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2020 Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding
François Bachoc, Alexandra Suvorikova, David Ginsbourger, Jean-Michel Loubes, Vladimir Spokoiny
Electron. J. Statist. 14(2): 2742-2772 (2020). DOI: 10.1214/20-EJS1725

Abstract

In this work, we propose a way to construct Gaussian processes indexed by multidimensional distributions. More precisely, we tackle the problem of defining positive definite kernels between multivariate distributions via notions of optimal transport and appealing to Hilbert space embeddings. Besides presenting a characterization of radial positive definite and strictly positive definite kernels on general Hilbert spaces, we investigate the statistical properties of our theoretical and empirical kernels, focusing in particular on consistency as well as the special case of Gaussian distributions. A wide set of applications is presented, both using simulations and implementation with real data.

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François Bachoc. Alexandra Suvorikova. David Ginsbourger. Jean-Michel Loubes. Vladimir Spokoiny. "Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding." Electron. J. Statist. 14 (2) 2742 - 2772, 2020. https://doi.org/10.1214/20-EJS1725

Information

Received: 1 March 2019; Published: 2020
First available in Project Euclid: 22 July 2020

zbMATH: 1448.60085
MathSciNet: MR4125856
Digital Object Identifier: 10.1214/20-EJS1725

Subjects:
Primary: 60G15

JOURNAL ARTICLE
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Vol.14 • No. 2 • 2020
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