Download or read book Analysis and Testing of Sparse High Dimensional Discrete Data written by Amanda Rae Plunkett and published by . This book was released on 2015 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: High dimensional data analysis has been one of the most challenging problems in statistics and related areas for the last two decades. High dimensions occur in many applications where computers are able to capture large amounts of information related to a collected sample. Applications include genetic research, image processing, natural language processing, and signal processing to name a few. We focus on the problem of two-sample hypothesis testing for two cases: 1) sparse high dimensional multinomial data, and 2) sparse high dimensional binary data. We propose new statistical tests for each, prove their theoretical validity, and test their performance in various scenarios through simulations and analysis of applied problems. Additionally, we perform follow up analysis of these datasets using statistical classification methods.

Download or read book Sparse Graphical Modeling for High Dimensional Data written by Faming Liang and published by CRC Press. This book was released on 2023-08-02 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general framework for learning sparse graphical models with conditional independence tests Complete treatments for different types of data, Gaussian, Poisson, multinomial, and mixed data Unified treatments for data integration, network comparison, and covariate adjustment Unified treatments for missing data and heterogeneous data Efficient methods for joint estimation of multiple graphical models Effective methods of high-dimensional variable selection Effective methods of high-dimensional inference

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 High Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Download or read book Introduction to Nonparametric Estimation written by Alexandre B. Tsybakov and published by Springer Science & Business Media. This book was released on 2008-10-22 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from lecture notes and ready to be used for a course on the graduate level, this concise text aims to introduce the fundamental concepts of nonparametric estimation theory while maintaining the exposition suitable for a first approach in the field.

Download or read book Test Data Engineering written by Kojiro Shojima and published by Springer Nature. This book was released on 2022-08-13 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first technical book that considers tests as public tools and examines how to engineer and process test data, extract the structure within the data to be visualized, and thereby make test results useful for students, teachers, and the society. The author does not differentiate test data analysis from data engineering and information visualization. This monograph introduces the following methods of engineering or processing test data, including the latest machine learning techniques: classical test theory (CTT), item response theory (IRT), latent class analysis (LCA), latent rank analysis (LRA), biclustering (co-clustering), and Bayesian network model (BNM). CTT and IRT are methods for analyzing test data and evaluating students’ abilities on a continuous scale. LCA and LRA assess examinees by classifying them into nominal and ordinal clusters, respectively, where the adequate number of clusters is estimated from the data. Biclustering classifies examinees into groups (latent clusters) while classifying items into fields (factors). Particularly, the infinite relational model discussed in this book is a biclustering method feasible under the condition that neither the number of groups nor the number of fields is known beforehand. Additionally, the local dependence LRA, local dependence biclustering, and bicluster network model are methods that search and visualize inter-item (or inter-field) network structure using the mechanism of BNM. As this book offers a new perspective on test data analysis methods, it is certain to widen readers’ perspective on test data analysis.

Download or read book Categorical Data Analysis written by Alan Agresti and published by John Wiley & Sons. This book was released on 2013-04-08 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Second Edition "A must-have book for anyone expecting to do research and/or applications in categorical data analysis." —Statistics in Medicine "It is a total delight reading this book." —Pharmaceutical Research "If you do any analysis of categorical data, this is an essential desktop reference." —Technometrics The use of statistical methods for analyzing categorical data has increased dramatically, particularly in the biomedical, social sciences, and financial industries. Responding to new developments, this book offers a comprehensive treatment of the most important methods for categorical data analysis. Categorical Data Analysis, Third Edition summarizes the latest methods for univariate and correlated multivariate categorical responses. Readers will find a unified generalized linear models approach that connects logistic regression and Poisson and negative binomial loglinear models for discrete data with normal regression for continuous data. This edition also features: An emphasis on logistic and probit regression methods for binary, ordinal, and nominal responses for independent observations and for clustered data with marginal models and random effects models Two new chapters on alternative methods for binary response data, including smoothing and regularization methods, classification methods such as linear discriminant analysis and classification trees, and cluster analysis New sections introducing the Bayesian approach for methods in that chapter More than 100 analyses of data sets and over 600 exercises Notes at the end of each chapter that provide references to recent research and topics not covered in the text, linked to a bibliography of more than 1,200 sources A supplementary website showing how to use R and SAS; for all examples in the text, with information also about SPSS and Stata and with exercise solutions Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and methodologists, such as biostatisticians and researchers in the social and behavioral sciences, medicine and public health, marketing, education, finance, biological and agricultural sciences, and industrial quality control.

