Finite-dimensional Gaussian approximation with linear inequality\n constraints

Abstract

Introducing inequality constraints in Gaussian process (GP) models can lead\nto more realistic uncertainties in learning a great variety of real-world\nproblems. We consider the finite-dimensional Gaussian approach from Maatouk and\nBay (2017) which can satisfy inequality conditions everywhere (either\nboundedness, monotonicity or convexity). Our contributions are threefold.\nFirst, we extend their approach in order to deal with general sets of linear\ninequalities. Second, we explore several Markov Chain Monte Carlo (MCMC)\ntechniques to approximate the posterior distribution. Third, we investigate\ntheoretical and numerical properties of the constrained likelihood for\ncovariance parameter estimation. According to experiments on both artificial\nand real data, our full framework together with a Hamiltonian Monte Carlo-based\nsampler provides efficient results on both data fitting and uncertainty\nquantification.\n