Title: Transport based kernel for GP models
Authors: Jean-Michel Loubes - University of Toulouse (France) [presenting]
Abstract: 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. 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. Then we consider the asymptotic properties of the forecast process.