Download or read book Variable Selection in High Dimensional Complex Data and Bayesian Estimation of Reduction Subspace written by Moumita Karmakar and published by . This book was released on 2015 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays researchers are collecting large amount of data for which the number of predictors p is often too large to allow a thorough graphical visualization of the data for regression modeling. Commonly regression data are collected jointly on (Y, X) where X = (X1, ⋯, Xp)T is a random p-dimensional predictor and Y is a univariate response. In high dimensional setup, frequently encountered problems for variable selection or estimation in regression analyses are i) nonlinear relationship among predictors and response, ii) number of predictors much larger than sample size, iii) presence of sparsity.
Download or read book Variable Selection for High dimensional Complex Data written by Fei Xue and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Solutions to High dimensional Data Challenges Using Hybrid Search written by Shiqiang Jin and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the era of Big Data, variable selection with high-dimensional data has drawn increasing attention. With a large number of predictors, there rises a big challenge for model fitting and prediction. In this dissertation, we propose three different yet interconnected methodologies, which include theory, computation, and real applications for various scenarios of regression analysis. The primary goal in this dissertation is to develop powerful Bayesian solutions to high-dimensional data challenges using a new variable selection strategy, called hybrid search. To effectively reduce computation costs in high-dimensional data analysis, we propose novel computational strategies that can quickly evaluate a large number of marginal likelihoods simultaneously within a single computation. In Chapter 1, we discuss background and current challenges in high-dimensional variable selection. The motivation of our study is also justified. In Chapter 2, we introduce a new Bayesian method of best subset selection in the context of linear regression. The proposed method rapidly finds the best subset via a hybrid search algorithm that combines deterministic local search and stochastic global search. In Chapter 3, on the basis of the approach in Chapter 2, we extend it to a framework of multivariate linear regression model, which analyzes the relationship between multiple response variables and a common set of predictors. In Chapter 4, we propose a general Bayesian method to perform high-dimensional variable selection for various data types, such as binary, count, continuous and time-to-event (survival) data. Using Bayesian approximation techniques, we develop a general computing strategy that enables us to assess the marginal likelihoods of many candidate models within a single computation. In addition, to accelerate the convergence, we employ a hybrid search algorithm that can quickly explore the model spaces and accurately obtain the global maximum of marginal posterior probabilities.
Download or read book Perspectives on Big Data Analysis written by S. Ejaz Ahmed and published by American Mathematical Society. This book was released on 2014-08-20 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Workshop on Perspectives on High-dimensional Data Analysis II, held May 30-June 1, 2012, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. This book collates applications and methodological developments in high-dimensional statistics dealing with interesting and challenging problems concerning the analysis of complex, high-dimensional data with a focus on model selection and data reduction. The chapters contained in this book deal with submodel selection and parameter estimation for an array of interesting models. The book also presents some surprising results on high-dimensional data analysis, especially when signals cannot be effectively separated from the noise, it provides a critical assessment of penalty estimation when the model may not be sparse, and it suggests alternative estimation strategies. Readers can apply the suggested methodologies to a host of applications and also can extend these methodologies in a variety of directions. This volume conveys some of the surprises, puzzles and success stories in big data analysis and related fields. This book is co-published with the Centre de Recherches Mathématiques.
Download or read book Variable Selection for High dimensional Data with Error Control written by Han Fu (Ph. D. in biostatistics) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many high-throughput genomic applications involve a large set of covariates and it is crucial to discover which variables are truly associated with the response. It is often desirable for researchers to select variables that are indeed true and reproducible in followup studies. Effectively controlling the false discovery rate (FDR) increases the reproducibility of the discoveries and has been a major challenge in variable selection research, especially for high-dimensional data. Existing error control approaches include augmentation approaches which utilize artificial variables as benchmarks for decision making, such as model-X knockoffs. We introduce another augmentation-based selection framework extended from a Bayesian screening approach called reference distribution variable selection. Ordinal responses, which were not previously considered in this area, were used to compare different variable selection approaches. We constructed various importance measures that fit into the selection frameworks, using either L1 penalized regression or machine learning techniques, and compared these measures in terms of the FDR and power using simulated data. Moreover, we applied these selection methods to high-throughput methylation data for identifying features associated with the progression from normal liver tissue to hepatocellular carcinoma to further compare and contrast their performances. Having established the effectiveness of FDR control for model-X knockoffs, we turned our attention to another important data type - survival data with long-term survivors. Medical breakthroughs in recent years have led to cures for many diseases, resulting in increased observations of long-term survivors. The mixture cure model (MCM) is a type of survival model that is often used when a cured fraction exists. Unfortunately, currently few variable selection methods exist for MCMs when there are more predictors than samples. To fill the gap, we developed penalized MCMs for high-dimensional datasets which allow for identification of prognostic factors associated with both cure status and/or survival. Both parametric models and semi-parametric proportional hazards models were considered for modeling the survival component. For penalized parametric MCMs, we demonstrated how the estimation proceeded using two different iterative algorithms, the generalized monotone incremental forward stagewise (GMIFS) and Expectation-Maximization (E-M). For semi-parametric MCMs where multiple types of penalty functions were considered, the coordinate descent algorithm was combined with E-M for optimization. The model-X knockoffs method was combined with these algorithms to allow for FDR control in variable selection. Through extensive simulation studies, our penalized MCMs have been shown to outperform alternative methods on multiple metrics and achieve high statistical power with FDR being controlled. In two acute myeloid leukemia (AML) applications with gene expression data, our proposed approaches identified important genes associated with potential cure or time-to-relapse, which may help inform treatment decisions for AML patients.
