Sparse approximation for Gaussian process with derivative observations

We propose a sparse Gaussian process model to approximate full Gaussian process with derivatives when a large number of function observations t and derivative observations t' exist. By introducing a small number of inducing point m, the complexity of posterior computation can be reduced from O((t+t') 3 ) to O((t+t')m 2 ). We also find the usefulness of our approach in Bayesian optimisation. Experiments demonstrate the superiority of our approach.