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A Gaussian Process Regression Model for Distribution Inputs

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. 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 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.
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Contributor : Nil Venet <>
Submitted on : Friday, January 26, 2018 - 6:31:06 PM
Last modification on : Friday, June 12, 2020 - 10:55:30 AM


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  • HAL Id : hal-01450002, version 2
  • ARXIV : 1701.09055


François Bachoc, Fabrice Gamboa, Jean-Michel Loubes, Nil Venet. A Gaussian Process Regression Model for Distribution Inputs. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2018, 64 (10), pp.6620 - 6637. ⟨hal-01450002v2⟩



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