Lin Dahua. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 233-250). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Problem We are Facing --- p.1 / Chapter 1.2 --- Generative vs. Discriminative Models --- p.2 / Chapter 1.3 --- Statistical Feature Extraction: Success and Challenge --- p.3 / Chapter 1.4 --- Overview of Our Works --- p.5 / Chapter 1.4.1 --- New Linear Discriminant Methods: Generalized LDA Formulation and Performance-Driven Sub space Learning --- p.5 / Chapter 1.4.2 --- Coupled Learning Models: Coupled Space Learning and Inter Modality Recognition --- p.6 / Chapter 1.4.3 --- Informative Learning Approaches: Conditional Infomax Learning and Information Chan- nel Model --- p.6 / Chapter 1.5 --- Organization of the Thesis --- p.8 / Chapter I --- History and Background --- p.10 / Chapter 2 --- Statistical Pattern Recognition --- p.11 / Chapter 2.1 --- Patterns and Classifiers --- p.11 / Chapter 2.2 --- Bayes Theory --- p.12 / Chapter 2.3 --- Statistical Modeling --- p.14 / Chapter 2.3.1 --- Maximum Likelihood Estimation --- p.14 / Chapter 2.3.2 --- Gaussian Model --- p.15 / Chapter 2.3.3 --- Expectation-Maximization --- p.17 / Chapter 2.3.4 --- Finite Mixture Model --- p.18 / Chapter 2.3.5 --- A Nonparametric Technique: Parzen Windows --- p.21 / Chapter 3 --- Statistical Learning Theory --- p.24 / Chapter 3.1 --- Formulation of Learning Model --- p.24 / Chapter 3.1.1 --- Learning: Functional Estimation Model --- p.24 / Chapter 3.1.2 --- Representative Learning Problems --- p.25 / Chapter 3.1.3 --- Empirical Risk Minimization --- p.26 / Chapter 3.2 --- Consistency and Convergence of Learning --- p.27 / Chapter 3.2.1 --- Concept of Consistency --- p.27 / Chapter 3.2.2 --- The Key Theorem of Learning Theory --- p.28 / Chapter 3.2.3 --- VC Entropy --- p.29 / Chapter 3.2.4 --- Bounds on Convergence --- p.30 / Chapter 3.2.5 --- VC Dimension --- p.35 / Chapter 4 --- History of Statistical Feature Extraction --- p.38 / Chapter 4.1 --- Linear Feature Extraction --- p.38 / Chapter 4.1.1 --- Principal Component Analysis (PCA) --- p.38 / Chapter 4.1.2 --- Linear Discriminant Analysis (LDA) --- p.41 / Chapter 4.1.3 --- Other Linear Feature Extraction Methods --- p.46 / Chapter 4.1.4 --- Comparison of Different Methods --- p.48 / Chapter 4.2 --- Enhanced Models --- p.49 / Chapter 4.2.1 --- Stochastic Discrimination and Random Subspace --- p.49 / Chapter 4.2.2 --- Hierarchical Feature Extraction --- p.51 / Chapter 4.2.3 --- Multilinear Analysis and Tensor-based Representation --- p.52 / Chapter 4.3 --- Nonlinear Feature Extraction --- p.54 / Chapter 4.3.1 --- Kernelization --- p.54 / Chapter 4.3.2 --- Dimension reduction by Manifold Embedding --- p.56 / Chapter 5 --- Related Works in Feature Extraction --- p.59 / Chapter 5.1 --- Dimension Reduction --- p.59 / Chapter 5.1.1 --- Feature Selection --- p.60 / Chapter 5.1.2 --- Feature Extraction --- p.60 / Chapter 5.2 --- Kernel Learning --- p.61 / Chapter 5.2.1 --- Basic Concepts of Kernel --- p.61 / Chapter 5.2.2 --- The Reproducing Kernel Map --- p.62 / Chapter 5.2.3 --- The Mercer Kernel Map --- p.64 / Chapter 5.2.4 --- The Empirical Kernel Map --- p.65 / Chapter 5.2.5 --- Kernel Trick and Kernelized Feature Extraction --- p.66 / Chapter 5.3 --- Subspace Analysis --- p.68 / Chapter 5.3.1 --- Basis and Subspace --- p.68 / Chapter 5.3.2 --- Orthogonal Projection --- p.69 / Chapter 5.3.3 --- Orthonormal Basis --- p.70 / Chapter 5.3.4 --- Subspace Decomposition --- p.70 / Chapter 5.4 --- Principal Component Analysis --- p.73 / Chapter 5.4.1 --- PCA Formulation --- p.73 / Chapter 5.4.2 --- Solution to PCA --- p.75 / Chapter 5.4.3 --- Energy Structure of PCA --- p.76 / Chapter 5.4.4 --- Probabilistic Principal Component Analysis --- p.78 / Chapter 5.4.5 --- Kernel Principal Component Analysis --- p.81 / Chapter 5.5 --- Independent Component Analysis --- p.83 / Chapter 5.5.1 --- ICA Formulation --- p.83 / Chapter 5.5.2 --- Measurement of Statistical Independence --- p.84 / Chapter 5.6 --- Linear Discriminant Analysis --- p.85 / Chapter 5.6.1 --- Fisher's Linear Discriminant Analysis --- p.85 / Chapter 5.6.2 --- Improved Algorithms for Small Sample Size Problem . --- p.89 / Chapter 5.6.3 --- Kernel Discriminant Analysis --- p.92 / Chapter II --- Improvement in Linear Discriminant Analysis --- p.100 / Chapter 6 --- Generalized LDA --- p.101 / Chapter 6.1 --- Regularized LDA --- p.101 / Chapter 6.1.1 --- Generalized LDA Implementation Procedure --- p.101 / Chapter 6.1.2 --- Optimal Nonsingular Approximation --- p.103 / Chapter 6.1.3 --- Regularized LDA algorithm --- p.104 / Chapter 6.2 --- A Statistical View: When is LDA optimal? --- p.105 / Chapter 6.2.1 --- Two-class Gaussian Case --- p.106 / Chapter 6.2.2 --- Multi-class Cases --- p.107 / Chapter 6.3 --- Generalized LDA Formulation --- p.108 / Chapter 6.3.1 --- Mathematical Preparation --- p.108 / Chapter 6.3.2 --- Generalized Formulation --- p.110 / Chapter 7 --- Dynamic Feedback Generalized LDA --- p.112 / Chapter 7.1 --- Basic Principle --- p.112 / Chapter 7.2 --- Dynamic Feedback Framework --- p.113 / Chapter 7.2.1 --- Initialization: K-Nearest Construction --- p.113 / Chapter 7.2.2 --- Dynamic Procedure --- p.115 / Chapter 7.3 --- Experiments --- p.115 / Chapter 7.3.1 --- Performance in Training Stage --- p.116 / Chapter 7.3.2 --- Performance on Testing set --- p.118 / Chapter 8 --- Performance-Driven Subspace Learning --- p.119 / Chapter 8.1 --- Motivation and Principle --- p.119 / Chapter 8.2 --- Performance-Based Criteria --- p.121 / Chapter 8.2.1 --- The Verification Problem and Generalized Average Margin --- p.122 / Chapter 8.2.2 --- Performance Driven Criteria based on Generalized Average Margin --- p.123 / Chapter 8.3 --- Optimal Subspace Pursuit --- p.125 / Chapter 8.3.1 --- Optimal threshold --- p.125 / Chapter 8.3.2 --- Optimal projection matrix --- p.125 / Chapter 8.3.3 --- Overall procedure --- p.129 / Chapter 8.3.4 --- Discussion of the Algorithm --- p.129 / Chapter 8.4 --- Optimal Classifier Fusion --- p.130 / Chapter 8.5 --- Experiments --- p.131 / Chapter 8.5.1 --- Performance Measurement --- p.131 / Chapter 8.5.2 --- Experiment Setting --- p.131 / Chapter 8.5.3 --- Experiment Results --- p.133 / Chapter 8.5.4 --- Discussion --- p.139 / Chapter III --- Coupled Learning of Feature Transforms --- p.140 / Chapter 9 --- Coupled Space Learning --- p.141 / Chapter 9.1 --- Introduction --- p.142 / Chapter 9.1.1 --- What is Image Style Transform --- p.142 / Chapter 9.1.2 --- Overview of our Framework --- p.143 / Chapter 9.2 --- Coupled Space Learning --- p.143 / Chapter 9.2.1 --- Framework of Coupled Modelling --- p.143 / Chapter 9.2.2 --- Correlative Component Analysis --- p.145 / Chapter 9.2.3 --- Coupled Bidirectional Transform --- p.148 / Chapter 9.2.4 --- Procedure of Coupled Space Learning --- p.151 / Chapter 9.3 --- Generalization to Mixture Model --- p.152 / Chapter 9.3.1 --- Coupled Gaussian Mixture Model --- p.152 / Chapter 9.3.2 --- Optimization by EM Algorithm --- p.152 / Chapter 9.4 --- Integrated Framework for Image Style Transform --- p.154 / Chapter 9.5 --- Experiments --- p.156 / Chapter 9.5.1 --- Face Super-resolution --- p.156 / Chapter 9.5.2 --- Portrait Style Transforms --- p.157 / Chapter 10 --- Inter-Modality Recognition --- p.162 / Chapter 10.1 --- Introduction to the Inter-Modality Recognition Problem . . . --- p.163 / Chapter 10.1.1 --- What is Inter-Modality Recognition --- p.163 / Chapter 10.1.2 --- Overview of Our Feature Extraction Framework . . . . --- p.163 / Chapter 10.2 --- Common Discriminant Feature Extraction --- p.165 / Chapter 10.2.1 --- Formulation of the Learning Problem --- p.165 / Chapter 10.2.2 --- Matrix-Form of the Objective --- p.168 / Chapter 10.2.3 --- Solving the Linear Transforms --- p.169 / Chapter 10.3 --- Kernelized Common Discriminant Feature Extraction --- p.170 / Chapter 10.4 --- Multi-Mode Framework --- p.172 / Chapter 10.4.1 --- Multi-Mode Formulation --- p.172 / Chapter 10.4.2 --- Optimization Scheme --- p.174 / Chapter 10.5 --- Experiments --- p.176 / Chapter 10.5.1 --- Experiment Settings --- p.176 / Chapter 10.5.2 --- Experiment Results --- p.177 / Chapter IV --- A New Perspective: Informative Learning --- p.180 / Chapter 11 --- Toward Information Theory --- p.181 / Chapter 11.1 --- Entropy and Mutual Information --- p.181 / Chapter 11.1.1 --- Entropy --- p.182 / Chapter 11.1.2 --- Relative Entropy (Kullback Leibler Divergence) --- p.184 / Chapter 11.2 --- Mutual Information --- p.184 / Chapter 11.2.1 --- Definition of Mutual Information --- p.184 / Chapter 11.2.2 --- Chain rules --- p.186 / Chapter 11.2.3 --- Information in Data Processing --- p.188 / Chapter 11.3 --- Differential Entropy --- p.189 / Chapter 11.3.1 --- Differential Entropy of Continuous Random Variable . --- p.189 / Chapter 11.3.2 --- Mutual Information of Continuous Random Variable . --- p.190 / Chapter 12 --- Conditional Infomax Learning --- p.191 / Chapter 12.1 --- An Overview --- p.192 / Chapter 12.2 --- Conditional Informative Feature Extraction --- p.193 / Chapter 12.2.1 --- Problem Formulation and Features --- p.193 / Chapter 12.2.2 --- The Information Maximization Principle --- p.194 / Chapter 12.2.3 --- The Information Decomposition and the Conditional Objective --- p.195 / Chapter 12.3 --- The Efficient Optimization --- p.197 / Chapter 12.3.1 --- Discrete Approximation Based on AEP --- p.197 / Chapter 12.3.2 --- Analysis of Terms and Their Derivatives --- p.198 / Chapter 12.3.3 --- Local Active Region Method --- p.200 / Chapter 12.4 --- Bayesian Feature Fusion with Sparse Prior --- p.201 / Chapter 12.5 --- The Integrated Framework for Feature Learning --- p.202 / Chapter 12.6 --- Experiments --- p.203 / Chapter 12.6.1 --- A Toy Problem --- p.203 / Chapter 12.6.2 --- Face Recognition --- p.204 / Chapter 13 --- Channel-based Maximum Effective Information --- p.209 / Chapter 13.1 --- Motivation and Overview --- p.209 / Chapter 13.2 --- Maximizing Effective Information --- p.211 / Chapter 13.2.1 --- Relation between Mutual Information and Classification --- p.211 / Chapter 13.2.2 --- Linear Projection and Metric --- p.212 / Chapter 13.2.3 --- Channel Model and Effective Information --- p.213 / Chapter 13.2.4 --- Parzen Window Approximation --- p.216 / Chapter 13.3 --- Parameter Optimization on Grassmann Manifold --- p.217 / Chapter 13.3.1 --- Grassmann Manifold --- p.217 / Chapter 13.3.2 --- Conjugate Gradient Optimization on Grassmann Manifold --- p.219 / Chapter 13.3.3 --- Computation of Gradient --- p.221 / Chapter 13.4 --- Experiments --- p.222 / Chapter 13.4.1 --- A Toy Problem --- p.222 / Chapter 13.4.2 --- Face Recognition --- p.223 / Chapter 14 --- Conclusion --- p.230

