Tree-Structured Stick Breaking Processes for Hierarchical Data

Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeable. One can view our model as providing infinite mixtures where the components have a dependency structure corresponding to an evolutionary diffusion down a tree. By using a stick-breaking approach, we can apply Markov chain Monte Carlo methods based on slice sampling to perform Bayesian inference and simulate from the posterior distribution on trees. We apply our method to hierarchical clustering of images and topic modeling of text data.

Copula Processes

We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility (GCPV), to predict the latent standard deviations of a sequence of random variables. To make predictions we use Bayesian inference, with the Laplace approximation, and with Markov chain Monte Carlo as an alternative. We find both methods comparable. We also find our model can outperform GARCH on simulated and financial data. And unlike GARCH, GCPV can easily handle missing data, incorporate covariates other than time, and model a rich class of covariance structures.

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.

A comparison of power losses for small (< 1 kW) induction motor drives adopting squarewave and sinusoidal PWM excitation

In this paper the influence of the form of motor excitation on the performance of a small (< 1 kW) induction motor drive is studied. Two forms of excitation, namely sine waves generated by pulse width modulation and simple square wave are explored. Sine wave excitation gives lower motor losses but increases inverter losses. Conversely, square wave excitation increases motor losses but decreases inverter losses. Losses have been measured directly by calorimetric means or, in the case of the inverter, predicted by a Pspice model that has been verified by calorimetric methods. The work shows that overall, the use of square wave excitation leads to a more efficient drive. © 2004 The Institution of Electrical Engineers.

APPROXIMATE GAUSS-MARKOV REALISATION OF MULTIVARIATE STOCHASTIC PROCESSES.

Given a spectral density matrix or, equivalently, a real autocovariance sequence, the author seeks to determine a finite-dimensional linear time-invariant system which, when driven by white noise, will produce an output whose spectral density is approximately PHI ( omega ), and an approximate spectral factor of PHI ( omega ). The author employs the Anderson-Faurre theory in his analysis.

The effect of work processes on the casing heat transfer of a transonic turbine

This paper considers the effect of the rotor tip on the casing heat load of a transonic axial flow turbine. The aim of the research is to understand the dominant causes of casing heat-transfer. Experimental measurements were conducted at engine-representative Mach number, Reynolds number and stage inlet to casing wall temperature ratio. Time-resolved heat-transfer coefficient and gas recovery temperature on the casing were measured using an array of heat-transfer gauges. Time-resolved static pressure on the casing wall was measured using Kulite pressure transducers. Time-resolved numerical simulations were undertaken to aid understanding of the mechanism responsible for casing heat load. The results show that between 35% and 60% axial chord the rotor tip-leakage flow is responsible for more than 50% of casing heat transfer. The effects of both gas recovery temperature and heat transfer coefficient were investigated separately and it is shown that an increased stagnation temperature in the rotor tip gap dominates casing heat-transfer. In the tip gap the stagnation temperature is shown to rise above that found at stage inlet (combustor exit) by as much as 35% of stage total temperature drop. The rise in stagnation temperature is caused by an isentropic work input to the tip-leakage fluid by the rotor. The size of this mechanism is investigated by computationally tracking fluid path-lines through the rotor tip gap to understand the unsteady work processes that occur. Copyright © 2005 by ASME.

Dynamics in dye-doped LC systems in presence of trans-cis isomerism

The excitation as well as relaxation dynamics of dye-doped nematic liquid crystal cells has been explored both experimentally and theoretically. Overshoots in the build up of the probe signal diffracted from gratings written onto dye-doped liquid crystal systems have often been observed. The overshoot behaviour makes the accurate measurement of nonlinear optical (NLO) response magnitude difficult and ambiguous. Moreover, it complicates the understanding of the dynamics and the physics of the NLO processes. On the basis of the system with trans-cis isomerisation as a mechanism of the NLO effect the quantitative model has been built to describe the experimental results which we observe. The two unknown material parameters: diffusion coefficient and cis species lifetime are calculated from the relaxation data. A quantitative model of the signal build-up uses these parameters. The calculated dynamic behaviour based on this model correlates very well with the experimental data. The model is used to predict the performance of the system with various dopant diffusion properties.

Analysis of basic processes inside the keyhole during deep penetration ND-YAG CW laser welding

During laser welding, the keyhole is generated by the recoil pressure induced by the evaporation processes occurring mainly on the front keyhole wall (KW). In order to characterize the evaporation process, we have measured this recoil pressure by using a plume deflection technique, where the plume generated for static conditions (i. e. with no sample displacement) is deflected by a transverse side gas jet. From the measurement of the plume deflection angle, the recoil pressure can be determined as a function of incident intensity and sample material. From these data one can estimate the pressure generated on the front KW, during laser welding. Therefore, the corresponding dynamic pressure exerted by the vapor plume expansion on the rear KW, in contact with the melt pool, can be also estimated. These pressures appear to be in close agreement with those generated by an additional side jet that has been used in previous experiments, for stabilizing the observed melt pool oscillations or fluctuations.

Continuous F0 in the source-excitation generation for HMM-based TTS: Do we need voiced/unvoiced classification?

Most HMM-based TTS systems use a hard voiced/unvoiced classification to produce a discontinuous F0 signal which is used for the generation of the source-excitation. When a mixed source excitation is used, this decision can be based on two different sources of information: the state-specific MSD-prior of the F0 models, and/or the frame-specific features generated by the aperiodicity model. This paper examines the meaning of these variables in the synthesis process, their interaction, and how they affect the perceived quality of the generated speech The results of several perceptual experiments show that when using mixed excitation, subjects consistently prefer samples with very few or no false unvoiced errors, whereas a reduction in the rate of false voiced errors does not produce any perceptual improvement. This suggests that rather than using any form of hard voiced/unvoiced classification, e.g., the MSD-prior, it is better for synthesis to use a continuous F0 signal and rely on the frame-level soft voiced/unvoiced decision of the aperiodicity model. © 2011 IEEE.

Enhanced poisson sum representation for alpha-stable processes

In this paper we present Poisson sum series representations for α-stable (αS) random variables and a-stable processes, in particular concentrating on continuous-time autoregressive (CAR) models driven by α-stable Lévy processes. Our representations aim to provide a conditionally Gaussian framework, which will allow parameter estimation using Rao-Blackwellised versions of state of the art Bayesian computational methods such as particle filters and Markov chain Monte Carlo (MCMC). To overcome the issues due to truncation of the series, novel residual approximations are developed. Simulations demonstrate the potential of these Poisson sum representations for inference in otherwise intractable α-stable models. © 2011 IEEE.