Finitedimensional Gaussian approximation with linear inequality constraints
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Finitedimensional Gaussian approximation with linear inequality constraints
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of realworld problems. We consider the finitedimensional 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 Carlobased sampler provides efficient results on both data fitting and uncertainty quantification.
Finitedimensional Gaussian approximation with linear inequality constraints
by Andrés F. LópezLopera, François Bachoc, Nicolas Durrande, Olivier Roustant
https://arxiv.org/pdf/1710.07453v1.pdf
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