I dedicate this thesis to my family. Acknowledgements

I would like to thank my supervisor, Prof. Neil Lawrence, for his invaluable guidance, endless support and patience during my studies; for making sure that I focus on the journey, not only on the destination. Neil trusted me with his many great ideas and, at the same time, encouraged me to confidently further develop and explore them in my own ways, always while offering invaluable advice. Overall, he has inspired me both as an academic and as a person and, therefore, I feel very privileged to have worked under his supervision. I am very grateful to Dr Michalis Titsias, who was always keen to discuss matters ranging from high level ideas to small mathematical details. Our close collaboration in the early days of my studies and in the material of Chapter 3 of this thesis meant a lot for the rest of my trajectory. I would like to thank Prof. Carl Henrik Ek; our initial work in material related to Chapter 5 evolved in a miscellany of ideas and an ongoing collaboration and friendship. Thanks to Dr James Hensman for the literally dozens of useful discussions, on matters related to this thesis and not only, throughout the whole period of my studies. Thanks to Prof. Magnus Rattray and to my mentor in Microsoft Research, Dr Ashish Kapoor, for useful discussions. I am grateful to the funding bodies that enabled me to pursue my studies, offering me a scholarship each: the Greek State Scholarships Foundation (IKY) and the University of Sheffield / Moody Endowment Fund. I feel lucky to be part of a motivating group in Sheffield within the unique environment of SITraN. A big thanks to all of my current and past lab mates, too many to mention each separately; they all made this an unforgettable experience in so many ways. A special thanks to those who helped in particular ways (discussions, proofreading sections) with the devel