Expectation Maximization Algorithms For Learning A Finite Mixture Of Univariate Survival Time Distributions From Partially Specified Class Values

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Expectation-maximization Algorithms for Learning a Finite Mixture of Univariate Survival Time Distributions from Partially Specified Class Values

Author :
Publisher :
ISBN 13 :
Total Pages : 131 pages
Book Rating : 4.:/5 (953 download)

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Book Synopsis Expectation-maximization Algorithms for Learning a Finite Mixture of Univariate Survival Time Distributions from Partially Specified Class Values by :

Download or read book Expectation-maximization Algorithms for Learning a Finite Mixture of Univariate Survival Time Distributions from Partially Specified Class Values written by and published by . This book was released on 2013 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heterogeneity exists on a data set when samples from di erent classes are merged into the data set. Finite mixture models can be used to represent a survival time distribution on heterogeneous patient group by the proportions of each class and by the survival time distribution within each class as well. The heterogeneous data set cannot be explicitly decomposed to homogeneous subgroups unless all the samples are precisely labeled by their origin classes; such impossibility of decomposition is a barrier to overcome for estimating nite mixture models. The expectation-maximization (EM) algorithm has been used to obtain maximum likelihood estimates of nite mixture models by soft-decomposition of heterogeneous samples without labels for a subset or the entire set of data. In medical surveillance databases we can find partially labeled data, that is, while not completely unlabeled there is only imprecise information about class values. In this study we propose new EM algorithms that take advantages of using such partial labels, and thus incorporate more information than traditional EM algorithms. We particularly propose four variants of the EM algorithm named EM-OCML, EM-PCML, EM-HCML and EM-CPCML, each of which assumes a specific mechanism of missing class values. We conducted a simulation study on exponential survival trees with five classes and showed that the advantages of incorporating substantial amount of partially labeled data can be highly signi cant. We also showed model selection based on AIC values fairly works to select the best proposed algorithm on each specific data set. A case study on a real-world data set of gastric cancer provided by Surveillance, Epidemiology and End Results (SEER) program showed a superiority of EM-CPCML to not only the other proposed EM algorithms but also conventional supervised, unsupervised and semi-supervised learning algorithms.

The Oxford Handbook of Quantitative Methods, Vol. 2: Statistical Analysis

Author : Todd D. Little
Publisher : Oxford University Press
ISBN 13 : 0199934908
Total Pages : 784 pages
Book Rating : 4.1/5 (999 download)

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Book Synopsis The Oxford Handbook of Quantitative Methods, Vol. 2: Statistical Analysis by : Todd D. Little

Download or read book The Oxford Handbook of Quantitative Methods, Vol. 2: Statistical Analysis written by Todd D. Little and published by Oxford University Press. This book was released on 2013-02-01 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research today demands the application of sophisticated and powerful research tools. Fulfilling this need, The Oxford Handbook of Quantitative Methods is the complete tool box to deliver the most valid and generalizable answers to todays complex research questions. It is a one-stop source for learning and reviewing current best-practices in quantitative methods as practiced in the social, behavioral, and educational sciences. Comprising two volumes, this handbook covers a wealth of topics related to quantitative research methods. It begins with essential philosophical and ethical issues related to science and quantitative research. It then addresses core measurement topics before delving into the design of studies. Principal issues related to modern estimation and mathematical modeling are also detailed. Topics in the handbook then segway into the realm of statistical inference and modeling with chapters dedicated to classical approaches as well as modern latent variable approaches. Numerous chapters associated with longitudinal data and more specialized techniques round out this broad selection of topics. Comprehensive, authoritative, and user-friendly, this two-volume set will be an indispensable resource for serious researchers across the social, behavioral, and educational sciences.

The Frailty Model

Author : Luc Duchateau
Publisher : Springer Science & Business Media
ISBN 13 : 038772835X
Total Pages : 329 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis The Frailty Model by : Luc Duchateau

Download or read book The Frailty Model written by Luc Duchateau and published by Springer Science & Business Media. This book was released on 2007-10-23 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readers will find in the pages of this book a treatment of the statistical analysis of clustered survival data. Such data are encountered in many scientific disciplines including human and veterinary medicine, biology, epidemiology, public health and demography. A typical example is the time to death in cancer patients, with patients clustered in hospitals. Frailty models provide a powerful tool to analyze clustered survival data. In this book different methods based on the frailty model are described and it is demonstrated how they can be used to analyze clustered survival data. All programs used for these examples are available on the Springer website.

