*AVVISO*
Si comunica che nei giorni
*martedì 11 febbraio (aula Mancini) martedì 18 febbraio (aula Mancini) martedì 25 febbraio (aula Tonelli)* si terranno i seguenti due cicli di seminari, con eventuale proseguimento da concordare:
*ore 11-12 Sigurd Assing ore 12-13 Michael Goldman* Il tema dei seminari è brevemente descritto qui di seguito. Tutti gli interessati sono invitati a partecipare.
------------------------ *Sigurd Assing* (University of Warwick)
TITLE: Bayesian Gaussian Process Latent Variable Model
ABSTRACT: We introduce a variational inference framework for training the Gaussian process latent variable model and thus performing Bayesian nonlinear dimensionality reduction. The maximization of the variational lower bound provides a Bayesian training procedure that is robust to overfitting and can automatically select the dimensionality of the nonlinear latent space.
------------------------ *Michael Goldman* (Université Paris Diderot)
TITLE: A variational approach to regularity in optimal transport and applications to the optimal matching problem.
ABSTRACT: In this course I will present the regularity theory for optimal transport maps recently developed together with M. Huesmann and F. Otto. The main point of the course is to show that as long as we are in a linearization regime, that is as long as the local displacement and the local distances of the two marginals to the Lebesgue measure are small, the displacement is quantitatively close to the gradient of the solution of a Poisson equation. We will see applications both to partial regularity and to (a variant of) the optimal matching problem. In particular, we will see how this theory allows to justify down to the microscopic scale some predictions made by Caracciolo and al for that problem.