本论文主要研究两类风险估计问题：一类是美式期权价格关于模型参数的敏感性估计， 另一类是投资组合的风险估计。针对这两类问题，我们相应地提出了高效的蒙特卡洛模拟方法。这构成了本文的两个主要部分。 / 第二章是本文的第一部分。在这章中，我们将美式期权的敏感性估计问题提成了更具一般性的估计问题：如果一个随机最优化问题依赖于某些模型参数， 我们该如何估计其最优目标函数关于参数的敏感性。在该问题中， 由于最优决策关于模型参数可能不连续，传统的无穷小扰动分析方法不能直接应用。针对这个困难，我们提出了一种广义的无穷小扰动分析方法，得到敏感性的无偏估计。 我们的方法显示, 在估计敏感性时， 其实并不需要样本路径关于参数的可微性。这是我们在理论上的新发现。另一方面， 该方法可以非常容易的应用于美式期权的敏感性估计。在实际应用中敏感性的无偏估计可以直接嵌入流行的美式期权定价算法，从而同时得到期权价格和价格关于模型参数的敏感性。包括高维问题和多种不同的随机过程模型在内的数值实验， 均显示该估计在计算上具有显著的优越性。最后，我们还从理论上刻画了美式期权的近似最优执行策略对敏感性估计的影响，给出了误差上界。 / 第三章是本文的第二部分。在本章中，我们研究投资组合的风险估计问题。该问题也可被推广成一个一般性的估计问题：如何估计条件期望在作用上一个非线性泛函之后的期望。针对该类估计问题，我们提出了一种多层模拟方法。我们的估计量实际上是一些简单嵌套估计量的线性组合。我们的方法非常容易实现，并且可以被广泛应用于不同的问题结构。理论分析表明我们的方法适用于不同维度的问题并且算法复杂性低于文献中现有的方法。包括低维和高维的数值实验验证了我们的理论分析。 / This dissertation mainly consists of two parts: a generalized infinitesimal perturbation analysis (IPA) approach for American option sensitivities estimation and a multilevel Monte Carlo simulation approach for portfolio risk estimation. / In the first part, we develop efficient Monte Carlo methods for estimating American option sensitivities. The problem can be re-formulated as how to perform sensitivity analysis for a stochastic optimization problem when it has model uncertainty. We introduce a generalized IPA approach to resolve the difficulty caused by discontinuity of the optimal decision with respect to the underlying parameter. The unbiased price-sensitivity estimators yielded from this approach demonstrate significant advantages numerically in both high dimensional environments and various process settings. We can easily embed them into many of the most popular pricing algorithms without extra simulation effort to obtain sensitivities as a by-product of the option price. This generalized approach also casts new insights on how to perform sensitivity analysis using IPA: we do not need pathwise differentiability to apply it. Another contribution of this chapter is to investigate how the estimation quality of sensitivities will be affected by the quality of approximated exercise times. / In the second part, we propose a multilevel nested simulation approach to estimate the expectation of a nonlinear function of a conditional expectation, which has a direct application in portfolio risk estimation problems under various risk measures. Our estimator consists of a linear combination of several standard nested estimators. It is very simple to implement and universally applicable across various problem settings. The results of theoretical analysis show that the algorithmic complexities of our estimators are independent of the problem dimensionality and are better than other alternatives in the literature. Numerical experiments, in both low and high dimensional settings, verify our theoretical analysis. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Liu, Yanchu. / "December 2012." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 89-96). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Abstract in Chinese --- p.iii / Acknowledgements --- p.v / Contents --- p.vii / List of Tables --- p.ix / List of Figures --- p.xii / Chapter 1. --- Overview --- p.1 / Chapter 2. --- American Option Sensitivities Estimation via a Generalized IPA Approach --- p.4 / Chapter 2.1. --- Introduction --- p.4 / Chapter 2.2. --- Formulation of the American Option Pricing Problem --- p.10 / Chapter 2.3. --- Main Results --- p.14 / Chapter 2.3.1. --- A Generalized IPA Approach in the Presence of a Decision Variable --- p.16 / Chapter 2.3.2. --- Unbiased First-Order Sensitivity Estimators --- p.21 / Chapter 2.4. --- Implementation Issues and Error Analysis --- p.23 / Chapter 2.5. --- Numerical Results --- p.26 / Chapter 2.5.1. --- Effects of Dimensionality --- p.27 / Chapter 2.5.2. --- Performance under Various Underlying Processes --- p.29 / Chapter 