Expectation Maximization Algorithm for Optimization of Piecewise-constant Models and Their Applications

Author : Pooya Tavallali
Publisher :
ISBN 13 :
Total Pages : 262 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Expectation Maximization Algorithm for Optimization of Piecewise-constant Models and Their Applications by : Pooya Tavallali

Download or read book Expectation Maximization Algorithm for Optimization of Piecewise-constant Models and Their Applications written by Pooya Tavallali and published by . This book was released on 2021 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Expectation-Maximization (EM) Algorithm is well-known in the literature of machine learning and has been widely used for training of probabilistic and some non-probabilistic models, such as mixture of Gaussians and K-means, respectively. Despite the vast volume of research on application of the EM algorithm for training probabilistic models, there has been little attempt toward usage of the EM algorithm for non-probabilistic models. In this dissertation, various piecewise constant models, and their learning procedures in the literature are reviewed. For each model, the EM-based optimization of reviewed model is proposed. The EM algorithms proposed in this dissertation have the same spirit as the original EM algorithm. For each model, the proposed EM algorithm is properly modified to fit the non-probabilistic nature of the model. The EM algorithm was originally designed to fit the modular structure of any intelligent model, such as neural networks or mixture models. In this dissertation, it is shown how with the EM algorithm it is possible to approach a piecewise constant model as a modular structure and optimize the model based on each module of the structure. The optimization procedure consists of two steps, Expectation/assignment step and Maximization/update step. More specifically, in the EM algorithm, for each module of the structure, a maximization/minimization problem has to be solved. The parameters of optimization problem for each module are provided by the expectation step for that module. In this dissertation, it is shown that such optimization problems are NP-hard and can often be approximated through a proper surrogate objective function. We proposed novel surrogate functions. The proposed EM-based approach is applied to several piecewise constant models, such as prototype nearest neighbor. Further, the convergence guarantee and computational complexity of the developed EM algorithms are presented for each model. Finally, through extensive experiments we show that the proposed EM-based algorithms have superior or similar performance when compared with several other similar state-of-the-art models and algorithms. Additionally, the proposed approach for optimizing the piecewise constant models provides an in-depth interpretability for training procedures. We specifically applied the proposed optimization algorithm to synthetic reduced nearest neighbor for classification, adversarial label-poisoning, robust synthetic reduced nearest neighbor and synthetic reduced nearest neighbor for regression.

Modeling Discrete Time-to-Event Data

Author : Gerhard Tutz
Publisher : Springer
ISBN 13 : 3319281585
Total Pages : 252 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Modeling Discrete Time-to-Event Data by : Gerhard Tutz

Download or read book Modeling Discrete Time-to-Event Data written by Gerhard Tutz and published by Springer. This book was released on 2016-06-14 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis in continuous time are explained. Each section includes a set of exercises on the respective topics. Various functions and tools for the analysis of discrete survival data are collected in the R package discSurv that accompanies the book.

Mixed Effects Models for Complex Data

Author : Lang Wu
Publisher : CRC Press
ISBN 13 : 9781420074086
Total Pages : 431 pages
Book Rating : 4.0/5 (74 download)

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Book Synopsis Mixed Effects Models for Complex Data by : Lang Wu

Download or read book Mixed Effects Models for Complex Data written by Lang Wu and published by CRC Press. This book was released on 2009-11-11 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.

Expectation Maximization Algorithms for Conditional Likelihoods

Author : Jarkko Salojärvi
Publisher :
ISBN 13 : 9789512275953
Total Pages : 10 pages
Book Rating : 4.2/5 (759 download)

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Book Synopsis Expectation Maximization Algorithms for Conditional Likelihoods by : Jarkko Salojärvi

Download or read book Expectation Maximization Algorithms for Conditional Likelihoods written by Jarkko Salojärvi and published by . This book was released on 2005 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Combined Algorithms for Constrained Estimation of Finite Mixture Distributions with Grouped Data and Conditional Data

Author : Juan Du
Publisher :
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.:/5 (754 download)

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Book Synopsis Combined Algorithms for Constrained Estimation of Finite Mixture Distributions with Grouped Data and Conditional Data by : Juan Du

