795 citations · 1.4k across the 64 of their papers we have counts for
66 papers
On the consistent reasoning paradox of intelligence and optimal trust in AI: The power of 'I don't know'
Alexander Bastounis, Paolo Campodonico, Mihaela van der Schaar +2
We introduce the Consistent Reasoning Paradox (CRP). Consistent reasoning, which lies at the core of human intelligence, is the ability to handle tasks that are equivalent, yet des…
Optimal approximation of infinite-dimensional holomorphic functions II: recovery from i.i.d. pointwise samples
Ben Adcock, Nick Dexter, Sebastian Moraga
Infinite-dimensional, holomorphic functions have been studied in detail over the last several decades, due to their relevance to parametric differential equations and computational…
CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions
Ben Adcock, Juan M. Cardenas, Nick Dexter
We introduce a general framework for active learning in regression problems. Our framework extends the standard setup by allowing for general types of data, rather than merely poin…
Optimal approximation of infinite-dimensional holomorphic functions
Ben Adcock, Nick Dexter, Sebastian Moraga
Over the last decade, approximating functions in infinite dimensions from samples has gained increasing attention in computational science and engineering, especially in computatio…
Restarts subject to approximate sharpness: A parameter-free and optimal scheme for first-order methods
Ben Adcock, Matthew J. Colbrook, Maksym Neyra-Nesterenko
Sharpness is an almost generic assumption in continuous optimization that bounds the distance from minima by objective function suboptimality. It facilitates the acceleration of fi…
Stable and accurate least squares radial basis function approximations on bounded domains
Ben Adcock, Daan Huybrechs, Cécile Piret
The computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-condition…
Near-optimal learning of Banach-valued, high-dimensional functions via deep neural networks
Ben Adcock, Simone Brugiapaglia, Nick Dexter +1
The past decade has seen increasing interest in applying Deep Learning (DL) to Computational Science and Engineering (CSE). Driven by impressive results in applications such as com…
CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning
Ben Adcock, Juan M. Cardenas, Nick Dexter
The problem of approximating smooth, multivariate functions from sample points arises in many applications in scientific computing, e.g., in computational Uncertainty Quantificatio…
On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples
Ben Adcock, Simone Brugiapaglia, Nick Dexter +1
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational…
NESTANets: Stable, accurate and efficient neural networks for analysis-sparse inverse problems
Maksym Neyra-Nesterenko, Ben Adcock
Solving inverse problems is a fundamental component of science, engineering and mathematics. With the advent of deep learning, deep neural networks have significant potential to ou…
Towards optimal sampling for learning sparse approximation in high dimensions
Ben Adcock, Juan M. Cardenas, Nick Dexter +1
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert…
An Adaptive sampling and domain learning strategy for multivariate function approximation on unknown domains
Ben Adcock, Juan M. Cardenas, Nick Dexter
Many problems in computational science and engineering can be described in terms of approximating a smooth function of variables, defined over an unknown domain of interest $Ω\…
Iterative and greedy algorithms for the sparsity in levels model in compressed sensing
Ben Adcock, Simone Brugiapaglia, Matthew King-Roskamp
Motivated by the question of optimal functional approximation via compressed sensing, we propose generalizations of the Iterative Hard Thresholding and the Compressive Sampling Mat…
Fast and stable approximation of analytic functions from equispaced samples via polynomial frames
Ben Adcock, Alexei Shadrin
We consider approximating analytic functions on the interval from their values at a set of equispaced nodes. A result of Platte, Trefethen \& Kuijlaars states that f…
Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data
Ben Adcock, Simone Brugiapaglia, Nick Dexter +1
Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged…
Improved recovery guarantees and sampling strategies for TV minimization in compressive imaging
Ben Adcock, Nick Dexter, Qinghong Xu
In this paper, we consider the use of Total Variation (TV) minimization for compressive imaging; that is, image reconstruction from subsampled measurements. Focusing on two importa…
The benefits of acting locally: Reconstruction algorithms for sparse in levels signals with stable and robust recovery guarantees
Ben Adcock, Simone Brugiapaglia, Matthew King-Roskamp
The sparsity in levels model recently inspired a new generation of effective acquisition and reconstruction modalities for compressive imaging. Moreover, it naturally arises in var…
The gap between theory and practice in function approximation with deep neural networks
Ben Adcock, Nick Dexter
Deep learning (DL) is transforming industry as decision-making processes are being automated by deep neural networks (DNNs) trained on real-world data. Driven partly by rapidly-exp…
The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems
Nina M. Gottschling, Vegard Antun, Anders C. Hansen +1
Methods inspired by Artificial Intelligence (AI) are starting to fundamentally change computational science and engineering through breakthrough performances on challenging problem…
Frame approximation with bounded coefficients
Ben Adcock, Mohsen Seifi
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or ev…
Near-optimal sampling strategies for multivariate function approximation on general domains
Ben Adcock, Juan M. Cardenas
In this paper, we address the problem of approximating a multivariate function defined on a general domain in dimensions from sample points. We consider weighted least-squares…
Do log factors matter? On optimal wavelet approximation and the foundations of compressed sensing
Ben Adcock, Simone Brugiapaglia, Matthew King-Roskamp
A signature result in compressed sensing is that Gaussian random sampling achieves stable and robust recovery of sparse vectors under optimal conditions on the number of measuremen…
Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling
Ben Adcock, Vegard Antun, Anders C. Hansen
Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier…
On instabilities of deep learning in image reconstruction - Does AI come at a cost?
Vegard Antun, Francesco Renna, Clarice Poon +2
Deep learning, due to its unprecedented success in tasks such as image classification, has emerged as a new tool in image reconstruction with potential to change the field. In this…