by Ka-Kit Tse. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references. / Acknowledgments --- p.i / List of tables --- p.v / Chapter Chapter 1: --- Overall Review --- p.1 / Chapter Chapter 2: --- Essay one - A Mathematical Programming Approach to Clusterwise Regression Model and its Extensions / Chapter 2.0. --- Abstract --- p.5 / Chapter 2.1. --- Introduction --- p.6 / Chapter 2.2. --- A Mathematical Programming Formulation of the Clusterwise Regression Model --- p.10 / Chapter 2.2.1. --- The Generalized Clusterwise Regression Model --- p.10 / Chapter 2.2.2. --- "Clusterwise Regression Model (Spath, 1979)" --- p.14 / Chapter 2.2.3. --- A Nonparametric Clusterwise Regression Model --- p.15 / Chapter 2.2.4. --- A Mixture Approach to Clusterwise Regression Model --- p.16 / Chapter 2.2.5. --- An Illustrative Application --- p.19 / Chapter 2.3. --- Mathematical Programming Formulation of the Clusterwise Discriminant Analysis --- p.21 / Chapter 2.4. --- Conclusion --- p.25 / Chapter 2.5. --- Appendix --- p.28 / Chapter 2.6. --- References --- p.32 / Chapter 2.7. --- Tables --- p.35 / Chapter Chapter 3: --- Essay two - A Mathematical Programming Approach to Clusterwise Rank Order Logit Model / Chapter 3.0. --- Abstract --- p.40 / Chapter 3.1. --- Introduction --- p.41 / Chapter 3.2. --- Clusterwise Rank Order Logit Model --- p.42 / Chapter 3.3. --- Numerical Illustration --- p.46 / Chapter 3.4. --- Conclustion --- p.48 / Chapter 3.5. --- References --- p.50 / Chapter 3.6. --- Tables --- p.52 / Chapter Chapter 4: --- Essay three - A Mathematical Programming Approach to Metric Unidimensional Scaling / Chapter 4.0. --- Abstract --- p.53 / Chapter 4.1. --- Introduction --- p.54 / Chapter 4.2. --- Nonlinear Programming Formulation --- p.56 / Chapter 4.3. --- Numerical Examples --- p.60 / Chapter 4.4. --- Possible Extensions --- p.61 / Chapter 4.5. --- Conclusion and Extensions --- p.63 / Chapter 4.6. --- References --- p.64 / Chapter 4.7. --- Tables --- p.66 / Chapter Chapter 5: --- Research Project in Progress / Chapter 5.1. --- Project 1 -- An Integrated Approach to Taste Test Experiment Within the Prospect Theory Framework --- p.68 / Chapter 5.1.1. --- Experiment Procedure --- p.68 / Chapter 5.1.2. --- Experimental Result --- p.72 / Chapter 5.2. --- Project 2 -- An Integrated Approach to Multi- Dimensional Scaling Problem --- p.75 / Chapter 5.2.1. --- Introduction --- p.75 / Chapter 5.2.2. --- Experiment Procedure --- p.76 / Chapter 5.2.3. --- Questionnaire --- p.78 / Chapter 5.2.4. --- Experimental Result --- p.78

Lui Ying Kin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 63-65). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Introduction to bootstrap and efficiency bootstrap simulation --- p.5 / Chapter 2.1 --- Background of bootstrap --- p.5 / Chapter 2.2 --- Basic idea of bootstrap --- p.7 / Chapter 2.3 --- Variance reduction methods --- p.10 / Chapter 2.3.1 --- Control variates --- p.10 / Chapter 2.3.2 --- Common random numbers --- p.12 / Chapter 2.3.3 --- Antithetic variates --- p.14 / Chapter 2.3.4 --- Importance Sampling --- p.15 / Chapter 2.4 --- Efficient bootstrap simulation --- p.17 / Chapter 2.4.1 --- Linear approximation --- p.18 / Chapter 2.4.2 --- Centring method --- p.19 / Chapter 2.4.3 --- Balanced resampling --- p.20 / Chapter 2.4.4 --- Antithetic resampling --- p.21 / Chapter 3 --- Methodology --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Cluster analysis --- p.24 / Chapter 3.3 --- Regression estimator and mixture experiment --- p.25 / Chapter 3.4 --- Estimate of standard error and bias --- p.30 / Chapter 4 --- Simulation study --- p.45 / Chapter 4.1 --- Introduction --- p.45 / Chapter 4.2 --- Ratio estimation --- p.46 / Chapter 4.3 --- Time series problem --- p.50 / Chapter 4.4 --- Regression problem --- p.54 / Chapter 5 --- Conclusion and discussion --- p.60 / Reference --- p.63

