###Theoretical Foundations of Multi-Output Gaussian Processes
Project ID: 2228bd1121 (You will need this ID for your application)
Research Theme: Mathematical Sciences
UCL Lead department: Statistical Science
Lead Supervisor: Francois-Xavier Briol
Project Summary:
Multi-output Gaussian processes (MOGPs) are a powerful machine learning tool for modelingcomplex systems with multiple outputs. They are used in a wide range of safety-critical fieldsincluding health, economics and climate because of their ability to not only provide accuratepredictions, but also quantify our uncertainty over those predictions. However, despite theirwidespread use, our theoretical understanding of MOGPs is limited, and there is a need formore general and rigorous results that can provide insight into their behaviour and properties.In this project, we propose to develop a theoretical framework for MOGPs, with the goal ofestablishing fundamental results that can guide the development and application of MOGPs in arange of settings. The main aim of the project will be to establish the conditions under whichMOGPS can provide reliable predictions—as well as settings in which they fail to do so. This isessential to further encourage their use in application areas where the error in our predictionscould have a significant negative economic or health impact.The ideal candidate for this project has studied machine learning or statistics and has strongmathematical foundations. They are interested in researching the mathematical foundations ofstatistical machine learning, and have some experience of working with Gaussian processes orreproducing kernel Hilbert spaces. The student will also be strongly encouraged to collaboratewith other PhD students at UCL who focus on applications of Gaussian processes for tacklingclimate modelling problems.