# 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.