Information consistency of dependent convolved Gaussian processes regression

This paper presents a non-parametric Bayesian approach for modeling multiple response variables using a Gaussian process regression (GPR) model. The response functions are modeled using a dependent Gaussian process (GP) prior, and the estimation, prediction, and inference issues are discussed within this framework. To establish the information consistency of the dependent GPs prediction strategy, a stretching-restriction method is proposed. The covariance structure is constructed using convolved Gaussian processes (CGPs) to illustrate the results. Simulations and real data analyses show that the proposed dependent GPR yields reasonably good prediction accuracy.