CERAMATHS-DMATHS Seminar: Presentation by Anis Fradi

The CÉRAMATHS Department of Mathematics seminar will host Anis Fradi (Lumière Lyon 2 University) at 2:00 p.m. on Thursday, July 2, 2026, for the following talk:

Bayesian Inference on Grassmannian Manifolds via Lagrangian Monte Carlo

Hamiltonian Monte Carlo (HMC) improves upon the efficiency of traditional Markov chain Monte Carlo (MCMC) methods by reducing random walk effects. Lagrangian Monte Carlo (LMC) further enhances this efficiency by replacing the Hamiltonian formulation with dynamics derived from Lagrangian mechanics.

In this work, we utilize LMC to propose a new Bayesian regression model on Grassmannian manifolds, whose parameters are estimated using an LMC scheme adapted to Grassmannian geometry (GLMC). This approach takes full advantage of the Riemannian structure to achieve statistical inference adapted to the manifold.

We show that solving the Lagrangian dynamics equations is equivalent to following the geodesic flow, which enables efficient computation. Finally, we study the asymptotic properties of the resulting posterior distribution and establish strong theoretical guarantees regarding the validity of the inference.