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作者： Mingzhu Sun The University of Queensland

学位级别：博士

This thesis addresses two important problems in modern statistics: discriminant analysis of big data and dimension reduction of high-dimensional data such as microarray gene expression data. These problems are commonly encountered in various scientific fields and can pose considerable challenges since traditional approaches might not work properly or even break down in the high-dimensional setting. For the first problem of discriminant analysis of big data, one of the widely used parametric approaches is to model the distribution of the feature vector in each of the predefined classes via a normal mixture distribution. The component-covariance matrices in the normal mixture for a class are highly parameterized, thus, rendering them impractical for high-dimensional datasets. Therefore, as the dimension increases, some forms of regularization need to be implemented. In this thesis, an innovative factor model approach, called mixtures of common factor ana- lyzers for discriminant analysis (MCFDA), is proposed. With this approach, the component- covariance matrices are taken to have a factor-analytic form with common loadings across the classes (common before the transformation of the factors into white noise). This approach also allows the data to be viewed in low-dimensional spaces by plotting the (estimated) values of the latent factors corresponding to the observed data points. To improve the robustness of our MCFDA approach for data which have heavy tails or atypical observations, we also adopt the multivariate t-family for the component-error and factor distri- butions. We refer to this model as the mixtures of common t-factor analyzers for discriminant analysis (MCtFDA). With this approach, both the common factor loadings and the diagonal matrix of error terms need to be specified as the same across the classes. This approach has great flexibility for modelling data which are non-normal or with outliers. For the second problem of dimension reduction, we focus on

关键词： finite mixture models discriminant analysis clustering microarray gene expression data expectation-maximization algorithm factor analysis model dimension reduction machine learning error rates

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A class of bivariate Erlang distributions and ruin probabilities in multivariate risk models

A class of bivariate Erlang distributions and ruin probabili...

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作者： Groparu-Cojocaru, Ionica Université de Montréal

学位级别：doctor

Nous y introduisons une nouvelle classe de distributions bivariées de type Marshall-Olkin, la distribution Erlang bivariée. La transformée de Laplace, les moments et les densités conditionnelles y sont obtenus. Les applications potentielles en assurance-vie et en finance sont prises en considération. Les estimateurs du maximum de vraisemblance des paramètres sont calculés par l''algorithme Espérance-Maximisation. Ensuite, notre projet de recherche est consacré à l''étude des processus de risque multivariés, qui peuvent être utiles dans l''étude des problèmes de la ruine des compagnies d''assurance avec des classes dépendantes. Nous appliquons les résultats de la théorie des processus de Markov déterministes par morceaux afin d''obtenir les martingales exponentielles, nécessaires pour établir des bornes supérieures calculables pour la probabilité de ruine, dont les expressions sont intraitables.%%%%In this contribution, we introduce a new class of bivariate distributions of Marshall-Olkin type, called bivariate Erlang distributions. The Laplace transform, product moments and conditional densities are derived. Potential applications of bivariate Erlang distributions in life insurance and finance are considered. Further, our research project is devoted to the study of multivariate risk processes, which may be useful in analyzing ruin problems for insurance companies with a portfolio of dependent classes of business. We apply results from the theory of piecewise deterministic Markov processes in order to derive exponential martingales needed to establish computable upper bounds of the ruin probabilities, as their exact expressions are intractable

关键词： Education - Mathematics / éducation - Mathématiques (UMI 0280) Distribution Erlang algorithme Espérance-Maximisation Processus de Markov déterministes par morceaux Modèle de risque multivarié Probabilité de ruine Modèle de Poisson avec chocs communs Processus de renouvellement Copules Erlang distribution expectation-maximization algorithm Piecewise deterministic Markov processes Multivariate risk model Ruin probability Poisson model with common shocks Renewal processes Copulas

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Detection of land-cover transitions by combining multidate classifiers

Detection of land-cover transitions by combining multidate c...