2.5.3. --- Effects of Exercising Policies --- p.31 / Chapter 2.6. --- Conclusion Remarks and Future Work --- p.33 / Chapter 2.7. --- Appendix --- p.35 / Chapter 2.7.1. --- Proofs of the Main Results --- p.35 / Chapter 2.7.2. --- Likelihood Ratio Estimators --- p.43 / Chapter 2.7.3. --- Derivation of Example 2.3 --- p.49 / Chapter 3. --- Multilevel Monte Carlo Nested Simulation for Risk Estimation --- p.52 / Chapter 3.1. --- Introduction --- p.52 / Chapter 3.1.1. --- Examples --- p.53 / Risk Measurement of Financial Portfolios --- p.53 / Derivatives Pricing --- p.55 / Partial Expected Value of Perfect Information --- p.56 / Chapter 3.1.2. --- A Standard Nested Estimator --- p.57 / Chapter 3.1.3. --- Literature Review --- p.59 / Chapter 3.1.4. --- Summary of Our Contributions --- p.61 / Chapter 3.2. --- The Multilevel Approach --- p.63 / Chapter 3.2.1. --- Motivation --- p.63 / Chapter 3.2.2. --- Multilevel Construction --- p.65 / Chapter 3.2.3. --- Theoretical Analysis --- p.67 / Chapter 3.2.4. --- Further Improvement by Extrapolation --- p.69 / Chapter 3.3. --- Numerical Experiments --- p.72 / Chapter 3.3.1. --- Single Asset Setting --- p.73 / Chapter 3.3.2. --- Multiple Asset Setting --- p.74 / Chapter 3.4. --- Concluding Remarks --- p.77 / Chapter 3.5. --- Appendix: Technical Assumptions and Proofs of the Main Results --- p.79 / Bibliography --- p.89

Digitized by Kansas Correctional Industries

Les études d'association à grande échelle sont devenus un outil très performant pour détecter les variants génétiques associés aux maladies. Ce manuscrit de doctorat s'intéresse à plusieurs des aspects clés des nouvelles problématiques informatiques et statistiques qui ont émergé grâce à de telles recherches. Les résultats des études d'association à grande échelle sont critiqués, en partie, à cause du biais induit par la stratification des populations. Nous proposons une étude de comparaison des stratégies qui existent pour prendre en compte ce problème. Leurs avantages et limites sont discutés en s'appuyant sur divers scénarios de structure des populations dans le but de proposer des conseils et indications pratiques. Nous nous intéressons ensuite à l'interférence de la structure des populations dans la recherche génétique. Nous avons développé au cours de cette thèse un nouvel algorithme appelé SHIPS (Spectral Hierarchical clustering for the Inference of Population Structure). Cet algorithme a été appliqué à un ensemble de jeux de données simulés et réels, ainsi que de nombreux autres algorithmes utilisés en pratique à titre de comparaison. Enfin, la question du test multiple dans ces études d'association est abordée à plusieurs niveaux. Nous proposons une présentation générale des méthodes de tests multiples et discutons leur validité pour différents designs d'études. Nous nous concertons ensuite sur l'obtention de résultats interprétables aux niveaux de gènes, ce qui correspond à une problématique de tests multiples avec des tests dépendants. Nous discutons et analysons les différentes approches dédiées à cette fin. / Genome-Wide association studies have become powerful tools to detect genetic variants associated with diseases. This PhD thesis focuses on several key aspects of the new computational and methodological problematics that have arisen with such research. The results of Genome-Wide association studies have been questioned, in part because of the bias induced by population stratification. Many stratégies are available to account for population stratification scenarios are highlighted in order to propose pratical guidelines to account for population stratification. We