Probabilistic Modelling of Uncertainty with Bayesian nonparametric Machine Learning

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

A surrogate modelling approach based on nonlinear dimension reduction for uncertainty quantification in groundwater flow models

In this paper, we develop a surrogate modelling approach for capturing the output field (e.g., the pressure head) from groundwater flow models involving a stochastic input field (e.g., the hy- draulic conductivity). We use a Karhunen-Lo`eve expansion for a log-normally distributed input field, and apply manifold learning (local tangent space alignment) to perform Gaussian process Bayesian inference using Hamiltonian Monte Carlo in an abstract feature space, yielding outputs for arbitrary unseen inputs. We also develop a framework for forward uncertainty quantification in such problems, including analytical approximations of the mean of the marginalized distri- bution (with respect to the inputs). To sample from the distribution we present Monte Carlo approach. Two examples are presented to demonstrate the accuracy of our approach: a Darcy flow model with contaminant transport in 2-d and a Richards equation model in 3-d

Low temperature thermal expansion of pure and inert gas-doped Fullerite C60

The low temperature (2-24 K) thermal expansion of pure (single crystal and polycrystalline) C60 and polycrystalline C60 intercalated with He, Ne, Ar, and Kr has been investigated using high-resolution capacitance dilatometer. The investigation of the time dependence of the sample length variations on heating shows that the thermal expansion is determined by the sum of positive and negative contributions, which have different relaxation times. The negative thermal expansion usually prevails at helium temperatures. The positive expansion is connected with the phonon thermalization of the system. The negative expansion is caused by reorientation of the C60 molecules. It is assumed that the reorientation is of quantum character. The inert gas impurities affect very strongly the reorientation of the C60 molecules especially at liquid helium temperatures. A temperature hysteresis of the thermal expansion coefficient of Kr- and He- C60 solutions has been revealed. The hysteresis is attributed to orientational polyamorphous transformation in these systems.Comment: 18 pages, 12 figure

Enriched mixtures of generalised Gaussian process experts

Mixtures of experts probabilistically divide the input space into regions, where the assumptions of each expert, or conditional model, need only hold locally. Combined with Gaussian process (GP) experts, this results in a powerful and highly flexible model. We focus on alternative mixtures of GP experts, which model the joint distribution of the inputs and targets explicitly. We highlight issues of this approach in multi-dimensional input spaces, namely, poor scalability and the need for an unnecessarily large number of experts, degrading the predictive performance and increasing uncertainty. We construct a novel model to address these issues through a nested partitioning scheme that automatically infers the number of components at both levels. Multiple response types are accommodated through a generalised GP framework, while multiple input types are included through a factorised exponential family structure. We show the effectiveness of our approach in estimating a parsimonious probabilistic description of both synthetic data of increasing dimension and an Alzheimer's challenge dataset.Peer reviewe

Evaluation of Internet-Based Clinical Decision Support Systems

BACKGROUND: Scientifically based clinical guidelines have become increasingly used to educate physicians and improve quality of care. While individual guidelines are potentially useful, repeated studies have shown that guidelines are ineffective in changing physician behavior. The Internet has evolved as a potentially useful tool for guideline education, dissemination, and implementation because of its open standards and its ability to provide concise, relevant clinical information at the location and time of need. OBJECTIVE: Our objective was to develop and test decision support systems (DSS) based on clinical guidelines which could be delivered over the Internet for two disease models: asthma and tuberculosis (TB) preventive therapy. METHODS: Using open standards of HTML and CGI, we developed an acute asthma severity assessment DSS and a preventative tuberculosis treatment DSS based on content from national guidelines that are recognized as standards of care. Both DSS's are published on the Internet and operate through a decision algorithm developed from the parent guidelines with clinical information provided by the user at the point of clinical care. We tested the effectiveness of each DSS in influencing physician decisions using clinical scenario testing. RESULTS: We first validated the asthma algorithm by comparing asthma experts' decisions with the decisions reached by nonpulmonary nurses using the computerized DSS. Using the DSS, nurses scored the same as experts (89% vs. 88%; p = NS). Using the same scenario test instrument, we next compared internal medicine residents using the DSS with residents using a printed version of the National Asthma Education Program-2 guidelines. Residents using the computerized DSS scored significantly better than residents using the paper-based guidelines (92% vs. 84%; p <0.002). We similarly compared residents using the computerized TB DSS to residents using a printed reference card; the residents using the computerized DSS scored significantly better (95.8% vs. 56.6% correct; p<0.001). CONCLUSIONS: Previous work has shown that guidelines disseminated through traditional educational interventions have minimal impact on physician behavior. Although computerized DSS have been effective in altering physician behavior, many of these systems are not widely available. We have developed two clinical DSS's based on national guidelines and published them on the Internet. Both systems improved physician compliance with national guidelines when tested in clinical scenarios. By providing information that is coupled to relevant activity, we expect that these widely available DSS's will serve as effective educational tools to positively impact physician behavior