Download or read book Statistical Foundations of Data Science written by Jianqing Fan and published by CRC Press. This book was released on 2020-09-21 with total page 942 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.
Download or read book Variable Selection in High Dimensional Data Analysis with Applications written by and published by . This book was released on 2015 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to High Dimensional Statistics written by Christophe Giraud and published by CRC Press. This book was released on 2021-08-25 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the first edition: "[This book] succeeds singularly at providing a structured introduction to this active field of research. ... it is arguably the most accessible overview yet published of the mathematical ideas and principles that one needs to master to enter the field of high-dimensional statistics. ... recommended to anyone interested in the main results of current research in high-dimensional statistics as well as anyone interested in acquiring the core mathematical skills to enter this area of research." —Journal of the American Statistical Association Introduction to High-Dimensional Statistics, Second Edition preserves the philosophy of the first edition: to be a concise guide for students and researchers discovering the area and interested in the mathematics involved. The main concepts and ideas are presented in simple settings, avoiding thereby unessential technicalities. High-dimensional statistics is a fast-evolving field, and much progress has been made on a large variety of topics, providing new insights and methods. Offering a succinct presentation of the mathematical foundations of high-dimensional statistics, this new edition: Offers revised chapters from the previous edition, with the inclusion of many additional materials on some important topics, including compress sensing, estimation with convex constraints, the slope estimator, simultaneously low-rank and row-sparse linear regression, or aggregation of a continuous set of estimators. Introduces three new chapters on iterative algorithms, clustering, and minimax lower bounds. Provides enhanced appendices, minimax lower-bounds mainly with the addition of the Davis-Kahan perturbation bound and of two simple versions of the Hanson-Wright concentration inequality. Covers cutting-edge statistical methods including model selection, sparsity and the Lasso, iterative hard thresholding, aggregation, support vector machines, and learning theory. Provides detailed exercises at the end of every chapter with collaborative solutions on a wiki site. Illustrates concepts with simple but clear practical examples.
Download or read book Generalized Principal Component Analysis written by René Vidal and published by Springer. This book was released on 2016-04-11 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.
Download or read book Computational Intelligence for Multimedia Big Data on the Cloud with Engineering Applications written by Arun Kumar Sangaiah and published by Academic Press. This book was released on 2018-08-21 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Intelligence for Multimedia Big Data on the Cloud with Engineering Applications covers timely topics, including the neural network (NN), particle swarm optimization (PSO), evolutionary algorithm (GA), fuzzy sets (FS) and rough sets (RS), etc. Furthermore, the book highlights recent research on representative techniques to elaborate how a data-centric system formed a powerful platform for the processing of cloud hosted multimedia big data and how it could be analyzed, processed and characterized by CI. The book also provides a view on how techniques in CI can offer solutions in modeling, relationship pattern recognition, clustering and other problems in bioengineering. It is written for domain experts and developers who want to understand and explore the application of computational intelligence aspects (opportunities and challenges) for design and development of a data-centric system in the context of multimedia cloud, big data era and its related applications, such as smarter healthcare, homeland security, traffic control trading analysis and telecom, etc. Researchers and PhD students exploring the significance of data centric systems in the next paradigm of computing will find this book extremely useful. Presents a brief overview of computational intelligence paradigms and its significant role in application domains Illustrates the state-of-the-art and recent developments in the new theories and applications of CI approaches Familiarizes the reader with computational intelligence concepts and technologies that are successfully used in the implementation of cloud-centric multimedia services in massive data processing Provides new advances in the fields of CI for bio-engineering application
Download or read book Data Clustering written by and published by BoD – Books on Demand. This book was released on 2022-08-17 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: In view of the considerable applications of data clustering techniques in various fields, such as engineering, artificial intelligence, machine learning, clinical medicine, biology, ecology, disease diagnosis, and business marketing, many data clustering algorithms and methods have been developed to deal with complicated data. These techniques include supervised learning methods and unsupervised learning methods such as density-based clustering, K-means clustering, and K-nearest neighbor clustering. This book reviews recently developed data clustering techniques and algorithms and discusses the development of data clustering, including measures of similarity or dissimilarity for data clustering, data clustering algorithms, assessment of clustering algorithms, and data clustering methods recently developed for insurance, psychology, pattern recognition, and survey data.