then focus on the inference of population structure that has many applications for genetic research. We have developed and present in this manuscript a new clustering algoritm called Spectral Hierarchical clustering for the Inference of Population Structure (SHIPS). This algorithm in the field to propose a comparison of their performances. Finally, the issue of multiple-testing in Genome-Wide association studies is discussed on several levels. We propose a review of the multiple-testing corrections and discuss their validity for different study settings. We then focus on deriving gene-wise interpretation of the findings that corresponds to multiple-stategy to obtain valid gene-disease association measures.

Cheung Shu Fai. / "August 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 117-123). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

This thesis includes three parts. The overarching theme is how to analyze multilevel structured datasets, particularly in the areas of survey and causal inference. The first part discusses model selection of hierarchical models, in the context of a national political survey. I found that the commonly used model selection criteria based on predictive accuracy, such as cross validation, don't perform very well in the case of political survey and explore the possible causes. The second part centers around a unique data set on the presidential election collected through an online platform. I show that with adequate modeling, meaningful and highly accurate information could be extracted from this highly-biased data set. The third part builds on a formal causal inference framework for group-structured data, such as meta-analysis and multi-site trials. In particular, I develop a Gaussian Process model under this framework and demonstrate additional insights that can be gained compared with traditional parametric models.

We consider several problems motivated by issues faced in the mining industry. In recent years, it has become clear that mines have substantial tail risk in the form of environmental disasters, and this tail risk is not incorporated into common pricing and risk models. However, data sets of the extremal climate behavior that drive this risk are very small, and generally inadequate for properly estimating the tail behavior. We propose a data-driven methodology that comes up with reasonable worst-case scenarios, given the data size constraints, and we incorporate this into a real options based model for the valuation of mines. We propose several different iterations of the model, to allow the end-user to choose the degree to which they wish to specify the financial consequences of the disaster scenario. Next, in order to perform a risk analysis on a portfolio of mines, we propose a method of estimating the correlation structure of high-dimensional max-stable processes. Using the techniques of (Liu Et al, 2017) to map the relationship between normal correlations and max-stable correlations, we can then use techniques inspired by (Bickel et al, 2008, Liu et al, 2014, Rothman et al, 2009) to estimate the underlying correlation matrix, while preserving a sparse, positive-definite structure. The correlation matrices are then used in the calculation of model-robust risk metrics (VaR, CVAR) using the the Sample-Out-of-Sample methodology (Blanchet and Kang, 2017). We conclude with several new techniques that were developed in the field of robust performance analysis, that while not directly applied to mining, were motivated by our studies into distributionally robust optimization in order to address these problems.

