7 papers
Near-Optimal Learning of Gaussian Sobolev Operators
Ben Adcock, Michael Griebel, Gregor Maier
A key question in operator learning is how to design surrogate operators with provable approximation guarantees in reasonable computational time. Whereas smooth operators can be ap…
A unified framework for learning with nonlinear model classes from arbitrary linear samples
Ben Adcock, Juan M. Cardenas, Nick Dexter
We study the fundamental problem of learning an unknown object from data using a prescribed model class. We introduce a unified framework that accommodates objects in arbitrary Hil…
Fourier extensions for matrix-function block encodings with error-independent subnormalization bounds
Peter Brearley, Thomas L. Howarth, Thomas Howarth +1
Block encodings of non-unitary matrix functions are central to quantum numerical linear algebra. Hamiltonian simulation is a natural input model for Hermitian matrices, but accurat…
Optimal sampling for least-squares approximation
Ben Adcock
Least-squares approximation is one of the most important methods for recovering an unknown function from data. While in many applications the data is fixed, in many others there is…
The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian Measures
Ben Adcock, Michael Griebel, Gregor Maier
Operator learning, the approximation of mappings between infinite-dimensional function spaces using machine learning, has gained increasing research attention in recent years. Appr…
Function recovery and optimal sampling in the presence of nonuniform evaluation costs
Ben Adcock
We consider recovering a function in an -dimensional linear subspace from i.i.d. pointwise samples via (weighted) least-squares esti…