Finite-dimensional Gaussian approximation with linear inequality constraints
This work enables more realistic uncertainty quantification in Gaussian process models for various real-world applications by incorporating inequality constraints, representing an incremental extension of existing constrained GP methods.
The authors extended a finite-dimensional Gaussian approach to handle general linear inequality constraints in Gaussian process models, and developed MCMC techniques including Hamiltonian Monte Carlo for posterior approximation. Their framework showed efficient results in data fitting and uncertainty quantification on both artificial and real data.
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.