Student-t Processes as Alternatives to Gaussian Processes

We investigate the Student-t process as an alternative to the Gaussian process as a nonparametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the covariance kernel of a Gaussian process model. We show surprising equivalences between different hierarchical Gaussian process models leading to Student-t processes, and derive a new sampling scheme for the inverse Wishart process, which helps elucidate these equivalences. Overall, we show that a Student-t process can retain the attractive properties of a Gaussian process -- a nonparametric representation, analytic marginal and predictive distributions, and easy model selection through covariance kernels -- but has enhanced flexibility, and predictive covariances that, unlike a Gaussian process, explicitly depend on the values of training observations. We verify empirically that a Student-t process is especially useful in situations where there are changes in covariance structure, or in applications like Bayesian optimization, where accurate predictive covariances are critical for good performance. These advantages come at no additional computational cost over Gaussian processes.Comment: 13 pages, 6 figures, 1 table. To appear in "The Seventeenth International Conference on Artificial Intelligence and Statistics (AISTATS), 2014.

Making Fitness to Plead Fit for Purpose

Abstract: In the England and Wales criminal justice system, consideration of a defendant's ability to stand trial is known as 'fitness to plead'. No accused person may face trial unless they are fit to plead to the charges against them. The fitness to plead criteria date back to the 19th century, and have been virtually unchanged. Developed from case law relating to sensory impairment and intellectual disability, they are now routinely utilised for severe and enduring mental illnesses, predominantly psychotic disorders. The fitness to plead criteria are no longer appropriate to meet modern understanding of complex mental disorders, and are shamefully archaic in comparison to civil capacity legislation. This paper outlines the development of the fitness to plead criteria and process, summarises current criticisms and proposes potential reform in this fundamental area of mental health law

Behavior of L-shaped reinforced concrete columns under combined biaxial bending and compression

Combined biaxial and axial compression for L-shaped reinforced concrete short columns is a common design Problem. Current code, provisions and the available design aids do not offer an insight into the determination of strength and ductility of biaxially loaded reinforced concrete column. An experimental and analytical investigation of the moment-deformation behavior of biaxially loaded L-shaped short columns were undertaken. Four 1/2 scaled specimens were tested till failure. Moment-curvature and load-deflection curves were developed from the experimental and the analytical results. The analytical results were obtained using a computer program developed by Hsu (1). From the investigation it is deduced that the computer program developed by Hsu (1) can be used to find the ultimate strength, the moment-deformation characteristics, the stress and the strain distributions across the section of L-shaped, biaxially loaded column with large and small eccentricities

Bayesian single- and multi- objective optimisation with nonparametric priors

Optimisation is integral to all sorts of processes in science, economics and arguably underpins the fruition of human intelligence through millions of years of optimisation, or $\textit{evolution}$. Scarce resources make it crucial to maximise their efficient usage. In this thesis, we consider the task of maximising unknown functions which we are able to query point-wise. The function is deemed to be $\textit{costly}$ to evaluate e.g. larger run time or financial expense, requiring a judicious querying strategy given previous observations. We adopt a probabilistic framework for modelling the unknown function and Bayesian non-parametric modelling. In particular, we focus on the $\textit{Gaussian process}$ (GP), a popular non-parametric Bayesian prior on functions. We motivate these choices and give an overview of the Gaussian process in the introduction, and its application to $\textit{Bayesian optimisation}$. A GP's behaviour is intimately controlled by the choice of $\textit{kernel}$ or covariance function, typically chosen to be a parametric function. In chapter 2 we instead place a non-parametric Bayesian prior, known as an Inverse Wishart process prior, over a GP kernel function, and show that this may be marginalised analytically leading to a \textit{Student-t process} (TP). Furthermore we explore a larger class of $\textit{elliptical processes}$, and show that the TP is the most general for which analytic calculation is possible, and apply it successfully for Bayesian optimisation. The remainder of the thesis focusses on various Bayesian optimisation settings. In chapter 3, we consider a setting where we are able to evaluate a function at multiple locations in parallel. Our approach is to consider a measure of information, $\textit{entropy}$, to decide which batch of points to evaluate a function at next. We similarly apply information gain for $\textit{multi-objective}$ Bayesian optimisation in chapter 4. Here, one wishes to find a $\textit{Pareto frontier}$ of efficient settings with respect to several different objectives through sequential evaluation. Finally, in chapter 5 we exploit the idea that in a multi-objective setting, functions are $\textit{correlated}$, incorporating this belief in our choice of prior distribution over the multiple objectives

An Empirical Study of Stochastic Variational Algorithms for the Beta Bernoulli Process

Stochastic variational inference (SVI) is emerging as the most promising candidate for scaling inference in Bayesian probabilistic models to large datasets. However, the performance of these methods has been assessed primarily in the context of Bayesian topic models, particularly latent Dirichlet allocation (LDA). Deriving several new algorithms, and using synthetic, image and genomic datasets, we investigate whether the understanding gleaned from LDA applies in the setting of sparse latent factor models, specifically beta process factor analysis (BPFA). We demonstrate that the big picture is consistent: using Gibbs sampling within SVI to maintain certain posterior dependencies is extremely effective. However, we find that different posterior dependencies are important in BPFA relative to LDA. Particularly, approximations able to model intra-local variable dependence perform best.Comment: ICML, 12 pages. Volume 37: Proceedings of The 32nd International Conference on Machine Learning, 201

Targeting Proteins to Cancer Cell Membranes Using the pH Low Insertion Peptide

The pH Low Insertion Peptide (pHLIP) is able to unidirectionally insert itself in membranes at low pH, a physiological marker of cancerous cells. Thus, the pHLIP peptide has potential use as a dual targeting and delivery system for cancer therapeutics. We are investigating pHLIP-protein constructs to further our understanding of protein-membrane interactions and pHLIP dynamics in an attempt to target proteins to cancer cell membranes