Download or read book Combined Algorithms for Constrained Estimation of Finite Mixture Distributions with Grouped Data and Conditional Data written by Juan Du and published by . This book was released on 2002 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Finite Mixture Models

Author : Geoffrey McLachlan
Publisher : John Wiley & Sons
ISBN 13 : 047165406X
Total Pages : 419 pages
Book Rating : 4.4/5 (716 download)

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Book Synopsis Finite Mixture Models by : Geoffrey McLachlan

Download or read book Finite Mixture Models written by Geoffrey McLachlan and published by John Wiley & Sons. This book was released on 2004-03-22 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Bayesian Data Analysis, Third Edition

Author : Andrew Gelman
Publisher : CRC Press
ISBN 13 : 1439840954
Total Pages : 677 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Bayesian Data Analysis, Third Edition by : Andrew Gelman

Download or read book Bayesian Data Analysis, Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Frailty Models in Survival Analysis

Author : Andreas Wienke
Publisher : CRC Press
ISBN 13 : 9781420073911
Total Pages : 324 pages
Book Rating : 4.0/5 (739 download)

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Book Synopsis Frailty Models in Survival Analysis by : Andreas Wienke

Download or read book Frailty Models in Survival Analysis written by Andreas Wienke and published by CRC Press. This book was released on 2010-07-26 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of frailty offers a convenient way to introduce unobserved heterogeneity and associations into models for survival data. In its simplest form, frailty is an unobserved random proportionality factor that modifies the hazard function of an individual or a group of related individuals. Frailty Models in Survival Analysis presents a comprehensive overview of the fundamental approaches in the area of frailty models. The book extensively explores how univariate frailty models can represent unobserved heterogeneity. It also emphasizes correlated frailty models as extensions of univariate and shared frailty models. The author analyzes similarities and differences between frailty and copula models; discusses problems related to frailty models, such as tests for homogeneity; and describes parametric and semiparametric models using both frequentist and Bayesian approaches. He also shows how to apply the models to real data using the statistical packages of R, SAS, and Stata. The appendix provides the technical mathematical results used throughout. Written in nontechnical terms accessible to nonspecialists, this book explains the basic ideas in frailty modeling and statistical techniques, with a focus on real-world data application and interpretation of the results. By applying several models to the same data, it allows for the comparison of their advantages and limitations under varying model assumptions. The book also employs simulations to analyze the finite sample size performance of the models.

Cluster Analysis

Author : Brian S. Everitt
Publisher :
ISBN 13 :
Total Pages : 122 pages
Book Rating : 4.:/5 (878 download)

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Book Synopsis Cluster Analysis by : Brian S. Everitt

Download or read book Cluster Analysis written by Brian S. Everitt and published by . This book was released on 1977 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:

All of Statistics

Author : Larry Wasserman
Publisher : Springer Science & Business Media
ISBN 13 : 0387217363
Total Pages : 446 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis All of Statistics by : Larry Wasserman

Download or read book All of Statistics written by Larry Wasserman and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.

Modeling Ordered Choices

Author : William H. Greene
Publisher : Cambridge University Press
ISBN 13 : 1139485954
Total Pages : 383 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Modeling Ordered Choices by : William H. Greene

Download or read book Modeling Ordered Choices written by William H. Greene and published by Cambridge University Press. This book was released on 2010-04-08 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is increasingly common for analysts to seek out the opinions of individuals and organizations using attitudinal scales such as degree of satisfaction or importance attached to an issue. Examples include levels of obesity, seriousness of a health condition, attitudes towards service levels, opinions on products, voting intentions, and the degree of clarity of contracts. Ordered choice models provide a relevant methodology for capturing the sources of influence that explain the choice made amongst a set of ordered alternatives. The methods have evolved to a level of sophistication that can allow for heterogeneity in the threshold parameters, in the explanatory variables (through random parameters), and in the decomposition of the residual variance. This book brings together contributions in ordered choice modeling from a number of disciplines, synthesizing developments over the last fifty years, and suggests useful extensions to account for the wide range of sources of influence on choice.

