A Gaussian Process Regression Model for Distribution Inputs

@article{Bachoc2017AGP,
  title={A Gaussian Process Regression Model for Distribution Inputs},
  author={François Bachoc and Fabrice Gamboa and Jean-Michel Loubes and Nil Venet},
  journal={IEEE Transactions on Information Theory},
  year={2017},
  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… CONTINUE READING
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SHOWING 1-10 OF 58 REFERENCES

Interpolation of Spatial Data: Some Theory for Kriging

  • Technometrics
  • 2000
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Asymptotic analysis of covariance parameter estimation for gaussian processes in the misspecified case

——
  • Bernoulli, forthcoming, 2016.
  • 2016
VIEW 1 EXCERPT

Modèles de régression gaussienne pour des distributions en entrée

N. Venet, F. Bachoc, F. Gamboa, J.-M. Loubes
  • 49è Journées de statistique, 2016.
  • 2016
VIEW 1 EXCERPT