# A Gaussian Process Regression Model for Distribution Inputs

@article{Bachoc2018AGP, title={A Gaussian Process Regression Model for Distribution Inputs}, author={F. Bachoc and F. Gamboa and Jean-Michel Loubes and N. Venet}, journal={IEEE Transactions on Information Theory}, year={2018}, volume={64}, pages={6620-6637} }

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 a probabilistic understanding of these kernels and characterize the corresponding… Expand

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