BIMSA > Seminar on Control Theory and Nonlinear Filtering Fast and Smooth Interpolation on Wasserstein Space
Fast and Smooth Interpolation on Wasserstein Space
Organizer
Shing Toung Yau
Speaker
Jia Yi Kang
Time
Monday, April 3, 2023 2:30 PM - 3:00 PM
Venue
Online
Abstract
In this report, I will report a paper where they propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, they reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox of spline interpolation. Unlike previous approaches to measure-valued splines, their interpolated curves (i) have a clear interpretation as governing particle flows, which is natural for applications, and (ii) come with the first approximation guarantees on Wasserstein space. Finally, they demonstrate the broad applicability of our interpolation methodology by fitting surfaces of measures using thin-plate splines.