As data is a predominant resource in applications, Riemannian geometry is a natural
framework to model and unify complex nonlinear sources of data. However, the …

This paper proposes and studies a numerical method for approximation of posterior
expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size …

In this chapter, we identify fundamental geometric structures that underlie the problems of
sampling, optimization, inference, and adaptive decision-making. Based on this …

A complete recipe of measure-preserving diffusions in Euclidean space was recently
derived unifying several MCMC algorithms into a single framework. In this paper, we …

Optimization tasks are crucial in statistical machine learning. Recently, there has been great
interest in leveraging tools from dynamical systems to derive accelerated and robust …

Stochastically evolving geometric systems are studied in shape analysis and computational
anatomy for modeling random evolutions of human organ shapes. The notion of geodesic …

Abstract Hamiltonian Monte Carlo and its descendants have found success in machine
learning and computational statistics due to their ability to draw samples in high dimensions …

In this thesis we build a geometric theory of Hamiltonian Monte Carlo, with an emphasis on
symmetries and its bracket generalisations, construct the canonical geometry of smooth …

It is well-known that irreversible MCMC algorithms converge faster to their stationary
distributions than reversible ones. Using the special geometric structure of Lie …

In this paper we show that the Hamiltonian Monte Carlo method for compact Lie groups
constructed in 20 using a symplectic structure can be recovered from canonical geometric …