General multivariate distributions are notoriously expensive to sample from, particularly the
high-dimensional posterior distributions in PDE-constrained inverse problems. This paper …

We propose a deep importance sampling method that is suitable for estimating rare event
probabilities in high-dimensional problems. We approximate the optimal importance …

We present a novel offline-online method to mitigate the computational burden of the
characterization of posterior random variables in statistical learning. In the offline phase, the …

Low-rank tensor approximations have shown great potential for uncertainty quantification in
high dimensions, for example, to build surrogate models that can be used to speed up large …

Stochastic Galerkin methods for non-affine coefficient representations are known to cause
major difficulties from theoretical and numerical points of view. In this work, an adaptive …

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 …

Deterministic interpolation and quadrature methods are often unsuitable to address
Bayesian inverse problems depending on computationally expensive forward mathematical …

The reconstruction of the structure of biological tissue using electromyographic (EMG) data
is a non-invasive imaging method with diverse medical applications. Mathematically, this …

We consider the problem of the estimation of a high-dimensional probability distribution from
iid samples of the distribution using model classes of functions in tree-based tensor formats …