Robust Mixture Modeling
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Robust Mixture Modeling
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Author : Chun Yu
language : en
Publisher:
Release Date : 2014
Robust Mixture Modeling written by Chun Yu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. In this proposal, we first review and describe some available and popular robust techniques, including some recent developed ones, and compare them in terms of breakdown point and efficiency. In addition, we also use a simulation study and a real data application to compare the performance of existing robust methods under different scenarios. Finite mixture models are widely applied in a variety of random phenomena. However, inference of mixture models is a challenging work when the outliers exist in the data. The traditional maximum likelihood estimator (MLE) is sensitive to outliers. In this proposal, we propose a Robust Mixture via Mean shift penalization (RMM) in mixture models and Robust Mixture Regression via Mean shift penalization (RMRM) in mixture regression, to achieve simultaneous outlier detection and parameter estimation. A mean shift parameter is added to the mixture models, and penalized by a nonconvex penalty function. With this model setting, we develop an iterative thresholding embedded EM algorithm to maximize the penalized objective function. Comparing with other existing robust methods, the proposed methods show outstanding performance in both identifying outliers and estimating the parameters.
Statistical Learning For Large Dimensional Data By Finite Mixture Modeling
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Author : Xiao Chen
language : en
Publisher:
Release Date : 2021
Statistical Learning For Large Dimensional Data By Finite Mixture Modeling written by Xiao Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Electronic books categories.
The goal of mixture modeling is to model the data as a mixture of processes or populations with distinct data patterns. l\lixture modeling can find combinations of hidden group memberships for many kinds of models. While mixture models based on Gaussian distributions still popular, they are sensitive to outliers and varying tails. Thus, robust mixture models are getting increasingly popular. In this thesis, we mainly considered replacing Gaussian density distributions with exponential power distributions in mixture modelling. The exponential power distribution is quite flex- ible: it can deal with both leptokurtic distributions and platykurtic distributions. In addition, the normal distribution is a particular case of EP distributions, which means that EP distributions allow continuous variation from being normal to non-normal. This thesis contributes to the mixture modeling in 3 ways. First, a family of mixtures of univariate exponential power distributions and a family of mixtures of multivariate exponential power distributions are considered. The EP mixture model is an attractive alternative to Gaussian mixture models and t mixture models in model-based clustering and density estimation. lt can deal with Gaussian, light- tailed, and heavy-tailed components at the same time. in this thesis, we used the penalty likelihood method proposed in Huang et al. 120171 to determine the number of components for mixtures of univariate power exponential distributions and mixtures of multivariate power exponential distributions, and we have proved the consistency of the order selection procedure. The proposed algorithm performs better than classical methods in order selection for EP mixture models, and it is not computing-intensive. Second, robust mixtures of regression models with EP distributions are introduced. These models provide a flexible framework for heterogeneous dependencies on the observed variables. Here we used the penalized log-likelihood for selecting the number of components. Simulations and real data analyses illustrate the robustness of the proposed model and the performance of the proposed penalized method in order selection. Lastly, we proposed mixtures of robust probabilistic principal component analyzers with EP distributions and proved the robustness of our method through toy examples and real data analysis. This method could model high-dimensional non-linear data using a combination of local linear models when there are outliers or heavy-tails. It could be used for high-dimensional clustering and data generation.
Finite Mixture Models
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Author : Geoffrey McLachlan
language : en
Publisher: John Wiley & Sons
Release Date : 2004-03-22
Finite Mixture Models written by Geoffrey McLachlan and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-22 with Mathematics categories.