Sin Ka Yu = 抽取臉孔特徵及辨認臉孔的統計學方法 / 冼家裕. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 86-90). / Text in English; abstracts in English and Chinese. / Sin Ka Yu = Chou qu lian kong te zheng ji bian ren lian kong de tong ji xue fang fa / Xian Jiayu. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- Motivation --- p.1 / Chapter 1.2. --- Objectives --- p.4 / Chapter 1.3. --- Organization of the thesis --- p.4 / Chapter Chapter 2. --- Facial Feature Extraction --- p.6 / Chapter 2.1. --- Introduction --- p.6 / Chapter 2.2. --- Reviews of Statistical Approach --- p.8 / Chapter 2.2.1. --- Eigenfaces --- p.8 / Chapter 2.2.1.1. --- Eigenfeatures Error! Bookmark not defined / Chapter 2.2.3. --- Singular Value Decomposition --- p.14 / Chapter 2.2.4. --- Summary --- p.15 / Chapter 2.3. --- Review of fiducial point localization methods --- p.16 / Chapter 2.3.1. --- Symmetry based Approach --- p.16 / Chapter 2.3.2. --- Color Based Approaches --- p.17 / Chapter 2.3.3. --- Integral Projection --- p.17 / Chapter 2.3.4. --- Deformable Template --- p.20 / Chapter 2.4. --- Corner-based Fiducial Point Localization --- p.22 / Chapter 2.4.1. --- Facial Region Extraction --- p.22 / Chapter 2.4.2. --- Corner Detection --- p.25 / Chapter 2.4.3. --- Corner Selection --- p.27 / Chapter 2.4.3.1. --- Mouth Corner Pairs Detection --- p.27 / Chapter 2.4.3.2. --- Iris Detection --- p.27 / Chapter 2.5. --- Experimental Results --- p.30 / Chapter 2.6. --- Conclusions --- p.30 / Chapter 2.7. --- Notes on Publications --- p.30 / Chapter Chapter 3. --- Fiducial Point Extraction with Shape Constraint --- p.32 / Chapter 3.1. --- Introduction --- p.32 / Chapter 3.2. --- Statistical Theory of Shape --- p.33 / Chapter 3.2.1. --- Shape Space --- p.33 / Chapter 3.2.2. --- Shape Distribution --- p.34 / Chapter 3.3. --- Shape Guided Fiducial Point Localization --- p.38 / Chapter 3.3.1. --- Shape Constraints --- p.38 / Chapter 3.3.2. --- Intelligent Search --- p.40 / Chapter 3.4. --- Experimental Results --- p.40 / Chapter 3.5. --- Conclusions --- p.42 / Chapter 3.6. --- Notes on Publications --- p.42 / Chapter Chapter 4. --- Statistical Pattern Recognition --- p.43 / Chapter 4.1. --- Introduction --- p.43 / Chapter 4.2. --- Bayes Decision Rule --- p.44 / Chapter 4.3. --- Gaussian Maximum Probability Classifier --- p.46 / Chapter 4.4. --- Maximum Likelihood Estimation of Mean and Covariance Matrix --- p.48 / Chapter 4.5. --- Small Sample Size Problem --- p.50 / Chapter 4.5.1. --- Dispersed Eigenvalues --- p.50 / Chapter 4.5.2. --- Distorted Classification Rule --- p.55 / Chapter 4.6. --- Review of Methods Handling the Small Sample Size Problem --- p.57 / Chapter 4.6.1. --- Linear Discriminant Classifier --- p.57 / Chapter 4.6.2. --- Regularized Discriminant Analysis --- p.59 / Chapter 4.6.3. --- Leave-one-out Likelihood Method --- p.63 / Chapter 4.6.4. --- Bayesian Leave-one-out Likelihood method --- p.65 / Chapter 4.7. --- Proposed Method --- p.68 / Chapter 4.7.1. --- A New Covariance Estimator --- p.70 / Chapter 4.7.2. --- Model Selection --- p.75 / Chapter 4.7.3. --- The Mixture Parameter --- p.76 / Chapter 4.8. --- Experimental results --- p.77 / Chapter 4.8.1. --- Implementation --- p.77 / Chapter 4.8.2. --- Results --- p.79 / Chapter 4.9. --- Conclusion --- p.81 / Chapter 4.10. --- Notes on Publications --- p.82 / Chapter Chapter 5. --- Conclusions and Future works --- p.83 / Chapter 5.1. --- Conclusions and Contributions --- p.83 / Chapter 5.2. --- Future Works --- p.84

