Variational inference for diffusion processes

Diffusion processes are a family of continuous-time continuous-state stochastic processes that are in general only partially observed. The joint estimation of the forcing parameters and the system noise (volatility) in these dynamical systems is a crucial, but non-trivial task, especially when the system is nonlinear and multimodal. We propose a variational treatment of diffusion processes, which allows us to compute type II maximum likelihood estimates of the parameters by simple gradient techniques and which is computationally less demanding than most MCMC approaches. We also show how a cheap estimate of the posterior over the parameters can be constructed based on the variational free energy.

An investigation into inductive parameter learning in complex hierarchical knowledge structures representing clinical expertise

This dissertation investigates the very important and current problem of modelling human expertise. This is an apparent issue in any computer system emulating human decision making. It is prominent in Clinical Decision Support Systems (CDSS) due to the complexity of the induction process and the vast number of parameters in most cases. Other issues such as human error and missing or incomplete data present further challenges. In this thesis, the Galatean Risk Screening Tool (GRiST) is used as an example of modelling clinical expertise and parameter elicitation. The tool is a mental health clinical record management system with a top layer of decision support capabilities. It is currently being deployed by several NHS mental health trusts across the UK. The aim of the research is to investigate the problem of parameter elicitation by inducing them from real clinical data rather than from the human experts who provided the decision model. The induced parameters provide an insight into both the data relationships and how experts make decisions themselves. The outcomes help further understand human decision making and, in particular, help GRiST provide more accurate emulations of risk judgements. Although the algorithms and methods presented in this dissertation are applied to GRiST, they can be adopted for other human knowledge engineering domains.

Replication-based inference algorithms for hard computational problems

Inference algorithms based on evolving interactions between replicated solutions are introduced and analyzed on a prototypical NP-hard problem: the capacity of the binary Ising perceptron. The efficiency of the algorithm is examined numerically against that of the parallel tempering algorithm, showing improved performance in terms of the results obtained, computing requirements and simplicity of implementation. © 2013 American Physical Society.

Estimation and inference under economic restrictions

Estimation of economic relationships often requires imposition of constraints such as positivity or monotonicity on each observation. Methods to impose such constraints, however, vary depending upon the estimation technique employed. We describe a general methodology to impose (observation-specific) constraints for the class of linear regression estimators using a method known as constraint weighted bootstrapping. While this method has received attention in the nonparametric regression literature, we show how it can be applied for both parametric and nonparametric estimators. A benefit of this method is that imposing numerous constraints simultaneously can be performed seamlessly. We apply this method to Norwegian dairy farm data to estimate both unconstrained and constrained parametric and nonparametric models.

Interactions of personality variables with inductive and deductive teaching strategies

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Category structure affects the developmental trajectory of children’s inductive inferences for both natural kinds and artefacts

Inductive reasoning is fundamental to human cognition, yet it remains unclear how we develop this ability and what might influence our inductive choices. We created novel categories in which crucial factors such as domain and category structure were manipulated orthogonally. We trained 403 4-9-year-old children to categorise well-matched natural kind and artefact stimuli with either featural or relational category structure, followed by induction tasks. This wide age range allowed for the first full exploration of the developmental trajectory of inductive reasoning in both domains. We found a gradual transition from perceptual to categorical induction with age. This pattern was stable across domains, but interestingly, children showed a category bias one year later for relational categories. We hypothesise that the ability to use category information in inductive reasoning develops gradually, but is delayed when children need to process and apply more complex category structures. © 2014 © 2014 Taylor & Francis.

Message-passing for inference and optimization of real variables on sparse graphs

The inference and optimization in sparse graphs with real variables is studied using methods of statistical mechanics. Efficient distributed algorithms for the resource allocation problem are devised. Numerical simulations show excellent performance and full agreement with the theoretical results. © Springer-Verlag Berlin Heidelberg 2006.

Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

Inference of helicopter airframe condition

The goal of this paper is to model normal airframe conditions for helicopters in order to detect changes. This is done by inferring the flying state using a selection of sensors and frequency bands that are best for discriminating between different states. We used non-linear state-space models (NLSSM) for modelling flight conditions based on short-time frequency analysis of the vibration data and embedded the models in a switching framework to detect transitions between states. We then created a density model (using a Gaussian mixture model) for the NLSSM innovations: this provides a model for normal operation. To validate our approach, we used data with added synthetic abnormalities which was detected as low-probability periods. The model of normality gave good indications of faults during the flight, in the form of low probabilities under the model, with high accuracy (>92 %). © 2013 IEEE.

Wireless power and data transfer via a common inductive link using frequency division multiplexing

For wireless power transfer (WPT) systems, communication between the primary side and the pickup side is a challenge because of the large air gap and magnetic interferences. A novel method, which integrates bidirectional data communication into a high-power WPT system, is proposed in this paper. The power and data transfer share the same inductive link between coreless coils. Power/data frequency division multiplexing technique is applied, and the power and data are transmitted by employing different frequency carriers and controlled independently. The circuit model of the multiband system is provided to analyze the transmission gain of the communication channel, as well as the power delivery performance. The crosstalk interference between two carriers is discussed. In addition, the signal-to-noise ratios of the channels are also estimated, which gives a guideline for the design of mod/demod circuits. Finally, a 500-W WPT prototype has been built to demonstrate the effectiveness of the proposed WPT system.

Simple approximate MAP inference for Dirichlet processes mixtures

The Dirichlet process mixture model (DPMM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as Gibbs sampling are required. As a result, DPMM-based methods, which have considerable potential, are restricted to applications in which computational resources and time for inference is plentiful. For example, they would not be practical for digital signal processing on embedded hardware, where computational resources are at a serious premium. Here, we develop a simplified yet statistically rigorous approximate maximum a-posteriori (MAP) inference algorithm for DPMMs. This algorithm is as simple as DP-means clustering, solves the MAP problem as well as Gibbs sampling, while requiring only a fraction of the computational effort. (For freely available code that implements the MAP-DP algorithm for Gaussian mixtures see http://www.maxlittle.net/.) Unlike related small variance asymptotics (SVA), our method is non-degenerate and so inherits the “rich get richer” property of the Dirichlet process. It also retains a non-degenerate closed-form likelihood which enables out-of-sample calculations and the use of standard tools such as cross-validation. We illustrate the benefits of our algorithm on a range of examples and contrast it to variational, SVA and sampling approaches from both a computational complexity perspective as well as in terms of clustering performance. We demonstrate the wide applicabiity of our approach by presenting an approximate MAP inference method for the infinite hidden Markov model whose performance contrasts favorably with a recently proposed hybrid SVA approach. Similarly, we show how our algorithm can applied to a semiparametric mixed-effects regression model where the random effects distribution is modelled using an infinite mixture model, as used in longitudinal progression modelling in population health science. Finally, we propose directions for future research on approximate MAP inference in Bayesian nonparametrics.

Improved inference in the evaluation of mutual fund performance using bootstrap methods

Two new methodologies are introduced to improve inference in the evaluation of mutual fund performance against benchmarks. First, the benchmark models are estimated using panel methods with both fund and time effects. Second, the non-normality of individual mutual fund returns is accounted for by using panel bootstrap methods. We also augment the standard benchmark factors with fund-specific characteristics, such as fund size. Using a dataset of UK equity mutual fund returns, we find that fund size has a negative effect on the average fund manager’s benchmark-adjusted performance. Further, when we allow for time effects and the non-normality of fund returns, we find that there is no evidence that even the best performing fund managers can significantly out-perform the augmented benchmarks after fund management charges are taken into account.