Generalised Wishart Processes

We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time varying) covariance matrices. Unlike existing models, it can capture a diverse class of covariance structures, it can easily handle missing data, the dependent variable can readily include covariates other than time, and it scales well with dimension; there is no need for free parameters, and optional parameters are easy to interpret. We describe how to construct the GWP, introduce general procedures for inference and predictions, and show that it outperforms its main competitor, multivariate GARCH, even on financial data that especially suits GARCH. We also show how to predict the mean of a multivariate process while accounting for dynamic correlations.

Projective Limit Random Probabilities on Polish Spaces

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the construction of the Dirichlet process from finite-dimensional Dirichlet distributions. This approach is both intuitive and applicable to the construction of arbitrary distributions on M(V), but also hamstrung by a number of technical difficulties. We show how these difficulties can be resolved if the domain V is a Polish topological space, and give a representation theorem directly applicable to the construction of any probability distribution on M(V) whose first moment measure is well-defined. The proof draws on a projective limit theorem of Bochner, and on properties of set functions on Polish spaces to establish countable additivity of the resulting random probabilities.

Exploiting variable-width features in large vocabulary speech recognition

The use of variable-width features (prosodics, broad structural information etc.) in large vocabulary speech recognition systems is discussed. Although the value of this sort of information has been recognized in the past, previous approaches have not been widely used in speech systems because either they have not been robust enough for realistic, large vocabulary tasks or they have been limited to certain recognizer architectures. A framework for the use of variable-width features is presented which employs the N-Best algorithm with the features being applied in a post-processing phase. The framework is flexible and widely applicable, giving greater scope for exploitation of the features than previous approaches. Large vocabulary speech recognition experiments using TIMIT show that the application of variable-width features has potential benefits.

Random lasing in a bistable smectic A liquid crystal

In this work, we examine the phenomenon of random lasing from the smectic A liquid crystal phase. We summarise our results to date on random lasing from the smectic A phase including the ability to control the output from the sample using applied electric fields. In addition, diffuse random lasing is demonstrated from the electrohydrodynamic instabilities of a smectic A liquid crystal phase that has been doped with a low concentration of ionic impurities. Using a siloxane-based liquid crystal doped with ionic impurities and a laser dye, nonresonant random laser emission is observed from the highly scattering texture of the smectic A phase which is stable in zero-field. With the application of a low frequency alternating current electric field, turbulence is induced due to motion of the ions. This is accompanied by a decrease in the emission linewidth and an increase in the intensity of the laser emission. The benefit in this case is that a field is not required to maintain the texture as the scattering and homeotropic states are both stable in zero field. This offers a lower power consumption alternative to the electric-field induced static scattering sample.

Gaussian mixture modeling with Gaussian process latent variable models

Density modeling is notoriously difficult for high dimensional data. One approach to the problem is to search for a lower dimensional manifold which captures the main characteristics of the data. Recently, the Gaussian Process Latent Variable Model (GPLVM) has successfully been used to find low dimensional manifolds in a variety of complex data. The GPLVM consists of a set of points in a low dimensional latent space, and a stochastic map to the observed space. We show how it can be interpreted as a density model in the observed space. However, the GPLVM is not trained as a density model and therefore yields bad density estimates. We propose a new training strategy and obtain improved generalisation performance and better density estimates in comparative evaluations on several benchmark data sets. © 2010 Springer-Verlag.

Variable repetition frequency femtosecond-pulse surface emitting semiconductor laser

We report a femtosecond-pulse vertical-external-cavity surface-emitting laser with a continuous repetition frequency tuning range of 8 near 1 GHz. A constant average output power of 56 ± 1 mW and near-transform-limited pulse duration of 450 ± 20 fs were observed across the entire tuning range. © 2011 American Institute of Physics.