4 accepted papers
We study the sample complexity of Bayesian recovery for solving inverse problems with general prior, forward operator and noise distributions. We consider posterior sampling according to an approximate prior $\mathcal{P}$, and establish sufficient conditions for stable and accurate recovery with hig…
This work considers the fundamental problem of learning an unknown object from training data using a given model class. We introduce a framework that allows for objects in arbitrary Hilbert spaces, general types of (random) linear measurements as training data and general types of nonlinear model cl…
Operator learning problems arise in many key areas of scientific computing where Partial Differential Equations (PDEs) are used to model physical systems. In such scenarios, the operators map between Banach or Hilbert spaces. In this work, we tackle the problem of learning operators between Banach s…
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 pointwise samples of the target function. This generalization covers many cases of practical interest, such as data acquired…