Fast and Smooth Interpolation on Wasserstein Space
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Publication:6352034
arXiv2010.12101MaRDI QIDQ6352034
Author name not available (Why is that?)
Publication date: 22 October 2020
Abstract: We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we 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, our 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, we demonstrate the broad applicability of our interpolation methodology by fitting surfaces of measures using thin-plate splines.
Has companion code repository: https://github.com/jrbotvinick/dynamic-ppmm
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