Gaussian process regression model for distribution inputs

François Bachoc (1) , Fabrice Gamboa , Jean-Michel Loubes , Nil Venet

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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. In this paper, 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 asymptotic results for covariance function estimation and prediction. We also provide numerical comparisons with other forecast methods based on distribution inputs.

Domaines: Statistiques [stat]

François Bachoc, Fabrice Gamboa, Jean-Michel Loubes, Nil Venet. Gaussian process regression model for distribution inputs. First UQSay seminar on UQ, DACE and related topics (UQSay #01), Mar 2019, Gif-sur-Yvette, France. ⟨hal-03109928⟩