Fast and Smooth Interpolation on Wasserstein Space
组织者
演讲者
时间
2023年04月03日 14:30 至 15:00
地点
Online
摘要
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.