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Bayesian Infinite Mixture Models For Gene Clustering And Simultaneous Context Selection Using High Throughput Gene Expression Data
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Book Synopsis Bayesian Infinite Mixture Models for Gene Clustering and Simultaneous Context Selection Using High-throughput Gene Expression Data by : Johannes M. Freudenberg
Download or read book Bayesian Infinite Mixture Models for Gene Clustering and Simultaneous Context Selection Using High-throughput Gene Expression Data written by Johannes M. Freudenberg and published by . This book was released on 2009 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applying clustering algorithms to identify groups of co-expressed genes is an important step in the analysis of high-throughput genomics data in order to elucidate affected biological pathways and transcriptional regulatory mechanisms. As these data are becoming ever more abundant the integration with both, existing biological knowledge and other experimental data becomes as crucial as the ability to perform such analysis in a meaningful but virtually unsupervised fashion. Clustering analysis often relies on ad-hoc methods such as k-means or hierarchical clustering with Euclidean distance but model-based methods such as the Bayesian Infinite Mixtures approach have been shown to produce better, more reproducible results. Further improvements have been accomplished by context-specific gene clustering algorithms designed to determine groups of co-expressed genes within a given subset of biological samples termed context. The complementary problem of finding differentially co-expressed genes given two or more contexts has been addressed but relies on the a priori definition of contexts and has not been used to facilitate the clustering of biological samples. Here we describe a new computational method using Bayesian infinite mixture models to cluster genes simultaneously utilizing the concept of differential co-expression as a unique similarity measure to find groups of similar samples. We compute a novel per-gene differential co-expression score that is reproducible and biologically meaningful. To evaluate, annotate, and display clustering results we present the integrated software package CLEAN which contains functionality for performing Clustering Enrichment Analysis, a method to functionally annotate clustering results and to assign a novel gene-specific functional coherence score. We apply our method to a number of simulated datasets comparing it to other commonly used clustering algorithms, and we re-analyze several breast cancer studies. We find that our unsupervised method determines patient groupings highly predictive of clinically relevant factors such as estrogen receptor status, tumor grade, and disease specific survival. Integrating these data with computationally and literature-derived information by applying CLEAN to the corresponding clusterings as well as the DCS signature substantiates these findings. Our results demonstrate the range of applications our methodology provides, offering a comprehensive analysis tool to study gene co-expression and differential co-expression patterns specific to the biological conditions of interest while simultaneously determining subsets of such biological conditions using a unique similarity measure that is complementary to the currently existing methods. It allows us to further our understanding of highly complex diseases such as breast cancer, and it has the potential to greatly facilitate research in many other, not yet as intensively studied areas.
Book Synopsis Bayesian Inference for Gene Expression and Proteomics by : Kim-Anh Do
Download or read book Bayesian Inference for Gene Expression and Proteomics written by Kim-Anh Do and published by Cambridge University Press. This book was released on 2006-07-24 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expert overviews of Bayesian methodology, tools and software for multi-platform high-throughput experimentation.
Book Synopsis Nonlinear Mixture Models: A Bayesian Approach by : Tatiana V Tatarinova
Download or read book Nonlinear Mixture Models: A Bayesian Approach written by Tatiana V Tatarinova and published by World Scientific. This book was released on 2014-12-30 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by two mathematicians from the University of Southern California, provides a broad introduction to the important subject of nonlinear mixture models from a Bayesian perspective. It contains background material, a brief description of Markov chain theory, as well as novel algorithms and their applications. It is self-contained and unified in presentation, which makes it ideal for use as an advanced textbook by graduate students and as a reference for independent researchers. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.In this book the authors present Bayesian methods of analysis for nonlinear, hierarchical mixture models, with a finite, but possibly unknown, number of components. These methods are then applied to various problems including population pharmacokinetics and gene expression analysis. In population pharmacokinetics, the nonlinear mixture model, based on previous clinical data, becomes the prior distribution for individual therapy. For gene expression data, one application included in the book is to determine which genes should be associated with the same component of the mixture (also known as a clustering problem). The book also contains examples of computer programs written in BUGS. This is the first book of its kind to cover many of the topics in this field.