Download or read book High Dimensional Data Analysis with Low Dimensional Models written by John Wright and published by Cambridge University Press. This book was released on 2022-01-13 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: Connects fundamental mathematical theory with real-world problems, through efficient and scalable optimization algorithms.

Download or read book Large Dimensional Factor Analysis written by Jushan Bai and published by Now Publishers Inc. This book was released on 2008 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large Dimensional Factor Analysis provides a survey of the main theoretical results for large dimensional factor models, emphasizing results that have implications for empirical work. The authors focus on the development of the static factor models and on the use of estimated factors in subsequent estimation and inference. Large Dimensional Factor Analysis discusses how to determine the number of factors, how to conduct inference when estimated factors are used in regressions, how to assess the adequacy pf observed variables as proxies for latent factors, how to exploit the estimated factors to test unit root tests and common trends, and how to estimate panel cointegration models.

Download or read book Role of Sparsity in High Dimensional Signal Detection and Estimation written by Manqi Zhao and published by . This book was released on 2011 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Processing high dimensional data arises in a number of real world applications such as financial data analysis, hyperspectral imagery, and video surveillance. The data are organized in a rectangular array with n rows and p columns, where the rows represent different measurements and the columns represent different features. High dimensional statistical inference studies signal detection and estimation problems in the scenario when n “ p . The main challenge of high dimensional statistical inference is the curse of dimensionality phenomena. The curse of dimensionality leads to intractability of accurately approximating high-dimensional density function. Nevertheless, data samples in many high dimensional problems come from an underlying low dimensional space or manifold. This limits the degrees of freedom (DOF) in the ambient space. This structure can be exploited for statistical inference. Another feature of high dimensional data is concentration of measure phenomena, which states that certain smooth random functions in high dimensional space are nearly constant. The philosophy is that under mild conditions it is easy to predict the behavior of high dimensional data.In this thesis, we exploit the DOF structure in detection and estimation of high dimensional data together with concentration of measure inequalities to obtain new results. In particular we consider the sparsity model for compressed sensing, the joint sparse and Markov structure for blind deconvolution, the manifold model for outlier detection and the temporally local anomaly structure for time-series anomaly detection. We present a linear programming solution for signal support recovery from noisy measurements that leverages sparse constraint. We simultaneously reconstruct the unknown autoregressive filter and the driving process in light of the joint structure on sparsity and Markov property. We develop novel non-parametric adaptive anomaly detection algorithm for high dimensional data that can adapt to local sparse manifold structure. We develop a clustering algorithm that accounts for highly unbalanced proximal and complex shaped clusters based on the scheme of reweighting the graph edge similarity. We propose a new paradigm for time-series anomaly detection that exploits the local anomaly structure. Our analysis in compressed sensing shows that the achievable bound in terms of SNR, the number of measurements, and admissible sparsity level of a linear programming solution matches the optimal information-theoretic in an order-wise sense. Our result in anomaly detection suggests that estimating high dimensional level-set can be avoided by computing a sufficient p-value statistic. The resulting anomaly detector is asymptotically uniformly most powerful against any uniformly mixing density. We also provide a generalization of this p-value statistic in time-series anomaly detection with false alarm control.

