions
In this chapter, we discuss recent work on learning sparse approximation...
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01/31/2022
An Adaptive sampling and domain learning strategy for multivariate function approximation on unknown domains
Many problems in computational science and engineering can be described ...
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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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10/07/2021
On the possibility of fast stable approximation of analytic functions from equispaced samples via polynomial frames
We consider approximating analytic functions on the interval [-1,1] from...
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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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09/17/2020
Improved recovery guarantees and sampling strategies for TV minimization in compressive imaging
In this paper, we consider the use of Total Variation (TV) minimization ...
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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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01/16/2020
The gap between theory and practice in function approximation with deep neural networks
Deep learning (DL) is transforming whole industries as complicated decis...
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01/05/2020
The troublesome kernel: why deep learning for inverse problems is typically unstable
There is overwhelming empirical evidence that Deep Learning (DL) leads t...
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01/03/2020
Frame approximation with bounded coefficients
Due to their flexibility, frames of Hilbert spaces are attractive altern...
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08/04/2019
Optimal sampling strategies for multivariate function approximation on general domains
In this paper, we address the problem of approximating a multivariate fu...
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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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04/30/2019
Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling
Infinite-dimensional compressed sensing deals with the recovery of analo...
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02/21/2019
Convolutional Analysis Operator Learning: Dependence on Training Data
Convolutional analysis operator learning (CAOL) enables the unsupervised...
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02/14/2019
On instabilities of deep learning in image reconstruction - Does AI come at a cost?
Deep learning, due to its unprecedented success in tasks such as image c...
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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