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2nd International Workshop on Pattern Recognition for Remote Sensing

作者： Bruzzone, L Cossu, R Vernazza, G Univ Trent Dept Informat & Commun Technol I-38050 Trento Italy Univ Genoa Dept Biophys & Elect Engn I-16145 Genoa Italy

This paper addresses the problem of detecting land-cover transitions by analysing multitemporal remote-sensing images. In order to develop an effective system for the detection of land-cover transitions, an ensemble of non-parametric multitemporal classifiers is defined and integrated in the context of a multiple classifier system (MCS). Each multitemporal classifier is developed in the framework of the compound classification (CC) decision rule. To develop as uncorrelated as possible classification procedures, the estimates of statistical parameters of classifiers are carried out according to different approaches (i.e., multilayer perceptron neural networks, radial basis functions neural networks, and k-nearest neighbour technique). The outputs provided by different classifiers are combined according to three standard stratcaies extended to the compound classification case (i.e., Majority voting, Bayesian average, and Bayesian,weighted average). Experiments, carried out on a multitemporal. remote-sensing data set, confirm the effectiveness of the proposed system. (C) 2004 Elsevier B.V. All rights reserved.

关键词： detection of land-cover transitions change detection multitemporal classification multiple classifier systems multilayer perceptron neural networks radial basis function neural networks k-nn technique expectation-maximization algorithm remote sensing images

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Noise Benefits in Backpropagation and Deep Bidirectional Pre-training

Noise Benefits in Backpropagation and Deep Bidirectional Pre...

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International Joint Conference on Neural Networks (IJCNN)

作者： Audhkhasi, Kartik Osoba, Osonde Kosko, Bart Univ So Calif Signal & Image Proc Inst Dept Elect Engn Los Angeles CA 90089 USA

ISBN: (纸本)9781467361293;9781467361286

We prove that noise can speed convergence in the backpropagation algorithm. The proof consists of two separate results. The first result proves that the backpropagation algorithm is a special case of the generalized expectationmaximization (EM) algorithm for iterative maximum likelihood estimation. The second result uses the recent EM noise benefit to derive a sufficient condition for backpropagation training. The noise adds directly to the training data. A noise benefit also applies to the deep bidirectional pre-training of the neural network as well as to the backpropagation training of the network. The geometry of the noise benefit depends on the probability structure of the neurons at each layer. Logistic sigmoidal neurons produce a forbidden noise region that lies below a hyperplane. Then all noise on or above the hyperplane can only speed convergence of the neural network. The forbidden noise region is a sphere if the neurons have a Gaussian signal or activation function. These noise benefits all follow from the general noise benefit of the EM algorithm. Monte Carlo sample means estimate the population expectations in the EM algorithm. We demonstrate the noise benefits using MNIST digit classification.

关键词： Backpropagation bidirectional associative memory noise benefit neural network stochastic resonance expectation-maximization algorithm

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An Online Approach to Estimate Parameters of Phase-Type Distributions 49

An Online Approach to Estimate Parameters of Phase-Type Dist...

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49th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN)

作者： Buchholz, Peter Dohndorf, Iryna Kriege, Jan TU Dortmund Dept Comp Sci Dortmund Germany

ISBN: (纸本)9781728100562

The traditional expectation-maximization (EM) algorithm is a general purpose algorithm for maximum likelihood estimation in problems with incomplete data. Several variants of the algorithm exist to estimate the parameters of phase-type distributions (PHDs), a widely used class of distributions in performance and dependability modeling. EM algorithms are typical offline algorithms because they improve the likelihood function by iteratively running through a fixed sample. Nowadays data can be generated online in most systems such that offline algorithms seem to be outdated in this environment. This paper proposes an online EM algorithm for parameter estimation of PHDs. In contrast to the offline version, the online variant adds data immediately when it becomes available and includes no iteration. Different variants of the algorithms are proposed that exploit the specific structure of subclasses of PHDs like hyperexponential, hyper-Erlang or acyclic PHDs. The algorithm furthermore incorporates current methods to detect drifts or change points in a data stream and estimates a new PHD whenever such a behavior has been identified. Thus, the resulting distributions can be applied for online model prediction and for the generation of inhomogeneous PHDs as an extension of inhomogeneous Poisson processes. Numerical experiments with artificial and measured data streams show the applicability of the approach.

关键词： stochastic modeling phase-type distributions expectation-maximization algorithm online algorithm parameter estimation

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Covariances matrix under the multivariate-Gh funtion to desing portfolios

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Contaduria y Administracion 2016年第3期61卷 535-550页

作者： Núñez Mora, José Antonio Mata Mata, Leovardo EGADE Business School Tecnologico de Monterrey Mexico

In this paper we developed the estimation implementation of the generalized hyperbolic multivariate (GH) distribution with a non-fixed Bessel function. The covariance matrix estimated through the GH distribution complements the use of the Markowitz procedure to construct an efficient portfolio and reduce the variation coefficient of the expected return. The data are from the Stockholm index 30 from January 2010 to April 2014. © 2015 Universidad Nacional Autónoma de México, Facultad de Contaduría y Administración.