現代風險管理需要對金融產品的相關結構做出刻畫，而在實際生活中，我們通常使用相關係數和自相關係數去刻畫這種結構。然而，越來越多的人意識到自相關函數在度量相關結構上面被高估了，特別是在風險管理中我們更關心極端事件。同樣的，偏自相關函數也有這樣的短板。在這篇論文中，我們在有限維分佈服從有正尾係數的正則變差的嚴平穩過程上定義了Partial Extremogram。 這個指標僅僅依賴於隨機過程中的極端值。我們給出了它的一個估計并且研究了這個估計的漸進性質。此外，为了刻畫时间序列的負相關結構，我們把 Inverse Tail Dependence 的想法推廣到了隨機過程上面並且引入了Inverse Extremogram 的概念。我們給出了Inverse Extremogram 在ARMA模型中的顯示表達式。理論推導和數據模擬都說明這個指標可以很好的刻畫出一個隨機過程的尾部的負相關結構。 / Modern risk management calls for deeper understanding of the dependence structure of financial products, which is usually measured by correlation or autocorrelation functions. More and more people realized that autocorrelation function is overvalued as a tool to measure dependence, especially when one has to deal with extremal events in risk management. Likewise, partial autocorrelation function also suffers similar shortcomings as autocorrelation function. In this thesis, an analog of the partial autocorrelation function for a strictly stationary sequence of random variables whose finite-dimensional distributions are jointly regularly varying with positive index, the partial extremogram, is introduced. This function only depends on the extremal events of the underlying process. A natural estimator of the partial extremogram is also proposed and its asymptotic properties are studied. Furthermore, to measure the negative dependence of a time series, the idea of inverse tail dependence is extended to a stochastic process and the notion of inverse extremogram is proposed. A closed form of the inverse extremogram for an ARMA model is deduced. The theoretical and simulation results show that the inverse extremogram is a useful tool for measuring the negative tail dependence of a process. / Detailed summary in vernacular field only. / Chen, Pengcheng. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 53-56). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Tail Dependence --- p.2 / Chapter 1.2 --- Extremogram --- p.4 / Chapter 1.2.1 --- Regularly Varying Time Series --- p.4 / Chapter 1.2.2 --- Extremogram for Regularly Varying Time Series --- p.7 / Chapter 1.3 --- Motivation and Organization --- p.8 / Chapter 2 --- Partial Extremogram --- p.9 / Chapter 2.1 --- Definition of Partial Extremogram --- p.9 / Chapter 2.2 --- Applications of Partial Extremogram --- p.15 / Chapter 2.2.1 --- AR(1) Process --- p.15 / Chapter 2.2.2 --- MA(1) process --- p.17 / Chapter 2.2.3 --- Stochastic Volatility Model --- p.19 / Chapter 2.3 --- Estimation of Partial Extremogram --- p.19 / Chapter 2.4 --- Simulation Study --- p.22 / Chapter 3 --- Inverse Extremogram --- p.28 / Chapter 3.1 --- Definition of Inverse Extremogram --- p.28 / Chapter 3.2 --- Applications of Inverse Extremogram --- p.29 / Chapter 3.2.1 --- MA(q) Model --- p.29 / Chapter 3.2.2 --- MA(∞) Model --- p.35 / Chapter 3.2.3 --- ARMA Model --- p.40 / Chapter 3.2.4 --- GARCH Model and SV Model --- p.41 / Chapter 3.3 --- Simulation Study --- p.42 / Chapter 4 --- Conclusions and Further Research --- p.50 / Bibliography --- p.53

Cheung Wai-leung. / "July 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 110-129). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.