Accelerating Pseudo-Marginal MCMC using Gaussian Processes

Pseudo-marginal methods such as the grouped independence Metropolis-Hastings (GIMH) and Markov chain within Metropolis (MCWM) algorithms have been introduced in the literature as an approach to perform Bayesian inference in latent variable models. These methods replace intractable likelihood calculations with unbiased estimates within Markov chain Monte Carlo algorithms. The GIMH method has the posterior of interest as its limiting distribution, but suffers from poor mixing if it is too computationally intensive to obtain high-precision likelihood estimates. The MCWM algorithm has better mixing properties, but less theoretical support. In this paper we propose to use Gaussian processes (GP) to accelerate the GIMH method, whilst using a short pilot run of MCWM to train the GP. Our new method, GP-GIMH, is illustrated on simulated data from a stochastic volatility and a gene network model.

Speaker identification using higher order spectral phase features and their effectiveness vis-a-vis Mel-Cepstral features

The effectiveness of higher-order spectral (HOS) phase features in speaker recognition is investigated by comparison with Mel Cepstral features on the same speech data. HOS phase features retain phase information from the Fourier spectrum unlikeMel–frequency Cepstral coefficients (MFCC). Gaussian mixture models are constructed from Mel– Cepstral features and HOS features, respectively, for the same data from various speakers in the Switchboard telephone Speech Corpus. Feature clusters, model parameters and classification performance are analyzed. HOS phase features on their own provide a correct identification rate of about 97% on the chosen subset of the corpus. This is the same level of accuracy as provided by MFCCs. Cluster plots and model parameters are compared to show that HOS phase features can provide complementary information to better discriminate between speakers.

Bearing-only SLAM : a vision-based navigation system for autonomous robots

To navigate successfully in a previously unexplored environment, a mobile robot must be able to estimate the spatial relationships of the objects of interest accurately. A Simultaneous Localization and Mapping (SLAM) sys- tem employs its sensors to build incrementally a map of its surroundings and to localize itself in the map simultaneously. The aim of this research project is to develop a SLAM system suitable for self propelled household lawnmowers. The proposed bearing-only SLAM system requires only an omnidirec- tional camera and some inexpensive landmarks. The main advantage of an omnidirectional camera is the panoramic view of all the landmarks in the scene. Placing landmarks in a lawn field to define the working domain is much easier and more flexible than installing the perimeter wire required by existing autonomous lawnmowers. The common approach of existing bearing-only SLAM methods relies on a motion model for predicting the robot’s pose and a sensor model for updating the pose. In the motion model, the error on the estimates of object positions is cumulated due mainly to the wheel slippage. Quantifying accu- rately the uncertainty of object positions is a fundamental requirement. In bearing-only SLAM, the Probability Density Function (PDF) of landmark position should be uniform along the observed bearing. Existing methods that approximate the PDF with a Gaussian estimation do not satisfy this uniformity requirement. This thesis introduces both geometric and proba- bilistic methods to address the above problems. The main novel contribu- tions of this thesis are: 1. A bearing-only SLAM method not requiring odometry. The proposed method relies solely on the sensor model (landmark bearings only) without relying on the motion model (odometry). The uncertainty of the estimated landmark positions depends on the vision error only, instead of the combination of both odometry and vision errors. 2. The transformation of the spatial uncertainty of objects. This thesis introduces a novel method for translating the spatial un- certainty of objects estimated from a moving frame attached to the robot into the global frame attached to the static landmarks in the environment. 3. The characterization of an improved PDF for representing landmark position in bearing-only SLAM. The proposed PDF is expressed in polar coordinates, and the marginal probability on range is constrained to be uniform. Compared to the PDF estimated from a mixture of Gaussians, the PDF developed here has far fewer parameters and can be easily adopted in a probabilistic framework, such as a particle filtering system. The main advantages of our proposed bearing-only SLAM system are its lower production cost and flexibility of use. The proposed system can be adopted in other domestic robots as well, such as vacuum cleaners or robotic toys when terrain is essentially 2D.

