Estimating the parameters of mathematical models is a common problem in almost all
branches of science. However, this problem can prove notably difficult when processes and …

The curse of dimensionality is a longstanding challenge in Bayesian inference in high
dimensions. In this work, we propose a {projected Stein variational gradient …

Many recent invertible neural architectures are based on coupling block designs where
variables are divided in two subsets which serve as inputs of an easily invertible (usually …

To maximize the utility of seismic imaging and inversion results, we need to compute not
only a final image but also quantify the uncertainty in the image. Although the most thorough …

Projection-free optimization via different variants of the Frank–Wolfe method has become
one of the cornerstones of large scale optimization for machine learning and computational …

This paper presents a novel method for the accurate functional approximation of possibly
highly concentrated probability densities. It is based on the combination of several modern …

Due to their uncertainty quantification, Bayesian solutions to inverse problems are the
framework of choice in applications that are risk averse. These benefits come at the cost of …

I like to thank all the people that supported me during my studies and my doctoral research.
First and foremost I wish to show my gratitude to Martin Eigel for his mentoring and support …

This thesis is concerned with the expressibility of high dimensional densities arising in
Bayesian inverse problems by employing low-rank tensor techniques and controlling the …

The (physical) model gives π (y| x), the conditional probability of observing y given x.
However, to predict, control, optimise or quantify uncertainty, the interest is often really in π …