Book Synopsis Bayesian Growth Mixture Model for Clustering Longitudinal Data by : Zihang Lu
Download or read book Bayesian Growth Mixture Model for Clustering Longitudinal Data written by Zihang Lu and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies of growth patterns of longitudinal characteristics are vitally important to improve our understanding of the development course of diseases. In these studies, it is often of great interest to cluster individual trajectories based on repeated measurements collected over time. Non-linear growth trajectories are often seen in practice, and individual data can also be measured sparsely at irregular time points, which may complicate the modeling process. This thesis begins with proposing a shape invariant growth mixture model for better clustering growth trajectory data with these features (Chapter 3). In the proposed model, non-linear patterns are captured by cluster-specific cubic B-spline smoothing functions within a latent class mixed effect model framework, and random effects reflecting the size, timing and intensity of the individual growth trajectories are modeled within each cluster to account for variation that is not explained by latent classes. We also compare our model to the commonly used standard growth mixture model and functional clustering approach. To better understand the clinical implication of different growth patterns, interests are usually not limited to which individuals belong to which subgroup, but also what factors are associated with individuals' class membership. This information could help clinicians provide early intervention to prevent the development of abnormal trajectories and therefore the development of diseases. Despite its importance in facilitating medical findings, little work has been done in selecting the predictors related to class membership in the context of growth mixture models. Therefore, we aim to extend the shape invariant mixture model we proposed to a unified Bayesian growth mixture model to allow incorporating covariates. To achieve this objective, in Chapter 4 we first review the currently available Bayesian variable selection approaches and compare their performance in terms of variable selection and prediction. And in Chapter 5, we propose a unified growth mixture model allowing for simultaneously clustering growth trajectories and selecting important covariates that are associated with the class membership. Bayesian inference via Markov chain Monte Carlo (MCMC) algorithm is implemented to estimate the parameters of interest. Results from analyzing real and simulated data are presented and discussed throughout this thesis.
Book Synopsis Bayesian Analysis of Gene Expression Data by : Bani K. Mallick
Download or read book Bayesian Analysis of Gene Expression Data written by Bani K. Mallick and published by Wiley. This book was released on 2009-07-20 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of high-throughput genetic experimentation is evolving rapidly, with the advent of new technologies and new venues for data mining. Bayesian methods play a role central to the future of data and knowledge integration in the field of Bioinformatics. This book is devoted exclusively to Bayesian methods of analysis for applications to high-throughput gene expression data, exploring the relevant methods that are changing Bioinformatics. Case studies, illustrating Bayesian analyses of public gene expression data, provide the backdrop for students to develop analytical skills, while the more experienced readers will find the review of advanced methods challenging and attainable. This book: Introduces the fundamentals in Bayesian methods of analysis for applications to high-throughput gene expression data. Provides an extensive review of Bayesian analysis and advanced topics for Bioinformatics, including examples that extensively detail the necessary applications. Accompanied by website featuring datasets, exercises and solutions. Bayesian Analysis of Gene Expression Data offers a unique introduction to both Bayesian analysis and gene expression, aimed at graduate students in Statistics, Biomedical Engineers, Computer Scientists, Biostatisticians, Statistical Geneticists, Computational Biologists, applied Mathematicians and Medical consultants working in genomics. Bioinformatics researchers from many fields will find much value in this book.
Book Synopsis Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics by : Christine Sinoquet
Download or read book Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics written by Christine Sinoquet and published by OUP Oxford. This book was released on 2014-09-18 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays bioinformaticians and geneticists are faced with myriad high-throughput data usually presenting the characteristics of uncertainty, high dimensionality and large complexity. These data will only allow insights into this wealth of so-called 'omics' data if represented by flexible and scalable models, prior to any further analysis. At the interface between statistics and machine learning, probabilistic graphical models (PGMs) represent a powerful formalism to discover complex networks of relations. These models are also amenable to incorporating a priori biological information. Network reconstruction from gene expression data represents perhaps the most emblematic area of research where PGMs have been successfully applied. However these models have also created renewed interest in genetics in the broad sense, in particular regarding association genetics, causality discovery, prediction of outcomes, detection of copy number variations, and epigenetics. This book provides an overview of the applications of PGMs to genetics, genomics and postgenomics to meet this increased interest. A salient feature of bioinformatics, interdisciplinarity, reaches its limit when an intricate cooperation between domain specialists is requested. Currently, few people are specialists in the design of advanced methods using probabilistic graphical models for postgenomics or genetics. This book deciphers such models so that their perceived difficulty no longer hinders their use and focuses on fifteen illustrations showing the mechanisms behind the models. Probabilistic Graphical Models for Genetics, Genomics and Postgenomics covers six main themes: (1) Gene network inference (2) Causality discovery (3) Association genetics (4) Epigenetics (5) Detection of copy number variations (6) Prediction of outcomes from high-dimensional genomic data. Written by leading international experts, this is a collection of the most advanced work at the crossroads of probabilistic graphical models and genetics, genomics, and postgenomics. The self-contained chapters provide an enlightened account of the pros and cons of applying these powerful techniques.
