Measure-valued spline curves: an optimal transport viewpoint
arXiv:1801.0318643 citationsh-index: 51
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This work addresses the problem of interpolating probability measures for applications in data analysis and machine learning, offering a principled approach that bridges spline theory and optimal transport.
The paper introduces a method for smoothly interpolating probability measures by extending spline curves to the space of measures using optimal transport, providing a novel geometric framework for measure-valued interpolation.
The aim of this article is to introduce and address the problem to smoothly interpolate (empirical) probability measures. To this end, we lift the concept of a spline curve from the setting of points in a Euclidean space that that of probability measures, using the framework of optimal transport.