Improved GMM-based speaker verification using SVM-driven impostor dataset selection

The problem of impostor dataset selection for GMM-based speaker verification is addressed through the recently proposed data-driven background dataset refinement technique. The SVM-based refinement technique selects from a candidate impostor dataset those examples that are most frequently selected as support vectors when training a set of SVMs on a development corpus. This study demonstrates the versatility of dataset refinement in the task of selecting suitable impostor datasets for use in GMM-based speaker verification. The use of refined Z- and T-norm datasets provided performance gains of 15% in EER in the NIST 2006 SRE over the use of heuristically selected datasets. The refined datasets were shown to generalise well to the unseen data of the NIST 2008 SRE.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

Statistical analysis and reduction of multiple access interference in MC-CDMA systems

Multicarrier code division multiple access (MC-CDMA) is a very promising candidate for the multiple access scheme in fourth generation wireless communi- cation systems. During asynchronous transmission, multiple access interference (MAI) is a major challenge for MC-CDMA systems and significantly affects their performance. The main objectives of this thesis are to analyze the MAI in asyn- chronous MC-CDMA, and to develop robust techniques to reduce the MAI effect. Focus is first on the statistical analysis of MAI in asynchronous MC-CDMA. A new statistical model of MAI is developed. In the new model, the derivation of MAI can be applied to different distributions of timing offset, and the MAI power is modelled as a Gamma distributed random variable. By applying the new statistical model of MAI, a new computer simulation model is proposed. This model is based on the modelling of a multiuser system as a single user system followed by an additive noise component representing the MAI, which enables the new simulation model to significantly reduce the computation load during computer simulations. MAI reduction using slow frequency hopping (SFH) technique is the topic of the second part of the thesis. Two subsystems are considered. The first sub- system involves subcarrier frequency hopping as a group, which is referred to as GSFH/MC-CDMA. In the second subsystem, the condition of group hopping is dropped, resulting in a more general system, namely individual subcarrier frequency hopping MC-CDMA (ISFH/MC-CDMA). This research found that with the introduction of SFH, both of GSFH/MC-CDMA and ISFH/MC-CDMA sys- tems generate less MAI power than the basic MC-CDMA system during asyn- chronous transmission. Because of this, both SFH systems are shown to outper- form MC-CDMA in terms of BER. This improvement, however, is at the expense of spectral widening. In the third part of this thesis, base station polarization diversity, as another MAI reduction technique, is introduced to asynchronous MC-CDMA. The com- bined system is referred to as Pol/MC-CDMA. In this part a new optimum com- bining technique namely maximal signal-to-MAI ratio combining (MSMAIRC) is proposed to combine the signals in two base station antennas. With the applica- tion of MSMAIRC and in the absents of additive white Gaussian noise (AWGN), the resulting signal-to-MAI ratio (SMAIR) is not only maximized but also in- dependent of cross polarization discrimination (XPD) and antenna angle. In the case when AWGN is present, the performance of MSMAIRC is still affected by the XPD and antenna angle, but to a much lesser degree than the traditional maximal ratio combining (MRC). Furthermore, this research found that the BER performance for Pol/MC-CDMA can be further improved by changing the angle between the two receiving antennas. Hence the optimum antenna angles for both MSMAIRC and MRC are derived and their effects on the BER performance are compared. With the derived optimum antenna angle, the Pol/MC-CDMA system is able to obtain the lowest BER for a given XPD.

Improved GrabCut segmentation via GMM optimisation

Semi-automatic segmentation of still images has vast and varied practical applications. Recently, an approach "GrabCut" has managed to successfully build upon earlier approaches based on colour and gradient information in order to address the problem of efficient extraction of a foreground object in a complex environment. In this paper, we extend the GrabCut algorithm further by applying an unsupervised algorithm for modelling the Gaussian Mixtures that are used to define the foreground and background in the segmentation algorithm. We show examples where the optimisation of the GrabCut framework leads to further improvements in performance.