Yang, Haiqin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 98-109). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Time Series Prediction and Its Problems --- p.1 / Chapter 1.2 --- Major Contributions --- p.2 / Chapter 1.3 --- Thesis Organization --- p.3 / Chapter 1.4 --- Notation --- p.4 / Chapter 2 --- Literature Review --- p.5 / Chapter 2.1 --- Framework --- p.6 / Chapter 2.1.1 --- Data Processing --- p.8 / Chapter 2.1.2 --- Model Building --- p.10 / Chapter 2.1.3 --- Forecasting Procedure --- p.12 / Chapter 2.2 --- Model Descriptions --- p.13 / Chapter 2.2.1 --- Linear Models --- p.15 / Chapter 2.2.2 --- Non-linear Models --- p.17 / Chapter 2.2.3 --- ARMA Models --- p.21 / Chapter 2.2.4 --- Support Vector Machines --- p.23 / Chapter 3 --- Support Vector Regression --- p.27 / Chapter 3.1 --- Regression Problem --- p.27 / Chapter 3.2 --- Loss Function --- p.29 / Chapter 3.3 --- Kernel Function --- p.34 / Chapter 3.4 --- Relation to Other Models --- p.36 / Chapter 3.4.1 --- Relation to Support Vector Classification --- p.36 / Chapter 3.4.2 --- Relation to Ridge Regression --- p.38 / Chapter 3.4.3 --- Relation to Radial Basis Function --- p.40 / Chapter 3.5 --- Implemented Algorithms --- p.40 / Chapter 4 --- Margins in Support Vector Regression --- p.46 / Chapter 4.1 --- Problem --- p.47 / Chapter 4.2 --- General ε-insensitive Loss Function --- p.48 / Chapter 4.3 --- Accuracy Metrics and Risk Measures --- p.52 / Chapter 5 --- Margin Variation --- p.55 / Chapter 5.1 --- Non-fixed Margin Cases --- p.55 / Chapter 5.1.1 --- Momentum --- p.55 / Chapter 5.1.2 --- GARCH --- p.57 / Chapter 5.2 --- Experiments --- p.58 / Chapter 5.2.1 --- Momentum --- p.58 / Chapter 5.2.2 --- GARCH --- p.65 / Chapter 5.3 --- Discussions --- p.72 / Chapter 6 --- Relation between Downside Risk and Asymmetrical Margin Settings --- p.77 / Chapter 6.1 --- Mathematical Derivation --- p.77 / Chapter 6.2 --- Algorithm --- p.81 / Chapter 6.3 --- Experiments --- p.83 / Chapter 6.4 --- Discussions --- p.86 / Chapter 7 --- Conclusion --- p.92 / Chapter A --- Basic Results for Solving SVR --- p.94 / Chapter A.1 --- Dual Theory --- p.94 / Chapter A.2 --- Standard Method to Solve SVR --- p.96 / Bibliography --- p.98

