Kantorovich distance based kernel for Gaussian Processes: estimation and forecast

Jean-Michel Loubes (University Toulouse)
Wednesday, June 14, 2017 - 10:00am
Hausvogteiplatz 11a, 10117 Berlin, Room 4.13 (4th floor)

Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. Here, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provide a family of positive definite kernels built using transportation based distances. We provide a probabilistic understanding of these kernels and characterize the corresponding stochastic processes. We prove that the Gaussian processes indexed by distributions corresponding to these kernels can be efficiently forecast, opening new perspectives in Gaussian process modeling.