Book Synopsis Bayesian Non-parametric Parsimonious Mixtures for Model-based Clustering by : Marius Bartcus
Download or read book Bayesian Non-parametric Parsimonious Mixtures for Model-based Clustering written by Marius Bartcus and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on statistical learning and multi-dimensional data analysis. It particularly focuses on unsupervised learning of generative models for model-based clustering. We study the Gaussians mixture models, in the context of maximum likelihood estimation via the EM algorithm, as well as in the Bayesian estimation context by maximum a posteriori via Markov Chain Monte Carlo (MCMC) sampling techniques. We mainly consider the parsimonious mixture models which are based on a spectral decomposition of the covariance matrix and provide a flexible framework particularly for the analysis of high-dimensional data. Then, we investigate non-parametric Bayesian mixtures which are based on general flexible processes such as the Dirichlet process and the Chinese Restaurant Process. This non-parametric model formulation is relevant for both learning the model, as well for dealing with the issue of model selection. We propose new Bayesian non-parametric parsimonious mixtures and derive a MCMC sampling technique where the mixture model and the number of mixture components are simultaneously learned from the data. The selection of the model structure is performed by using Bayes Factors. These models, by their non-parametric and sparse formulation, are useful for the analysis of large data sets when the number of classes is undetermined and increases with the data, and when the dimension is high. The models are validated on simulated data and standard real data sets. Then, they are applied to a real difficult problem of automatic structuring of complex bioacoustic data issued from whale song signals. Finally, we open Markovian perspectives via hierarchical Dirichlet processes hidden Markov models.
Book Synopsis Bayesian Nonparametric Clusterings in Relational and High-dimensional Settings with Applications in Bioinformatics by : Dazhuo Li
Download or read book Bayesian Nonparametric Clusterings in Relational and High-dimensional Settings with Applications in Bioinformatics written by Dazhuo Li and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in high throughput methodologies offer researchers the ability to understand complex systems via high dimensional and multi-relational data. One example is the realm of molecular biology where disparate data (such as gene sequence, gene expression, and interaction information) are available for various snapshots of biological systems. This type of high dimensional and multirelational data allows for unprecedented detailed analysis, but also presents challenges in accounting for all the variability. High dimensional data often has a multitude of underlying relationships, each represented by a separate clustering structure, where the number of structures is typically unknown a priori. To address the challenges faced by traditional clustering methods on high dimensional and multirelational data, we developed three feature selection and cross-clustering methods: 1) infinite relational model with feature selection (FIRM) which incorporates the rich information of multirelational data; 2) Bayesian Hierarchical Cross-Clustering (BHCC), a deterministic approximation to Cross Dirichlet Process mixture (CDPM) and to cross-clustering; and 3) randomized approximation (RBHCC), based on a truncated hierarchy. An extension of BHCC, Bayesian Congruence Measuring (BCM), is proposed to measure incongruence between genes and to identify sets of congruent loci with identical evolutionary histories. We adapt our BHCC algorithm to the inference of BCM, where the intended structure of each view (congruent loci) represents consistent evolutionary processes. We consider an application of FIRM on categorizing mRNA and microRNA. The model uses latent structures to encode the expression pattern and the gene ontology annotations. We also apply FIRM to recover the categories of ligands and proteins, and to predict unknown drug-target interactions, where latent categorization structure encodes drug-target interaction, chemical compound similarity, and amino acid sequence similarity. BHCC and RBHCC are shown to have improved predictive performance (both in terms of cluster membership and missing value prediction) compared to traditional clustering methods. Our results suggest that these novel approaches to integrating multi-relational information have a promising future in the biological sciences where incorporating data related to varying features is often regarded as a daunting task.
