Gaussian processes with multidimensional distribution inputs via optimal transport and hilbertian embedding

François Bachoc, Alexandra Suvorikova, David Ginsbourger, Jean Michel Loubes, Vladimir Spokoiny

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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 ker-nels, 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.

Original languageEnglish
Pages (from-to)2742-2772
Number of pages31
JournalElectronic Journal of Statistics
Volume14
Issue number2
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • Hilbert space embeddings
  • Kernel methods
  • Wasserstein distance

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