关键词： Covariance matrix expectation-maximization algorithm Generalized hyperbolic distribution Markowitz portfolio

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NEETs and Youth Unemployment: A Longitudinal Comparison Across European Countries

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SOCIAL INDICATORS RESEARCH 2022年第2期162卷 739-761页

作者： Pennoni, Fulvia Bal-Domanska, Beata Univ Milano Bicocca Dept Stat & Quantitat Methods Milan Italy Wroclaw Univ Econ & Business Dept Reg Econ Wroclaw Poland

Young people's place in the labor market has been a topic of interest to the European Union and national governments for many years. This study analyzes young people who are Not in Employment nor in Education or Training (NEET) and Youth Unemployment (YU) in the European Union member states, through data collected over a period of sixteen years, considering the influence of some macroeconomic factors through an hidden Markov model. This approach is based on maximum likelihood estimation of the model parameters, and provides a dynamic classification of the countries into clusters representing different levels of the phenomena. We discover three clusters of countries, and we show that whereas Italy was the worst performing country in terms of both NEETs and YU, the Czech Republic was the best performing country in reducing NEETs, and Poland and Slovakia were the best performing in reducing YU.

关键词： expectation-maximization algorithm Discrete latent variable Hidden Markov model Model-based clustering Panel data NEET Youth unemployment

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Digital Image Forensics Using EM algorithm

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10th Pacific Rim Conference on Multimedia

作者： Lin, Tim-kun Huang, Chung-Lin Fo Guang Univ Dept Informat Ilan Taiwan

ISBN: (纸本)9783642104664

Digital image forensics has become a very important research topic This paper proposes a method to detect the forgery of digital image by (I) computing the interpolated coefficient for the Images using expectation-maximization (EM) algorithm, (2) generating the probability map. (3) obtaining the frequency spectrum of the probability map, (4) determining whether an image has been tampered based on the periodicity characteristics of the spectrum The experimental results show that our approach is effective to detect Mice different image forgeries (a) an-brush or brush strokes, (b) different blurring filters. and (c) composite image taken from different cameras

关键词： Digital Image Forensics expectation-maximization algorithm

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The Effect of Uniform Data Quantization on GMM-based Clustering by Means of EM algorithm 20

The Effect of Uniform Data Quantization on GMM-based Cluster...

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20th International Symposium on INFOTEH-JAHORINA (INFOTEH)

作者： Jovanovic, Aleksandra Peric, Zoran Nikolic, Jelena Aleksic, Danijela Univ Nis Dept Telecommun Fac Elect Engn Nish Serbia Telekom Srbija Dept Mobile Network Nis Nish Serbia

ISBN: (纸本)9781728182292

In this paper, unlike the commonly considered theoretical scenario in clustering, wherein data attributes are accurately presented, we research how successful clustering can be indeed performed in situations wherein before being grouped the data have to be quantized, that is, represented with smaller accuracy. This describes situation wherein before being grouped the data are compressed due to their transmission through the bandwidth-limited channel. We consider scenario wherein the data modeled with the one-dimensional two-component Gaussian mixture model (GMM) are uniformly quantized and, after that, grouped by using the expectation-maximization (EM) algorithm. We study how the number of quantization levels and the quantizer support limits influence on the results of clustering.

关键词： unsupervised learning clustering Gaussian mixture model expectation-maximization algorithm quantization

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Intergenerational mobility measurement with latent transition matrices

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JOURNAL OF ECONOMIC INEQUALITY 2023年第1期21卷 25-45页

作者： Bavaro, Michele Tullio, Federico Univ Oxford INET Oxford England Univ Oxford Dept Social Policy & Intervent Oxford England Bank Italy DG Econ Stat & Res Rome Italy

We propose a multivariate approach for the estimation of intergenerational transition matrices. Our methodology is grounded on the assumption that individuals' social status is unobservable and must be estimated. In this framework, parents and offspring are clustered on the basis of the observed levels of income and occupational categories, thus avoiding any discretionary rule in the definition of class boundaries. The resulting transition matrix is a function of the posterior probabilities of parents and young adults of belonging to each class. Estimation is carried out via maximum likelihood by means of an expectation-maximization algorithm. We illustrate the proposed method using National Longitudinal Survey Data from the United States in the period 1978-2006.

关键词： expectation-maximization algorithm Intergenerational mobility Transition matrix

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