Experimental and theoretical studies of the redox potentials of cyclic nitroxides

The redox potentials of 25 cyclic nitroxides from four different structural classes (pyrrolidine, piperidine, isoindoline, and azaphenalene) were determined experimentally by cyclic voltammetry in acetonitrile, and also via high-level ab initio molecular orbital calculations. It is shown that the potentials are influenced by the type of ring system, ring substituents and/or groups surrounding the radical moiety. For the pyrrolidine, piperidine, and isoindolines there is excellent agreement (mean absolute deviation of 0.05 V) between the calculated and experimental oxidation potentials; for the azaphenalenes, however, there is an extraordinary discrepancy (mean absolute deviation of 0.60 V), implying that their one-electron oxidation might involve additional processes not considered in the theoretical calculations. This recently developed azaphenalene class of nitroxide represents a new variant of a nitroxide ring fused to an aromatic system and details of the synthesis of five derivatives involving differing aryl substitution are also presented.

Impact of cognitive load and frustration on drivers’ speech [Abstract]

Secondary tasks such as cell phone calls or interaction with automated speech dialog systems (SDSs) increase the driver’s cognitive load as well as the probability of driving errors. This study analyzes speech production variations due to cognitive load and emotional state of drivers in real driving conditions. Speech samples were acquired from 24 female and 17 male subjects (approximately 8.5 h of data) while talking to a co-driver and communicating with two automated call centers, with emotional states (neutral, negative) and the number of necessary SDS query repetitions also labeled. A consistent shift in a number of speech production parameters (pitch, first format center frequency, spectral center of gravity, spectral energy spread, and duration of voiced segments) was observed when comparing SDS interaction against co-driver interaction; further increases were observed when considering negative emotion segments and the number of requested SDS query repetitions. A mel frequency cepstral coefficient based Gaussian mixture classifier trained on 10 male and 10 female sessions provided 91% accuracy in the open test set task of distinguishing co-driver interactions from SDS interactions, suggesting—together with the acoustic analysis—that it is possible to monitor the level of driver distraction directly from their speech.

Characterisation of Ni carbonate-bearing minerals by UV-Vis-NIR spectroscopy

Four nickel carbonate-bearing minerals from Australia have been investigated to study the effect of Ni for Mg substitution. The spectra of nullaginite, zaratite, widgiemoolthalite and takovite show three main features in the range of 26,720–25,855 cm−1 (ν1-band), 15,230–14,740 cm−1 (ν2-band) and 9,200–9,145 cm−1 (ν3-band) which are characteristic of divalent nickel in six-fold coordination. The Crystal Field Stabilization Energy (CFSE) of Ni2+ in the four carbonates is calculated from the observed 3A2g(3F) → 3T2g(3F) transition. CFSE is dependent on mineralogy, crystallinity and chemical composition (Al/Mg-content). The splitting of the ν1- and ν3-bands and non-Gaussian shape of ν3-band in the minerals are the effects of Ni-site distortion from regular octahedral. The effect of structural cation substitutions (Mg2+, Ni2+, Fe2+ and trivalent cations, Al3+, Fe3+) in the carbonate minerals is noticed on band shifts. Thus, electronic bands in the UV–Vis–NIR spectra and the overtones and combination bands of OH and carbonate ion in NIR show shifts to higher wavenumbers, particularly for widgiemoolthalite and takovite.

