Hadamard Langevin dynamics for the l1 priors

Title

Hadamard Langevin dynamics for the l1 priors

Speaker

Clarice Poon - University of Warwick

Abstract

Priors with non-smooth log densities have been widely used in Bayesian inverse problems, particularly in imaging, due to their sparsity inducing properties. To date, the majority of algorithms for handling such densities are based on proximal Langevin dynamics where one replaces the non-smooth part by a smooth approximation known as the Moreau envelope. In this work, we introduce a novel approach for sampling densities with l1-priors based on a Hadamard product parameterization. This builds upon the idea that the Laplace prior has a Gaussian mixture representation and our method can be seen as a form of overparametrization: by increasing the number of variables, we construct a density from which one can directly recover the original density. This is fundamentally different from proximal-type approaches since our resolution is exact, while proximal-based methods introduce additional bias due to the Moreau-envelope smoothing. For our new density, we present its Langevin dynamics in continuous time and establish well-posedness and geometric ergodicity. We also present a discretization scheme for the continuous dynamics and prove convergence as the time-step diminishes.

Bio

Clarice Poon is a Reader in the Mathematics Institute at the University of Warwick. She received her PhD in applied mathematics from the University of Cambridge and her undergraduate degree in Mathematics and Computer Science from the University of Oxford. Her research interests include compressed sensing, inverse problems on measures and optimisation for imaging problems.

When

Wednesday, April 2nd at 14:15

Where

Room 715, DIMA, Via Dodecaneso 35