# Graduate Student / Postdoc Seminar

#### Data-Driven Optimal Transport

Speaker: Esteban Tabak

Location: Warren Weaver Hall 1302

Date: Friday, October 18, 2013, 1 p.m.

Synopsis:

The optimal transport problem seeks a function $$y(x)$$, with $$x$$ and $$y$$ in $$\mathbb{R}^n$$, which maps a probability density $$\rho(x)$$ into another, $$\mu(y)$$, while minimizing a cost function $$C[y(x)]$$. We will discuss the frequently occurring situation in which $$\rho(x)$$ and $$\mu(y)$$ are only known through samples $${x_i}$$, $${y_j}$$, as well as extensions to more general scenarios where a plan $$\pi(x_1,x_2,x_3,...)$$ is sought with marginals $$\rho_j(x_j)$$ (here each $$x_j$$ is an $$n$$-dimensional vector and the marginals are only known through samples) that minimizes a cost $$C[\pi]$$. Applications include resource allocation, density estimation, medical diagnosis and treatment, portfolio optimization and fluid-flow reconstruction from tracers.