Improving automatic speaker verification using SVM techniques

Automatic recognition of people is an active field of research with important forensic and security applications. In these applications, it is not always possible for the subject to be in close proximity to the system. Voice represents a human behavioural trait which can be used to recognise people in such situations. Automatic Speaker Verification (ASV) is the process of verifying a persons identity through the analysis of their speech and enables recognition of a subject at a distance over a telephone channel { wired or wireless. A significant amount of research has focussed on the application of Gaussian mixture model (GMM) techniques to speaker verification systems providing state-of-the-art performance. GMM's are a type of generative classifier trained to model the probability distribution of the features used to represent a speaker. Recently introduced to the field of ASV research is the support vector machine (SVM). An SVM is a discriminative classifier requiring examples from both positive and negative classes to train a speaker model. The SVM is based on margin maximisation whereby a hyperplane attempts to separate classes in a high dimensional space. SVMs applied to the task of speaker verification have shown high potential, particularly when used to complement current GMM-based techniques in hybrid systems. This work aims to improve the performance of ASV systems using novel and innovative SVM-based techniques. Research was divided into three main themes: session variability compensation for SVMs; unsupervised model adaptation; and impostor dataset selection. The first theme investigated the differences between the GMM and SVM domains for the modelling of session variability | an aspect crucial for robust speaker verification. Techniques developed to improve the robustness of GMMbased classification were shown to bring about similar benefits to discriminative SVM classification through their integration in the hybrid GMM mean supervector SVM classifier. Further, the domains for the modelling of session variation were contrasted to find a number of common factors, however, the SVM-domain consistently provided marginally better session variation compensation. Minimal complementary information was found between the techniques due to the similarities in how they achieved their objectives. The second theme saw the proposal of a novel model for the purpose of session variation compensation in ASV systems. Continuous progressive model adaptation attempts to improve speaker models by retraining them after exploiting all encountered test utterances during normal use of the system. The introduction of the weight-based factor analysis model provided significant performance improvements of over 60% in an unsupervised scenario. SVM-based classification was then integrated into the progressive system providing further benefits in performance over the GMM counterpart. Analysis demonstrated that SVMs also hold several beneficial characteristics to the task of unsupervised model adaptation prompting further research in the area. In pursuing the final theme, an innovative background dataset selection technique was developed. This technique selects the most appropriate subset of examples from a large and diverse set of candidate impostor observations for use as the SVM background by exploiting the SVM training process. This selection was performed on a per-observation basis so as to overcome the shortcoming of the traditional heuristic-based approach to dataset selection. Results demonstrate the approach to provide performance improvements over both the use of the complete candidate dataset and the best heuristically-selected dataset whilst being only a fraction of the size. The refined dataset was also shown to generalise well to unseen corpora and be highly applicable to the selection of impostor cohorts required in alternate techniques for speaker verification.

Bootstrap approaches for estimation and confidence intervals of long term memory processes

In this work, we investigate an alternative bootstrap approach based on a result of Ramsey [F.L. Ramsey, Characterization of the partial autocorrelation function, Ann. Statist. 2 (1974), pp. 1296-1301] and on the Durbin-Levinson algorithm to obtain a surrogate series from linear Gaussian processes with long range dependence. We compare this bootstrap method with other existing procedures in a wide Monte Carlo experiment by estimating, parametrically and semi-parametrically, the memory parameter d. We consider Gaussian and non-Gaussian processes to prove the robustness of the method to deviations from normality. The approach is also useful to estimate confidence intervals for the memory parameter d by improving the coverage level of the interval.

Interleaved PC-OFDM to reduce peak-to-average power ratio

Parallel combinatory orthogonal frequency division multiplexing (PC-OFDM yields lower maximum peak-to-average power ratio (PAR), high bandwidth efficiency and lower bit error rate (BER) on Gaussian channels compared to OFDM systems. However, PC-OFDM does not improve the statistics of PAR significantly. In this chapter, the use of a set of fixed permutations to improve the statistics of the PAR of a PC-OFDM signal is presented. For this technique, interleavers are used to produce K-1 permuted sequences from the same information sequence. The sequence with the lowest PAR, among K sequences is chosen for the transmission. The PAR of a PC-OFDM signal can be further reduced by 3-4 dB by this technique. Mathematical expressions for the complementary cumulative density function (CCDF)of PAR of PC-OFDM signal and interleaved PC-OFDM signal are also presented.

Wide-angle visual feature matching for outdoor localization

Wide-angle images exhibit significant distortion for which existing scale-space detectors such as the scale-invariant feature transform (SIFT) are inappropriate. The required scale-space images for feature detection are correctly obtained through the convolution of the image, mapped to the sphere, with the spherical Gaussian. A new visual key-point detector, based on this principle, is developed and several computational approaches to the convolution are investigated in both the spatial and frequency domain. In particular, a close approximation is developed that has comparable computation time to conventional SIFT but with improved matching performance. Results are presented for monocular wide-angle outdoor image sequences obtained using fisheye and equiangular catadioptric cameras. We evaluate the overall matching performance (recall versus 1-precision) of these methods compared to conventional SIFT. We also demonstrate the use of the technique for variable frame-rate visual odometry and its application to place recognition.