title: Marginalised Gaussian Processes with Nested Sampling
abstract: Gaussian Process models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through optimisation of the kernel hyperparameters using the marginal likelihood as the objective. This work proposes nested sampling as a means of marginalising kernel hyperparameters,  because it is a technique that is well-suited to exploring complex, multi-modal distributions. We benchmark against Hamiltonian Monte Carlo on time-series and two-dimensional regression tasks, finding that a principled approach to quantifying hyperparameter uncertainty substantially improves the quality of prediction intervals.
  
authors: Fergus Simpson Vidhi Lalchand Carl Edward Rasmussen
hIndex: Carl Edward Rasmussen 54