  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.
