Abstract The Pairwise Conditional Gradients (PCG) algorithm is a powerful extension of the
Frank-Wolfe algorithm leading to particularly sparse solutions, which makes PCG very …

Calculation of Bayesian posteriors and model evidences typically requires numerical
integration. Bayesian quadrature (BQ), a surrogate-model-based approach to numerical …

Stein discrepancies have emerged as a powerful tool for retrospective improvement of
Markov chain Monte Carlo output. However, the question of how to design Markov chains …

We study kernel quadrature rules with convex weights. Our approach combines the spectral
properties of the kernel with recombination results about point measures. This results in …

Bayesian probabilistic numerical methods for numerical integration offer significant
advantages over their non-Bayesian counterparts: they can encode prior information about …

We study a quadrature, proposed by Ermakov and Zolotukhin in the sixties, through the lens
of kernel methods. The nodes of this quadrature rule follow the distribution of a …

This paper studies function approximation in Gaussian Sobolev spaces over the real line
and measures the error in a Gaussian-weighted $ L^ p $-norm. We construct two linear …

In recent years finite tensor products of reproducing kernel Hilbert spaces (RKHSs) of
Gaussian kernels on the one hand and of Hermite spaces on the other hand have been …

The Pairwise Conditional Gradients (PCG) algorithm is a powerful extension of the Frank-
Wolfe algorithm leading to particularly sparse solutions, which makes PCG very appealing …

These lectures concern the discrete approximation of objects that are in some sense infinite-
dimensional. This problem is ubiquitous to numerical computation in general. Specifically …