# Lorenzo Venturello: Wasserstein distance in algebraic statistics

**Time: **
Tue 2020-11-03 11.15

**Location: **
Zoom and KTH, F11

**Participating: **
Lorenzo Venturello, KTH

### Abstract

Any metric on the set of states of a discrete random variable induces a metric called Wasserstein distance on the probability simplex. The unit ball of this norm is a polytope, well known in discrete and tropical geometry. Given any data distribution, we seek to minimize its Wasserstein distance to an algebraic model, i.e., a model described by polynomials. The solution to this optimization problem is a piecewise algebraic function of the data. After a gentle introduction on the topic, I will comment on the combinatorial and algebraic complexity of the problem. This talk is based on joint work with Türkü Özlüm Çelik, Asgar Jamneshan, Guido Montúfar and Bernd Sturmfels.

**Notes:** The seminar will take place in F11 for **the first 18 people to arrive**. Overflow audience and those who are working from home can participate via Zoom with meeting ID
62586628413
.