Discovery and Extrapolation with Gaussian Processes

I thank Zoubin Ghahramani for always believing in me, and for grant-ing me the freedom to pursue my own research direction. I am happy to have had such a good hearted and inspiring supervisor. I am also thankful to my advisor Carl Edward Rasmussen, whose dedication to science is inspiring. The machine learning group at Cambridge has been a fantastic learning environment. I have learned so much from talking with others. I specifically thank Rich Turner, David Knowles, Sinead Williamson, John Cunningham, Ryan Turner, Matt Shannon, and Yunus Saatchi. I have enjoyed my time at Trinity College. The stimulating con-versations, wonderful music, beautiful architecture and culture are unique and unforgettable. Alex Gabrovsky, Charles Drummond, Adam Sproat, Robin Stephenson, Lennart Stern, and Dale Schwartz have par-ticularly made my time there memorable. My earliest memories are of my father excitedly taking me to observa-tories, showing me experiments, and amazing me with modern physics and the mysteries of the universe. I have since dedicated my life to science, and to understanding those mysteries. I am forever grateful to Cara, Jeremy, John, and my family, Gordon, Patricia, Josh, Willow, Lime, Leaf, Rain, Daisy, and Laska, for profoundly enriching my life, and for their constant good nature, unwavering support and interest. I dedicate this thesis especially to Cara, the love of my life. Declaration This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration except where specifi-cally indicated in the text. This disseration does not exceed seventy-one thousand five hundred words in length. No parts of this dissertation have been submitted for any other qualification. This dissertation contains 69,987 words and 39 figures