Ben Adcock | DeepAI

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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...

0 Ben Adcock, et al. ∙

∙ 05/29/2023

Optimal approximation of infinite-dimensional holomorphic functions

Over the last decade, approximating functions in infinite dimensions fro...

0 Ben Adcock, et al. ∙

∙ 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...

0 Ben Adcock, 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. ∙

∙ 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...

0 Ben Adcock, et al. ∙

∙ 08/25/2022

CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning

The problem of approximating smooth, multivariate functions from sample ...

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. ∙

∙ 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. ∙

∙ 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...

0 Maksym Neyra-Nesterenko, et al. ∙

∙ 02/04/2022

Towards optimal sampling for learning sparse approximation in high dimensions

In this chapter, we discuss recent work on learning sparse approximation...

0 Ben Adcock, et al. ∙

∙ 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 ...

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. ∙

∙ 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...

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. ∙

∙ 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 ...

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. ∙

∙ 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...

0 Ben Adcock, et al. ∙

∙ 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...

7 Nina M. Gottschling, et al. ∙

∙ 01/03/2020

Frame approximation with bounded coefficients

Due to their flexibility, frames of Hilbert spaces are attractive altern...

0 Ben Adcock, et al. ∙

∙ 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...

0 Ben Adcock, 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. ∙

∙ 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...

0 Ben Adcock, et al. ∙

∙ 02/21/2019

Convolutional Analysis Operator Learning: Dependence on Training Data

Convolutional analysis operator learning (CAOL) enables the unsupervised...

0 Il Yong Chun, et al. ∙

∙ 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...

14 Vegard Antun, 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. ∙