Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2018 030

Gaussian Process Forecast with multidimensional distributional entries

Francois Bachoc
Alexandra Suvorikova
Jean-Michel Loubes
Vladimir Spokoiny

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.

Gaussian Process, Kernel methods, Wasserstein Distance

JEL classification: