Dependent Gaussian Processes

Abstract

Gaussian processes are usually parameterised in terms of their covari-ance functions. However, this makes it difficult to deal with multiple outputs, because ensuring that the covariance matrix is positive definite is problematic. An alternative formulation is to treat Gaussian processes as white noise sources convolved with smoothing kernels, and to param-eterise the kernel instead. Using this, we extend Gaussian processes to handle multiple, coupled outputs. 1