Return to Colloquia & Seminar listing
Optimal Transport to Independence Models
Mathematics of Data & Decisions| Speaker: | Guido Montufar, UCLA (Math) |
| Related Webpage: | https://www.math.ucla.edu/~montufar/ |
| Location: | Zoom Lecture |
| Start time: | Tue, Dec 1 2020, 4:10PM |
An independence model for discrete random variables is a Segre-Veronese variety in a probability simplex. Any metric on the set of joint states of the random variables induces a Wasserstein metric on the probability simplex. The unit ball of this polyhedral norm is dual to the Lipschitz polytope. Given any data distribution, we seek to minimize its Wasserstein distance to a fixed independence model. The solution to this optimization problem is a piecewise algebraic function of the data. We compute this function explicitly in small instances, we examine its combinatorial structure and algebraic degrees in the general case, and we present some experimental case studies. This talk is based on joint work with Türkü Özlüm Çelik, Asgar Jamneshan, Bernd Sturmfels, Lorenzo Venturello.
https://arxiv.org/abs/1909.11716
https://arxiv.org/abs/2003.06725
zoom info available https://sites.google.com/view/maddd After the talk, we will do virtual tea/coffee get-together at https://gather.town/KOoFj0aKT5GkEj40/Alder-Room