Flexible and efficient Gaussian process models for machine learning

2007 I, Edward Snelson, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indi-cated in the thesis. 2 Gaussian process (GP) models are widely used to perform Bayesian nonlinear re-gression and classification — tasks that are central to many machine learning prob-lems. A GP is nonparametric, meaning that the complexity of the model grows as more data points are received. Another attractive feature is the behaviour of the error bars. They naturally grow in regions away from training data where we have high uncertainty about the interpolating function. In their standard form GPs have several limitations, which can be divided into two broad categories: computational difficulties for large data sets, and restrictive modelling assumptions for complex data sets. This thesis addresses various aspect