Abstract: The Bayesian approach to inverse problems has become very popular in the last decade after seminal work by Andrew Stuart (2010) and collaborators. Particularly in non-linear applications with PDEs and when using Gaussian process priors, this can leverage powerful MCMC methodology to tackle difficult high-dimensional and non-convex inference problems. Little is known in terms…

Abstract: One of the most basic problems in statistics is the estimation of the mean of a random vector, based on independent observations. This problem has received renewed attention in the last few years, both from statistical and computational points of view. In this talk we review some recent results on the statistical performance of…

Abstract:  In this talk we discuss the idea of data- driven regularisers for inverse imaging problems. We are in particular interested in the combination of mathematical models and purely data-driven approaches, getting the best from both worlds. In this context we will make a journey from “shallow” learning for computing optimal parameters for variational regularisation models…

Abstract: Wasserstein-based distributional robust optimization problems are formulated as min-max games in which a statistician chooses a parameter to minimize an expected loss against an adversary (say nature) which wishes to maximize the loss by choosing an appropriate probability model within a certain non-parametric class. Recently, these formulations have been studied in the context in…