Gaussian Process Forecast with multidimensional distributional entries

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: IRTG 1792 Discussion Paper ; No. 2018-030

Classification and Topics

• Classification: Wirtschaft ; Mathematical and Quantitative Methods: General
• Subject: Gaussian Process ; Kernel methods ; Wasserstein Distance

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Bachoc, Francois ; Suvorikova, Alexandra ; Loubes, Jean-Michel ; Spokoiny, Vladimir
• Event: Veröffentlichung
• (who): Humboldt-Universität zu Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"
• (where): Berlin
• (when): 2018

Further information

• Handle: http://hdl.handle.net/10419/230741
• Last update: 10.03.2025, 11:43 AM CET