46 citations · 112 across the 16 of their papers we have counts for
18 papers
Into the danger zone: stable extrapolation in high-dimensional function and operator learning
Ben Adcock, Simone Brugiapaglia, Xuemeng Wang
Out-of-distribution (OOD) generalization is a central challenge in scientific machine learning. We study regression problems in which the test distribution differs from the trainin…
Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximation
Anastasis Kratsios, Simone Brugiapaglia, Bum Jun Kim +2
Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes. While powerful, this perspective is incomplete: it primarily capture…
The devil in the (de)tails: an improved recovery guarantee for sparse approximation
Ben Adcock, Simone Brugiapaglia, Avi Gupta
Many functions exhibit approximate sparsity in their coefficients with respect to a given dictionary. In recent literature, sparse approximation in such a dictionary from i.i.d. po…
Learning smooth functions in high dimensions: from sparse polynomials to deep neural networks
Ben Adcock, Simone Brugiapaglia, Nick Dexter +1
Learning approximations to smooth target functions of many variables from finite sets of pointwise samples is an important task in scientific computing and its many applications in…
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…
Monte Carlo is a good sampling strategy for polynomial approximation in high dimensions
Ben Adcock, Simone Brugiapaglia
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computationa…
A coherence parameter characterizing generative compressed sensing with Fourier measurements
Aaron Berk, Simone Brugiapaglia, Babhru Joshi +3
In Bora et al. (2017), a mathematical framework was developed for compressed sensing guarantees in the setting where the measurement matrix is Gaussian and the signal structure is…
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…
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…
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…
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…
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…
Sparse approximation of multivariate functions from small datasets via weighted orthogonal matching pursuit
Ben Adcock, Simone Brugiapaglia
We show the potential of greedy recovery strategies for the sparse approximation of multivariate functions from a small dataset of pointwise evaluations by considering an extension…
On oracle-type local recovery guarantees in compressed sensing
Ben Adcock, Claire Boyer, Simone Brugiapaglia
We present improved sampling complexity bounds for stable and robust sparse recovery in compressed sensing. Our unified analysis based on l1 minimization encompasses the case where…
Correcting for unknown errors in sparse high-dimensional function approximation
Ben Adcock, Anyi Bao, Simone Brugiapaglia
We consider sparsity-based techniques for the approximation of high-dimensional functions from random pointwise evaluations. To date, almost all the works published in this field c…
Robustness to unknown error in sparse regularization
Simone Brugiapaglia, Ben Adcock
Quadratically-constrained basis pursuit has become a popular device in sparse regularization; in particular, in the context of compressed sensing. However, the majority of theoreti…
Compressed sensing approaches for polynomial approximation of high-dimensional functions
Ben Adcock, Simone Brugiapaglia, Clayton G. Webster
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of rece…
Recovery guarantees for compressed sensing with unknown errors
Simone Brugiapaglia, Ben Adcock, Richard K. Archibald
From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarant…