Bayesian Computation as Optimisation on the Wasserstein space

The next statistics seminar will be presented by A/Prof Minh-Ngoc Tran from our Business School.

Title: Bayesian Computation as Optimisation on the Wasserstein space
Speaker: A/Prof Minh-Ngoc Tran
Time and location : 2-3pm in Carslaw 275 or Zoom
Abstract :

Optimal Transport (OT) is a powerful mathematical theory that sits at the interface of several fundamental theories, including probability and optimisation. It provides a mathematically elegant tool for solving optimisation problems on the space of probability measures. By equipping the space of probability measures with the Wasserstein distance, it can be made into a Riemannian manifold with a rich geometric structure, which is useful for both optimisation and sampling related statistical applications.

In this talk, I will explore ways to use OT to design geometry-assisted and optimisation-guided Bayesian sampling techniques. Specifically, I will focus on a particle-based Variational Bayes approach, that traverses a set of particles to approximate the target distribution by iteratively solving a proximal point algorithm on the Wasserstein space. Additionally, I will discuss potential extensions of Nesterov’s method to accelerate optimisation on the Wasserstein space.