Download or read book Variable Selection in High Dimensional Setup written by Atreyee Majumder and published by . This book was released on 2017 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematics for Machine Learning written by Marc Peter Deisenroth and published by Cambridge University Press. This book was released on 2020-04-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
Download or read book Data Mining for Bioinformatics written by Sumeet Dua and published by CRC Press. This book was released on 2012-11-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering theory, algorithms, and methodologies, as well as data mining technologies, Data Mining for Bioinformatics provides a comprehensive discussion of data-intensive computations used in data mining with applications in bioinformatics. It supplies a broad, yet in-depth, overview of the application domains of data mining for bioinformatics to help readers from both biology and computer science backgrounds gain an enhanced understanding of this cross-disciplinary field. The book offers authoritative coverage of data mining techniques, technologies, and frameworks used for storing, analyzing, and extracting knowledge from large databases in the bioinformatics domains, including genomics and proteomics. It begins by describing the evolution of bioinformatics and highlighting the challenges that can be addressed using data mining techniques. Introducing the various data mining techniques that can be employed in biological databases, the text is organized into four sections: Supplies a complete overview of the evolution of the field and its intersection with computational learning Describes the role of data mining in analyzing large biological databases—explaining the breath of the various feature selection and feature extraction techniques that data mining has to offer Focuses on concepts of unsupervised learning using clustering techniques and its application to large biological data Covers supervised learning using classification techniques most commonly used in bioinformatics—addressing the need for validation and benchmarking of inferences derived using either clustering or classification The book describes the various biological databases prominently referred to in bioinformatics and includes a detailed list of the applications of advanced clustering algorithms used in bioinformatics. Highlighting the challenges encountered during the application of classification on biological databases, it considers systems of both single and ensemble classifiers and shares effort-saving tips for model selection and performance estimation strategies.
Download or read book Foundations of Data Science written by Avrim Blum and published by Cambridge University Press. This book was released on 2020-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.
Download or read book Regression Graphics written by R. Dennis Cook and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of regression graphics through computer graphics. Recent developments in computer technology have stimulated new and exciting uses for graphics in statistical analyses. Regression Graphics, one of the first graduate-level textbooks on the subject, demonstrates how statisticians, both theoretical and applied, can use these exciting innovations. After developing a relatively new regression context that requires few scope-limiting conditions, Regression Graphics guides readers through the process of analyzing regressions graphically and assessing and selecting models. This innovative reference makes use of a wide range of graphical tools, including 2D and 3D scatterplots, 3D binary response plots, and scatterplot matrices. Supplemented by a companion ftp site, it features numerous data sets and applied examples that are used to elucidate the theory. Other important features of this book include: * Extensive coverage of a relatively new regression context based on dimension-reduction subspaces and sufficient summary plots * Graphical regression, an iterative visualization process for constructing sufficient regression views * Graphics for regressions with a binary response * Graphics for model assessment, including residual plots * Net-effects plots for assessing predictor contributions * Graphics for predictor and response transformations * Inverse regression methods * Access to a Web site of supplemental plots, data sets, and 3D color displays. An ideal text for students in graduate-level courses on statistical analysis, Regression Graphics is also an excellent reference for professional statisticians.
Download or read book Data Science and Machine Learning written by Dirk P. Kroese and published by CRC Press. This book was released on 2019-11-20 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on mathematical understanding Presentation is self-contained, accessible, and comprehensive Full color throughout Extensive list of exercises and worked-out examples Many concrete algorithms with actual code
