Probabilistic Modelling of Uncertainty with Bayesian nonparametric Machine Learning

Abstract

This thesis addresses the use of probabilistic predictive modelling and machine learning for quantifying uncertainties. Predictive modelling makes inferences of a process from observations obtained using computational modelling, simulation, or experimentation. This is often achieved using statistical machine learning models which predict the outcome as a function of variable predictors and given process observations. Towards this end Bayesian nonparametric regression is used, which is a highly flexible and probabilistic type of statistical model and provides a natural framework in which uncertainties can be included. The contributions of this thesis are threefold. Firstly, a novel approach to quantify parametric uncertainty in the Gaussian process latent variable model is presented, which is shown to improve predictive performance when compared with the commonly used variational expectation maximisation approach. Secondly, an emulator using manifold learning (local tangent space alignment) is developed for the purpose of dealing with problems where outputs lie in a high dimensional manifold. Using this, a framework is proposed to solve the forward problem for uncertainty quantification and applied to two fluid dynamics simulations. Finally, an enriched clustering model for generalised mixtures of Gaussian process experts is presented, which improves clustering, scaling with the number of covariates, and prediction when compared with what is known as the alternative model. This is then applied to a study of Alzheimer’s disease, with the aim of improving prediction of disease progression