Gaussian Process Forecast with multidimensional distributional entries

Francois Bachoc, Alexandra Suvorikova, Jean-Michel Loubes and Vladimir Spokoiny

No 2018-030, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

Abstract: In this work, we propose to define Gaussian Processes indexed by multidimensional distributions. In the framework where the distributions can be modeled as i.i.d realizations of a measure on the set of distributions, we prove that the kernel defined as the quadratic distance between the transportation maps, that transport each distribution to the barycenter of the distributions, provides a valid covariance function. In this framework, we study the asymptotic properties of this process, proving micro ergodicity of the parameters.

Keywords: Gaussian Process; Kernel methods; Wasserstein Distance (search for similar items in EconPapers)
JEL-codes: C00 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (17)

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Persistent link: https://EconPapers.repec.org/RePEc:zbw:irtgdp:2018030

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