Book Synopsis Bayesian Learning Frameworks for Multivariate Beta Mixture Models by : Mahsa Amirkhani
Download or read book Bayesian Learning Frameworks for Multivariate Beta Mixture Models written by Mahsa Amirkhani and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixture models have been widely used as a statistical learning paradigm in various unsupervised machine learning applications, where labeling a vast amount of data is impractical and costly. They have shown a significant success and encouraging performance in many real-world problems from different fields such as computer vision, information retrieval and pattern recognition. One of the most widely used distributions in mixture models is Gaussian distribution, due to its characteristics, such as its simplicity and fitting capabilities. However, data obtained from some applications could have different properties like non-Gaussian and asymmetric nature. In this thesis, we propose multivariate Beta mixture models which offer flexibility, various shapes with promising attributes. These models can be considered as decent alternatives to Gaussian distributions. We explore multiple Bayesian inference approaches for multivariate Beta mixture models and propose a suitable solution for the problem of estimating parameters using Markov Chain Monte Carlo (MCMC) technique. We exploit Gibbs sampling within Metropolis-Hastings for learning parameters of our finite mixture model. Moreover, a fully Bayesian approach based on birth-death MCMC technique is proposed which simultaneously allows cluster assignments, parameters estimation and the selection of the optimal number of clusters. Finally, we develop a nonparametric Bayesian framework by extending our finite mixture model to infinity using Dirichlet process to tackle the model selection problem. Experimental results obtained from challenging applications (e.g., intrusion detection, medical, etc.) confirm that our proposed frameworks can provide effective solutions comparing to existing alternatives.
Book Synopsis Bayesian Mixtures and Gene Expression Profiling with Missing Data by : Xiaoqing Chang
Download or read book Bayesian Mixtures and Gene Expression Profiling with Missing Data written by Xiaoqing Chang and published by . This book was released on 2008 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: Missing values are one of the problems encountered in microarray data analysis. For many of the clustering algorithms applied in microarray data analysis, a complete data matrix is required. The traditional approach to solving the missing value problem is to fill in with estimates by imputation. Once the missing value estimates are imputed, they remain fixed during the following clustering process. Poorly estimated missing data points will impair reliability of the cluster analysis. In this particular study, we tested the ability of a novel clustering method based on a Bayesian infinite mixtures model (IMM) to accommodate missing data. In a simulation study and a prostate cancer dataset, by examining the specificity and sensitivity of clusters we demonstrated that the IMM method has increased precision of the cluster analysis without requirement of a prior imputation. IMM is more robust in clustering an incomplete dataset than traditional clustering methods, which require prior imputation.
Book Synopsis Bayesian Model Selection for High-dimensional High-throughput Data by : Adarsh Joshi
Download or read book Bayesian Model Selection for High-dimensional High-throughput Data written by Adarsh Joshi and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian methods are often criticized on the grounds of subjectivity. Furthermore, misspecified priors can have a deleterious effect on Bayesian inference. Noting that model selection is effectively a test of many hypotheses, Dr. Valen E. Johnson sought to eliminate the need of prior specification by computing Bayes' factors from frequentist test statistics. In his pioneering work that was published in the year 2005, Dr. Johnson proposed using so-called local priors for computing Bayes? factors from test statistics. Dr. Johnson and Dr. Jianhua Hu used Bayes' factors for model selection in a linear model setting. In an independent work, Dr. Johnson and another colleage, David Rossell, investigated two families of non-local priors for testing the regression parameter in a linear model setting. These non-local priors enable greater separation between the theories of null and alternative hypotheses. In this dissertation, I extend model selection based on Bayes' factors and use nonlocal priors to define Bayes' factors based on test statistics. With these priors, I have been able to reduce the problem of prior specification to setting to just one scaling parameter. That scaling parameter can be easily set, for example, on the basis of frequentist operating characteristics of the corresponding Bayes' factors. Furthermore, the loss of information by basing a Bayes' factors on a test statistic is minimal. Along with Dr. Johnson and Dr. Hu, I used the Bayes' factors based on the likelihood ratio statistic to develop a method for clustering gene expression data. This method has performed well in both simulated examples and real datasets. An outline of that work is also included in this dissertation. Further, I extend the clustering model to a subclass of the decomposable graphical model class, which is more appropriate for genotype data sets, such as single-nucleotide polymorphism (SNP) data. Efficient FORTRAN programming has enabled me to apply the methodology to hundreds of nodes. For problems that produce computationally harder probability landscapes, I propose a modification of the Markov chain Monte Carlo algorithm to extract information regarding the important network structures in the data. This modified algorithm performs well in inferring complex network structures. I use this method to develop a prediction model for disease based on SNP data. My method performs well in cross-validation studies.
