文章基本信息

标题：Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding
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作者：François Bachoc ; Alexandra Suvorikova ; David Ginsbourger 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2020
卷号：14
期号：2
页码：2742-2772
DOI：10.1214/20-EJS1725
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.
关键词：Kernel methods; Wasserstein distance; Hilbert space embeddings