On Algorithms for Restricted Maximum Likelihood Estimation

Author : Mortaza Jamshidian
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis On Algorithms for Restricted Maximum Likelihood Estimation by : Mortaza Jamshidian

Download or read book On Algorithms for Restricted Maximum Likelihood Estimation written by Mortaza Jamshidian and published by . This book was released on 2018 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work proposes a globally convergent algorithm, based on gradient projections, for maximum likelihood (ML) estimation under linear equality and inequality restrictions (constraints) on parameters. The proposed algorithm has wide applicability, and as an important special case its application to restricted expectation- maximization (EM) problems is described. Often, a class of algorithms that we call expectation-restricted-maximization (ERM) is used to deal with constraints in the EM setting. We describe two such ERM algorithms that handle linear equality constraints, and discuss their convergence. As we explain, the assumptions for global convergence of one of the algorithms may be practically too restrictive, and as such we suggest a modification. We provide an example where the second algorithm fails. In general we argue that the gradient projection (GP) algorithm is superior to ERM algorithms in terms of simplicity of implementation and time to converge. We give an example of application of GP to parameter estimation of mixtures of normal densities where linear inequality constraints are imposed, and compare CPU times required for the algorithms discussed.

Seamless R and C++ Integration with Rcpp

Author : Dirk Eddelbuettel
Publisher : Springer Science & Business Media
ISBN 13 : 146146868X
Total Pages : 236 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Seamless R and C++ Integration with Rcpp by : Dirk Eddelbuettel

Download or read book Seamless R and C++ Integration with Rcpp written by Dirk Eddelbuettel and published by Springer Science & Business Media. This book was released on 2013-06-04 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rcpp is the glue that binds the power and versatility of R with the speed and efficiency of C++. With Rcpp, the transfer of data between R and C++ is nearly seamless, and high-performance statistical computing is finally accessible to most R users. Rcpp should be part of every statistician's toolbox. -- Michael Braun, MIT Sloan School of Management "Seamless R and C++ integration with Rcpp" is simply a wonderful book. For anyone who uses C/C++ and R, it is an indispensable resource. The writing is outstanding. A huge bonus is the section on applications. This section covers the matrix packages Armadillo and Eigen and the GNU Scientific Library as well as RInside which enables you to use R inside C++. These applications are what most of us need to know to really do scientific programming with R and C++. I love this book. -- Robert McCulloch, University of Chicago Booth School of Business Rcpp is now considered an essential package for anybody doing serious computational research using R. Dirk's book is an excellent companion and takes the reader from a gentle introduction to more advanced applications via numerous examples and efficiency enhancing gems. The book is packed with all you might have ever wanted to know about Rcpp, its cousins (RcppArmadillo, RcppEigen .etc.), modules, package development and sugar. Overall, this book is a must-have on your shelf. -- Sanjog Misra, UCLA Anderson School of Management The Rcpp package represents a major leap forward for scientific computations with R. With very few lines of C++ code, one has R's data structures readily at hand for further computations in C++. Hence, high-level numerical programming can be made in C++ almost as easily as in R, but often with a substantial speed gain. Dirk is a crucial person in these developments, and his book takes the reader from the first fragile steps on to using the full Rcpp machinery. A very recommended book! -- Søren Højsgaard, Department of Mathematical Sciences, Aalborg University, Denmark "Seamless R and C ++ Integration with Rcpp" provides the first comprehensive introduction to Rcpp. Rcpp has become the most widely-used language extension for R, and is deployed by over one-hundred different CRAN and BioConductor packages. Rcpp permits users to pass scalars, vectors, matrices, list or entire R objects back and forth between R and C++ with ease. This brings the depth of the R analysis framework together with the power, speed, and efficiency of C++. Dirk Eddelbuettel has been a contributor to CRAN for over a decade and maintains around twenty packages. He is the Debian/Ubuntu maintainer for R and other quantitative software, edits the CRAN Task Views for Finance and High-Performance Computing, is a co-founder of the annual R/Finance conference, and an editor of the Journal of Statistical Software. He holds a Ph.D. in Mathematical Economics from EHESS (Paris), and works in Chicago as a Senior Quantitative Analyst.

Modern Multivariate Statistical Techniques

Author : Alan J. Izenman
Publisher : Springer Science & Business Media
ISBN 13 : 0387781897
Total Pages : 757 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Modern Multivariate Statistical Techniques by : Alan J. Izenman

Download or read book Modern Multivariate Statistical Techniques written by Alan J. Izenman and published by Springer Science & Business Media. This book was released on 2009-03-02 with total page 757 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on multivariate analysis to look at large data sets which describes the state of the art in analyzing such data. Material such as database management systems is included that has never appeared in statistics books before.