The overall theme of this thesis focuses on methods for functional regression and nonlinear mixed-effects models with applications to PET data. The first part considers the problem of variable selection in regression models with functional responses and scalar predictors. We pose the function-on-scalar model as a multivariate regression problem and use group-MCP for variable selection. We account for residual covariance by "pre-whitening" using an estimate of the covariance matrix, and establish theoretical properties for the resulting estimator. We further develop an iterative algorithm that alternately updates the spline coefficients and covariance. Our method is illustrated by the application to two-dimensional planar reaching motions in a study of the effects of stroke severity on motor control. The second part introduces a functional data analytic approach for the estimation of the IRF, which is necessary for describing the binding behavior of the radiotracer. Virtually all existing methods have three common aspects: summarizing the entire IRF with a single scalar measure; modeling each subject separately; and the imposition of parametric restrictions on the IRF. In contrast, we propose a functional data analytic approach that regards each subject's IRF as the basic analysis unit, models multiple subjects simultaneously, and estimates the IRF nonparametrically. We pose our model as a linear mixed effect model in which shrinkage and roughness penalties are incorporated to enforce identifiability and smoothness of the estimated curves, respectively, while monotonicity and non-negativity constraints impose biological information on estimates. We illustrate this approach by applying it to clinical PET data. The third part discusses a nonlinear mixed-effects modeling approach for PET data analysis under the assumption of a compartment model. The traditional NLS estimators of the population parameters are applied in a two-stage analysis, which brings instability issue and neglects the variation in rate parameters. In contrast, we propose to estimate the rate parameters by fitting nonlinear mixed-effects (NLME) models, in which all the subjects are modeled simultaneously by allowing rate parameters to have random effects and population parameters can be estimated directly from the joint model. Simulations are conducted to compare the power of detecting group effect in both rate parameters and summarized measures of tests based on both NLS and NLME models. We apply our NLME approach to clinical PET data to illustrate the model building procedure.

Neste trabalho estudamos modelos lineares de regressão para a análise de dados obtidos de pesquisas amostrais complexas. Foram considerados aspectos teóricos e aplicações a conjuntos de dados reais por meio do uso do aplicativo SUDAAN e da biblioteca ADAC da linguagem R. Nas aplicações foram abordados os modelos de regressão normal e logística. Foram realizados também estudos comparativos dos métodos estudados com os que assumem que as observações são selecionadas segundo amostragem aleatória simples. / We have studied linear regression models for data analysis when the data set comes from a complex sampling survey. We have considered theoretical aspects and some applications utilizing the SUDAAN software and the ADAC library for R language. The applications involved the normal and logistic regression models. The studied methods were compared with those obtained from simple random samples.

This thesis uses methods from functional data analysis (FDA) to solve problems from three scientific areas of study. While the areas of application are quite distinct, the common thread of functional data analysis ties them together. The first chapter describes interactive open-source software for explaining and disseminating results of functional data analyses. Chapters two and three use curve alignment, or registration, to solve common problems in accelerometry and neuroimaging, respectively. The final chapter introduces a novel regression method for modeling functional outcomes that are trajectories over time. The first chapter of this thesis details a software package for interactively visualizing functional data analyses. The software is designed to work for a wide range of datasets and several types of analyses. This chapter describes that software and provides an overview ofFDA in different contexts. The second chapter introduces a framework for curve alignment, or registration, of exponential family functional data. The approach distinguishes itself from previous registration methods in its ability to handle dense binary observations with computational efficiency. Motivation comes from the Baltimore Longitudinal Study on Aging, in which accelerometer data provides valuable insights into the timing of sedentary behavior. The third chapter takes lessons learned about curve registration from the second chapter and use them to develop methods in an entirely new context: large multisite brain imaging studies. Scanner effects in multisite imaging studies are non-biological variability due to technical differences across sites and scanner hardware. This method identifies and removes scanner effects by registering cumulative distribution functions of image intensities values. In the final chapter the focus shifts from curve registration to regression. Described within this chapter is an entirely new nonlinear regression framework that draws from both functional data analysis and systems of ordinary equations. This model is motivated by the neurobiology of skilled movement, and was developed to capture the relationship between neural activity and arm movement in mice.

This thesis investigates the use of newly-developed survival analysis tools for credit scoring. Credit scoring techniques are currently used by financial institutions to estimate the probability of a customer defaulting on a loan by a predetermined time in the future. While a number of classification techniques are currently used, banks are now becoming more concerned with estimating the lifetime of the loan rather than just the probability of default. Difficulties arise when using standard statistical techniques due to the presence of censoring in the data. Survival analysis, originating from medical and engineering fields, is an area of statistics that typically deals with censored lifetime data. The theoretical developments in this thesis revolve around linear regression for censored data, in particular the Buckley-James method. The Buckley-James method is analogous to linear regression and gives estimates of the mean expected lifetime given a set of explanato ry variables. The first development is a measure of fit for censored regression, similar to the classical r-squared of linear regression. Next, the variable-reduction technique of stepwise selection is extended to the Buckley-James method. For the last development, the Buckley-James algorithm is altered to incorporate non-linear regression methods such as neural networks and Multivariate Adaptive Regression Splines (MARS). MARS shows promise in terms of predictive power and interpretability in both simulation and empirical studies. The practical section of the thesis involves using the new techniques to predict the time to default and time to repayment of unsecured personal loans from a database obtained from a major Australian bank. The analyses are unique, being the first published work on applying Buckley-James and related methods to a large-scale financial database.

