Finite-dimensional Gaussian approximation with linear inequality constraints

Abstract : Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017) which can satisfy inequality conditions everywhere (either boundedness, monotonicity or convexity). Our contributions are threefold. First, we extend their approach in order to deal with general sets of linear inequalities. Second, we explore several Markov Chain Monte Carlo (MCMC) techniques to approximate the posterior distribution. Third, we investigate theoretical and numerical properties of the constrained likelihood for covariance parameter estimation. According to experiments on both artificial and real data, our full framework together with a Hamiltonian Monte Carlo-based sampler provides efficient results on both data fitting and uncertainty quantification.
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SIAM/ASA Journal on Uncertainty Quantification, ASA, American Statistical Association, 2018, 6 (3), pp.1224-1255. 〈10.1137/17M1153157〉
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https://hal.archives-ouvertes.fr/hal-01864332
Contributeur : Andrés Lopez-Lopera <>
Soumis le : mercredi 29 août 2018 - 16:39:35
Dernière modification le : mercredi 19 décembre 2018 - 15:46:49

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Andrés F. López-Lopera, François Bachoc, Nicolas Durrande, Olivier Roustant. Finite-dimensional Gaussian approximation with linear inequality constraints. SIAM/ASA Journal on Uncertainty Quantification, ASA, American Statistical Association, 2018, 6 (3), pp.1224-1255. 〈10.1137/17M1153157〉. 〈hal-01864332〉

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