Download or read book Analyzing Dependent Data with Vine Copulas written by Claudia Czado and published by Springer. This book was released on 2019-05-14 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a step-by-step introduction to the class of vine copulas, their statistical inference and applications. It focuses on statistical estimation and selection methods for vine copulas in data applications. These flexible copula models can successfully accommodate any form of tail dependence and are vital to many applications in finance, insurance, hydrology, marketing, engineering, chemistry, aviation, climatology and health. The book explains the pair-copula construction principles underlying these statistical models and discusses how to perform model selection and inference. It also derives simulation algorithms and presents real-world examples to illustrate the methodological concepts. The book includes numerous exercises that facilitate and deepen readers’ understanding, and demonstrates how the R package VineCopula can be used to explore and build statistical dependence models from scratch. In closing, the book provides insights into recent developments and open research questions in vine copula based modeling. The book is intended for students as well as statisticians, data analysts and any other quantitatively oriented researchers who are new to the field of vine copulas. Accordingly, it provides the necessary background in multivariate statistics and copula theory for exploratory data tools, so that readers only need a basic grasp of statistics and probability.

Download or read book Principles and Methods for Data Science written by and published by Elsevier. This book was released on 2020-05-28 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principles and Methods for Data Science, Volume 43 in the Handbook of Statistics series, highlights new advances in the field, with this updated volume presenting interesting and timely topics, including Competing risks, aims and methods, Data analysis and mining of microbial community dynamics, Support Vector Machines, a robust prediction method with applications in bioinformatics, Bayesian Model Selection for Data with High Dimension, High dimensional statistical inference: theoretical development to data analytics, Big data challenges in genomics, Analysis of microarray gene expression data using information theory and stochastic algorithm, Hybrid Models, Markov Chain Monte Carlo Methods: Theory and Practice, and more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Statistics series Updated release includes the latest information on Principles and Methods for Data Science

Download or read book Pattern Recognition and Image Analysis written by Jordi Vitria and published by Springer Science & Business Media. This book was released on 2011-06-01 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the refereed proceedings of the 5th Iberian Conference on Pattern Recognition and Image Analysis, IbPRIA 2011, held in Las Palmas de Gran Canaria, Spain, in June 2011. The 34 revised full papers and 58 revised poster papers presented were carefully reviewed and selected from 158 submissions. The papers are organized in topical sections on computer vision; image processing and analysis; medical applications; and pattern recognition.

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 Modern Statistical Methods for Health Research written by Yichuan Zhao and published by Springer Nature. This book was released on 2021-10-14 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together the voices of leading experts in the frontiers of biostatistics, biomedicine, and the health sciences to discuss the statistical procedures, useful methods, and novel applications in biostatistics research. It also includes discussions of potential future directions of biomedicine and new statistical developments for health research, with the intent of stimulating research and fostering the interactions of scholars across health research related disciplines. Topics covered include: Health data analysis and applications to EHR data Clinical trials, FDR, and applications in health science Big network analytics and its applications in GWAS Survival analysis and functional data analysis Graphical modelling in genomic studies The book will be valuable to data scientists and statisticians who are working in biomedicine and health, other practitioners in the health sciences, and graduate students and researchers in biostatistics and health.

Download or read book International Conference on Computational and Information Sciences ICCIS 2014 written by and published by DEStech Publications, Inc. This book was released on 2014-11-11 with total page 1356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 6th International Conference on Computational and Information Sciences (ICCIS2014) will be held in NanChong, China. The 6th International Conference on Computational and Information Sciences (ICCIS2014)aims at bringing researchers in the areas of computational and information sciences to exchange new ideas and to explore new ground. The goal of the conference is to push the application of modern computing technologies to science, engineering, and information technologies.Following the success of ICCIS2004,ICCIS2010 and ICCIS2011,ICCIS2012,ICCIS2013,ICCIS2014 conference will consist of invited keynote presentations and contributed presentations of latest developments in computational and information sciences. The 2014 International Conference on Computational and Information Sciences (ICCIS 2014), now in its sixth run, has become one of the premier conferences in this dynamic and exciting field. The goal of ICCIS is to catalyze the communications among various communities in computational and information sciences. ICCIS provides a venue for the participants to share their recent research and development, to seek for collaboration resources and opportunities, and to build professional networks.

Download or read book Statistics for High Dimensional Data written by Peter Bühlmann and published by Springer Science & Business Media. This book was released on 2011-06-08 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods’ great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.