Bachoc, Francois Suvorikova, Alexandra Loubes, Jean-Michel Spokoiny, Vladimir
Year of Publication:
IRTG 1792 Discussion Paper No. 2018-030
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