# Graduate Student / Postdoc Seminar

#### Estimating the Wasserstein distance

**Speaker:**
Jonathan Weed, CIMS

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, November 1, 2019, 1 p.m.

**Synopsis:**

Given two probability distributions, how many samples from each does it take to estimate whether the distributions are close together or far apart? The answer depends strongly on what measure of distance you choose! In this talk, we will survey this area and discuss applications to the Wasserstein distance, a measure of distance defined on probability distributions on metric spaces. We show new lower bounds for this problem and define a new model under which this distance can be estimated at a significantly faster rate. However, we give evidence that this problem possesses a computational-statistical gap, i.e., that any computationally efficient procedure requires many more samples than are theoretically necessary.

Joint work with Philippe Rigollet