An up-to-date, comprehensive account of major issues in finitemixture modeling This volume provides an up-to-date account of the theory andapplications of modeling via finite mixture distributions. With anemphasis on the applications of mixture models in both mainstreamanalysis and other areas such as unsupervised pattern recognition,speech recognition, and medical imaging, the book describes theformulations of the finite mixture approach, details itsmethodology, discusses aspects of its implementation, andillustrates its application in many common statisticalcontexts. Major issues discussed in this book include identifiabilityproblems, actual fitting of finite mixtures through use of the EMalgorithm, properties of the maximum likelihood estimators soobtained, assessment of the number of components to be used in themixture, and the applicability of asymptotic theory in providing abasis for the solutions to some of these problems. The author alsoconsiders how the EM algorithm can be scaled to handle the fittingof mixture models to very large databases, as in data miningapplications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and patternrecognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied andtheoretical statisticians as well as for researchers in the manyareas in which finite mixture models can be used to analyze data.
Robust Mixtures Of Regression Models
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Author : Xiuqin Bai
language : en
Publisher:
Release Date : 2014
Robust Mixtures Of Regression Models written by Xiuqin Bai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
This proposal contains two projects that are related to robust mixture models. In the robust project, we propose a new robust mixture of regression models (Bai et al., 2012). The existing methods for tting mixture regression models assume a normal distribution for error and then estimate the regression parameters by the maximum likelihood estimate (MLE). In this project, we demonstrate that the MLE, like the least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust estimation procedure and an EM-type algorithm to estimate the mixture regression models. Using a Monte Carlo simulation study, we demonstrate that the proposed new estimation method is robust and works much better than the MLE when there are outliers or the error distribution has heavy tails. In addition, the proposed robust method works comparably to the MLE when there are no outliers and the error is normal. In the second project, we propose a new robust mixture of linear mixed-effects models. The traditional mixture model with multiple linear mixed effects, assuming Gaussian distribution for random and error parts, is sensitive to outliers. We will propose a mixture of multiple linear mixed t-distributions to robustify the estimation procedure. An EM algorithm is provided to and the MLE under the assumption of t-distributions for error terms and random mixed effects. Furthermore, we propose to adaptively choose the degrees of freedom for the t-distribution using profile likelihood. In the simulation study, we demonstrate that our proposed model works comparably to the traditional estimation method when there are no outliers and the errors and random mixed effects are normally distributed, but works much better if there are outliers or the distributions of the errors and random mixed effects have heavy tails.
Mixture Models
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Author : Weixin Yao
language : en
Publisher: CRC Press
Release Date : 2024-04-18
Mixture Models written by Weixin Yao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-18 with Mathematics categories.
Mixture models are a powerful tool for analyzing complex and heterogeneous datasets across many scientific fields, from finance to genomics. Mixture Models: Parametric, Semiparametric, and New Directions provides an up-to-date introduction to these models, their recent developments, and their implementation using R. It fills a gap in the literature by covering not only the basics of finite mixture models, but also recent developments such as semiparametric extensions, robust modeling, label switching, and high-dimensional modeling. Features Comprehensive overview of the methods and applications of mixture models Key topics include hypothesis testing, model selection, estimation methods, and Bayesian approaches Recent developments, such as semiparametric extensions, robust modeling, label switching, and high-dimensional modeling Examples and case studies from such fields as astronomy, biology, genomics, economics, finance, medicine, engineering, and sociology Integrated R code for many of the models, with code and data available in the R Package MixSemiRob Mixture Models: Parametric, Semiparametric, and New Directions is a valuable resource for researchers and postgraduate students from statistics, biostatistics, and other fields. It could be used as a textbook for a course on model-based clustering methods, and as a supplementary text for courses on data mining, semiparametric modeling, and high-dimensional data analysis.
Mixture Models And Applications
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Author : Nizar Bouguila
language : en
Publisher: Springer
Release Date : 2019-08-13
Mixture Models And Applications written by Nizar Bouguila and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-13 with Technology & Engineering categories.
This book focuses on recent advances, approaches, theories and applications related to mixture models. In particular, it presents recent unsupervised and semi-supervised frameworks that consider mixture models as their main tool. The chapters considers mixture models involving several interesting and challenging problems such as parameters estimation, model selection, feature selection, etc. The goal of this book is to summarize the recent advances and modern approaches related to these problems. Each contributor presents novel research, a practical study, or novel applications based on mixture models, or a survey of the literature. Reports advances on classic problems in mixture modeling such as parameter estimation, model selection, and feature selection; Present theoretical and practical developments in mixture-based modeling and their importance in different applications; Discusses perspectives and challenging future works related to mixture modeling.