This thesis proposes several new techniques to improve the performance of speciated particle swarms in multimodal environments. We investigate how these algorithms can become more robust and adaptive, easier to use and able to solve a wider variety of optimisation problems. We then develop a technique that uses regression to vastly improve an algorithm's convergence speed without requiring extra evaluations. Speciation techniques play an important role in particle swarms. They allow an algorithm to locate multiple optima, providing the user with a choice of solutions. Speciation also provides diversity preservation, which can be critical for dynamic optimisation. By increasing diversity and tracking multiple peaks simultaneously, speciated algorithms are better able to handle the changes inherent in dynamic environments. Speciation algorithms often require a user to specify a parameter that controls how species form. This is a major drawback since the knowledge may not be available a priori. If the parameter is incorrectly set, the algorithm's performance is likely to be highly degraded. We propose using a time-based measure to control the speciation, allowing the algorithm to define species far more adaptively, using the population's characteristics and behaviour to control membership. Two new techniques presented in this thesis, ANPSO and ESPSO, use time-based convergence measures to define species. These methods are shown to be robust while still providing highly competitive performance. Both algorithms effectively optimised all of our test functions without requiring any tuning. Speciated algorithms are ideally suited to optimising dynamic environments, however the complexity of these environments makes them far more difficult to design algorithms for. To increase an algorithm's performance it is necessary to determine in what ways it should be improved. While all performance metrics allow optimisation techniques to be compared, they cannot show how to improve an algorithm. Until now this has been done largely by trial and error. This is extremely inefficient, in the same way it is inefficient trying to improve a program's speed without profiling it first. This thesis proposes a new metric that exclusively measures convergence speed. We show that an algorithm can be profiled by correlating the performance as measured by multiple metrics. By combining these two techniques, we can obtain far better insight into how best to improve an algorithm. Using this information, we then propose a local convergence enhancement that greatly increases performance by actively estimating the location of an optimum. The enhancement uses regression to fit a surface to the peak, guiding the search by estimating the peak's true location. By incorporating this technique, the algorithm is able to use the information contained within the fitness landscape far more effectively. We show that by combining the regression with an existing speciated algorithm, we are able to vastly improve the algorithm's performance. This technique will greatly enhance the utility of PSO on problems where fitness evaluations are expensive, or that require fast reaction to change.

Dans cette thèse nous étudions l'estimation de modèles probabilistes discriminants, surtout des aspects d'apprentissage semi-supervisé et de sélection de caractéristiques. Le but de l'apprentissage semi-supervisé est d'améliorer l'efficacité de l'apprentissage supervisé en utilisant des données non-étiquetées. Cet objectif est difficile à atteindre dans les cas des modèles discriminants. Les modèles probabilistes discriminants permettent de manipuler des représentations linguistiques riches, sous la forme de vecteurs de caractéristiques de très grande taille. Travailler en grande dimension pose des problèmes, en particulier computationnels, qui sont exacerbés dans le cadre de modèles de séquences tels que les champs aléatoires conditionnels (CRF). Notre contribution est double. Nous introduisons une méthode originale et simple pour intégrer des données non étiquetées dans une fonction objectif semi-supervisée. Nous démontrons alors que l'estimateur semi-supervisé correspondant est asymptotiquement optimal. Le cas de la régression logistique est illustré par des résultats d'expèriences. Dans cette étude, nous proposons un algorithme d'estimation pour les CRF qui réalise une sélection de modèle, par le truchement d'une pénalisation $L_1$. Nous présentons également les résultats d'expériences menées sur des tâches de traitement des langues (le chunking et la détection des entités nommées), en analysant les performances en généralisation et les caractéristiques sélectionnées. Nous proposons finalement diverses pistes pour améliorer l'efficacité computationelle de cette technique.

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