IMA Data Science Seminar: An Optimal Transport Perspective on Uncertainty Propagation
Data science seminars hosted by the The Institute for Mathematics and Its Applications (IMA) take place on Tuesdays from 1:25 p.m. - 2:25 p.m.
This week, Amir Sagiv (Columbia University), will be giving a lecture titled "An Optimal Transport Perspective on Uncertainty Propagation".
Registration is required to access the Zoom webinar.
Abstract
In many scientific areas, a deterministic model (e.g., a differential equation) is equipped with parameters. In practice, these parameters might be uncertain or noisy, and so an honest model should provide a statistical description of the quantity of interest. Underlying this computational question is a fundamental one - If two "similar" functions push-forward the same measure, are the new resulting measures close, and if so, in what sense? I will first show how the probability density function (PDF) can be approximated, using spectral and local methods, and present applications to nonlinear optics. We will then discuss the limitations of PDF approximation, and present an alternative Wasserstein-distance formulation of this problem, which yields a much simpler theory.
Biography
Amir Sagiv is a Chu Assistant Professor of Applied Mathematics at Columbia University. Before that, Amir completed his Ph.D. in Applied Mathematics at Tel Aviv University.