Finite Mixture Of Skewed Distributions
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Author : Víctor Hugo Lachos Dávila
language : en
Publisher: Springer
Release Date : 2018-11-12
Finite Mixture Of Skewed Distributions written by Víctor Hugo Lachos Dávila and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-12 with Mathematics categories.
This book presents recent results in finite mixtures of skewed distributions to prepare readers to undertake mixture models using scale mixtures of skew normal distributions (SMSN). For this purpose, the authors consider maximum likelihood estimation for univariate and multivariate finite mixtures where components are members of the flexible class of SMSN distributions. This subclass includes the entire family of normal independent distributions, also known as scale mixtures of normal distributions (SMN), as well as the skew-normal and skewed versions of some other classical symmetric distributions: the skew-t (ST), the skew-slash (SSL) and the skew-contaminated normal (SCN), for example. These distributions have heavier tails than the typical normal one, and thus they seem to be a reasonable choice for robust inference. The proposed EM-type algorithm and methods are implemented in the R package mixsmsn, highlighting the applicability of the techniques presented in the book. This work is a useful reference guide for researchers analyzing heterogeneous data, as well as a textbook for a graduate-level course in mixture models. The tools presented in the book make complex techniques accessible to applied researchers without the advanced mathematical background and will have broad applications in fields like medicine, biology, engineering, economic, geology and chemistry.
Optimal Mixture Experiments
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Author : B.K. Sinha
language : en
Publisher: Springer
Release Date : 2014-05-24
Optimal Mixture Experiments written by B.K. Sinha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-24 with Mathematics categories.
The book dwells mainly on the optimality aspects of mixture designs. As mixture models are a special case of regression models, a general discussion on regression designs has been presented, which includes topics like continuous designs, de la Garza phenomenon, Loewner order domination, Equivalence theorems for different optimality criteria and standard optimality results for single variable polynomial regression and multivariate linear and quadratic regression models. This is followed by a review of the available literature on estimation of parameters in mixture models. Based on recent research findings, the volume also introduces optimal mixture designs for estimation of optimum mixing proportions in different mixture models, which include Scheffé’s quadratic model, Darroch-Waller model, log- contrast model, mixture-amount models, random coefficient models and multi-response model. Robust mixture designs and mixture designs in blocks have been also reviewed. Moreover, some applications of mixture designs in areas like agriculture, pharmaceutics and food and beverages have been presented. Familiarity with the basic concepts of design and analysis of experiments, along with the concept of optimality criteria are desirable prerequisites for a clear understanding of the book. It is likely to be helpful to both theoreticians and practitioners working in the area of mixture experiments.
A Robust Approach To Finite Mixture Models Using The Multivariate Skew T Distribution
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Author :
language : en
Publisher:
Release Date : 2008
A Robust Approach To Finite Mixture Models Using The Multivariate Skew T Distribution written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Robust Mixture Regression Models Using T Distribution
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Author : Yan Wei
language : en
Publisher:
Release Date : 2012
Robust Mixture Regression Models Using T Distribution written by Yan Wei and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
In this report, we propose a robust mixture of regression based on t-distribution by extending the mixture of t-distributions proposed by Peel and McLachlan (2000) to the regression setting. This new mixture of regression model is robust to outliers in y direction but not robust to the outliers with high leverage points. In order to combat this, we also propose a modified version of the proposed method, which fits the mixture of regression based on t-distribution to the data after adaptively trimming the high leverage points. We further propose to adaptively choose the degree of freedom for the t-distribution using profile likelihood. The proposed robust mixture regression estimate has high efficiency due to the adaptive choice of degree of freedom. We demonstrate the effectiveness of the proposed new method and compare it with some of the existing methods through simulation study.