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.
Book Synopsis Conjugate Dirichlet Process Mixture Models by : David Boyack Dahl
Download or read book Conjugate Dirichlet Process Mixture Models written by David Boyack Dahl and published by . This book was released on 2004 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Sylvia Frühwirth-Schnatter Publisher :Springer Science & Business Media ISBN 13 :0387357688 Total Pages :506 pages Book Rating :4.3/5 (873 download)
Book Synopsis Finite Mixture and Markov Switching Models by : Sylvia Frühwirth-Schnatter
Download or read book Finite Mixture and Markov Switching Models written by Sylvia Frühwirth-Schnatter and published by Springer Science & Business Media. This book was released on 2006-11-24 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past decade has seen powerful new computational tools for modeling which combine a Bayesian approach with recent Monte simulation techniques based on Markov chains. This book is the first to offer a systematic presentation of the Bayesian perspective of finite mixture modelling. The book is designed to show finite mixture and Markov switching models are formulated, what structures they imply on the data, their potential uses, and how they are estimated. Presenting its concepts informally without sacrificing mathematical correctness, it will serve a wide readership including statisticians as well as biologists, economists, engineers, financial and market researchers.
Book Synopsis Sparse Model Building from Genome-wide Variation with Graphical Models by : Benjamin Alexander Logsdon
Download or read book Sparse Model Building from Genome-wide Variation with Graphical Models written by Benjamin Alexander Logsdon and published by . This book was released on 2011 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: High throughput sequencing and expression characterization have lead to an explosion of phenotypic and genotypic molecular data underlying both experimental studies and outbred populations. We develop a novel class of algorithms to reconstruct sparse models among these molecular phenotypes (e.g. expression products) and genotypes (e.g. single nucleotide polymorphisms), via both a Bayesian hierarchical model, when the sample size is much smaller than the model dimension (i.e. p n) and the well characterized adaptive lasso algo- rithm. Specifically, we propose novel approaches to the problems of increasing power to detect additional loci in genome-wide association studies using our variational algorithm, efficiently learning directed cyclic graphs from expression and genotype data using the adaptive lasso, and constructing genomewide undirected graphs among genotype, expression and downstream phenotype data using an extension of the variational feature selection algorithm. The Bayesian hierarchical model is derived for a parametric multiple regression model with a mixture prior of a point mass and normal distribution for each regression coefficient, and appropriate priors for the set of hyperparameters. When combined with a probabilistic consistency bound on the model dimension, this approach leads to very sparse solutions without the need for cross validation. We use a variational Bayes approximate inference approach in our algorithm, where we impose a complete factorization across all parameters for the approximate posterior distribution, and then minimize the KullbackLeibler divergence between the approximate and true posterior distributions. Since the prior distribution is non-convex, we restart the algorithm many times to find multiple posterior modes, and combine information across all discovered modes in an approximate Bayesian model averaging framework, to reduce the variance of the posterior probability estimates. We perform analysis of three major publicly available data-sets: the HapMap 2 genotype and expression data collected on immortalized lymphoblastoid cell lines, the genome-wide gene expression and genetic marker data collected for a yeast intercross, and genomewide gene expression, genetic marker, and downstream phenotypes related to weight in a mouse F2 intercross. Based on both simulations and data analysis we show that our algorithms can outperform other state of the art model selection procedures when including thousands to hundreds of thousands of genotypes and expression traits, in terms of aggressively controlling false discovery rate, and generating rich simultaneous statistical models.
Book Synopsis Mixture Models for the Analysis of Gene Expression by : Ivan Gesteira Costa Filho
Download or read book Mixture Models for the Analysis of Gene Expression written by Ivan Gesteira Costa Filho and published by . This book was released on 2008 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bayesian Networks for Omics Data Analysis by : Anand K. Gavai.
Download or read book Bayesian Networks for Omics Data Analysis written by Anand K. Gavai. and published by . This book was released on 2009 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
