Statistical Analysis Of High Dimensional Data

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Statistics for High-Dimensional Data

Statistics for High-Dimensional Data
  • Author : Peter Bühlmann,Sara van de Geer
  • Publisher : Springer Science & Business Media
  • Release Date : 2011-06-08
  • Total pages : 558
  • ISBN : 9783642201929
  • File Size : 43,7 Mb
  • Total Download : 658
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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.

Statistical Analysis for High-Dimensional Data

Statistical Analysis for High-Dimensional Data
  • Author : Arnoldo Frigessi,Peter Bühlmann,Ingrid Glad,Mette Langaas,Sylvia Richardson,Marina Vannucci
  • Publisher : Springer
  • Release Date : 2016-02-16
  • Total pages : 306
  • ISBN : 9783319270999
  • File Size : 40,6 Mb
  • Total Download : 585
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This book features research contributions from The Abel Symposium on Statistical Analysis for High Dimensional Data, held in Nyvågar, Lofoten, Norway, in May 2014. The focus of the symposium was on statistical and machine learning methodologies specifically developed for inference in “big data” situations, with particular reference to genomic applications. The contributors, who are among the most prominent researchers on the theory of statistics for high dimensional inference, present new theories and methods, as well as challenging applications and computational solutions. Specific themes include, among others, variable selection and screening, penalised regression, sparsity, thresholding, low dimensional structures, computational challenges, non-convex situations, learning graphical models, sparse covariance and precision matrices, semi- and non-parametric formulations, multiple testing, classification, factor models, clustering, and preselection. Highlighting cutting-edge research and casting light on future research directions, the contributions will benefit graduate students and researchers in computational biology, statistics and the machine learning community.

High-Dimensional Statistics

High-Dimensional Statistics
  • Author : Martin J. Wainwright
  • Publisher : Cambridge University Press
  • Release Date : 2019-02-21
  • Total pages : 571
  • ISBN : 9781108498029
  • File Size : 23,5 Mb
  • Total Download : 171
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A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.

Introduction to High-Dimensional Statistics

Introduction to High-Dimensional Statistics
  • Author : Christophe Giraud
  • Publisher : CRC Press
  • Release Date : 2021-08-25
  • Total pages : 364
  • ISBN : 9781000408324
  • File Size : 34,9 Mb
  • Total Download : 810
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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.

Analysis of Multivariate and High-Dimensional Data

Analysis of Multivariate and High-Dimensional Data
  • Author : Inge Koch
  • Publisher : Cambridge University Press
  • Release Date : 2013-12-02
  • Total pages : 229
  • ISBN : 9781107511859
  • File Size : 21,6 Mb
  • Total Download : 183
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'Big data' poses challenges that require both classical multivariate methods and contemporary techniques from machine learning and engineering. This modern text equips you for the new world - integrating the old and the new, fusing theory and practice and bridging the gap to statistical learning. The theoretical framework includes formal statements that set out clearly the guaranteed 'safe operating zone' for the methods and allow you to assess whether data is in the zone, or near enough. Extensive examples showcase the strengths and limitations of different methods with small classical data, data from medicine, biology, marketing and finance, high-dimensional data from bioinformatics, functional data from proteomics, and simulated data. High-dimension low-sample-size data gets special attention. Several data sets are revisited repeatedly to allow comparison of methods. Generous use of colour, algorithms, Matlab code, and problem sets complete the package. Suitable for master's/graduate students in statistics and researchers in data-rich disciplines.

High-Dimensional Data Analysis with Low-Dimensional Models

High-Dimensional Data Analysis with Low-Dimensional Models
  • Author : John Wright,Yi Ma
  • Publisher : Cambridge University Press
  • Release Date : 2022-01-13
  • Total pages : 717
  • ISBN : 9781108489737
  • File Size : 10,5 Mb
  • Total Download : 329
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Connects fundamental mathematical theory with real-world problems, through efficient and scalable optimization algorithms.

High-dimensional Data Analysis

High-dimensional Data Analysis
  • Author : Tianwen Tony Cai,Xiaotong Shen
  • Publisher : World Scientific Publishing Company Incorporated
  • Release Date : 2011
  • Total pages : 307
  • ISBN : 981432485X
  • File Size : 49,8 Mb
  • Total Download : 722
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Over the last few years, significant developments have been taking place in high-dimensional data analysis, driven primarily by a wide range of applications in many fields such as genomics and signal processing. In particular, substantial advances have been made in the areas of feature selection, covariance estimation, classification and regression. This book intends to examine important issues arising from high-dimensional data analysis to explore key ideas for statistical inference and prediction. It is structured around topics on multiple hypothesis testing, feature selection, regression, classification, dimension reduction, as well as applications in survival analysis and biomedical research. The book will appeal to graduate students and new researchers interested in the plethora of opportunities available in high-dimensional data analysis.

High-Dimensional Probability

High-Dimensional Probability
  • Author : Roman Vershynin
  • Publisher : Cambridge University Press
  • Release Date : 2018-09-27
  • Total pages : 299
  • ISBN : 9781108415194
  • File Size : 23,9 Mb
  • Total Download : 594
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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

High-Dimensional Data Analysis in Cancer Research

High-Dimensional Data Analysis in Cancer Research
  • Author : Xiaochun Li,Ronghui Xu
  • Publisher : Springer Science & Business Media
  • Release Date : 2008-12-19
  • Total pages : 392
  • ISBN : 9780387697659
  • File Size : 29,7 Mb
  • Total Download : 371
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Multivariate analysis is a mainstay of statistical tools in the analysis of biomedical data. It concerns with associating data matrices of n rows by p columns, with rows representing samples (or patients) and columns attributes of samples, to some response variables, e.g., patients outcome. Classically, the sample size n is much larger than p, the number of variables. The properties of statistical models have been mostly discussed under the assumption of fixed p and infinite n. The advance of biological sciences and technologies has revolutionized the process of investigations of cancer. The biomedical data collection has become more automatic and more extensive. We are in the era of p as a large fraction of n, and even much larger than n. Take proteomics as an example. Although proteomic techniques have been researched and developed for many decades to identify proteins or peptides uniquely associated with a given disease state, until recently this has been mostly a laborious process, carried out one protein at a time. The advent of high throughput proteome-wide technologies such as liquid chromatography-tandem mass spectroscopy make it possible to generate proteomic signatures that facilitate rapid development of new strategies for proteomics-based detection of disease. This poses new challenges and calls for scalable solutions to the analysis of such high dimensional data. In this volume, we will present the systematic and analytical approaches and strategies from both biostatistics and bioinformatics to the analysis of correlated and high-dimensional data.

Multivariate Statistics

Multivariate Statistics
  • Author : Yasunori Fujikoshi,Vladimir V. Ulyanov,Ryoichi Shimizu
  • Publisher : John Wiley & Sons
  • Release Date : 2011-08-15
  • Total pages : 512
  • ISBN : 9780470539866
  • File Size : 39,8 Mb
  • Total Download : 200
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A comprehensive examination of high-dimensional analysis of multivariate methods and their real-world applications Multivariate Statistics: High-Dimensional and Large-Sample Approximations is the first book of its kind to explore how classical multivariate methods can be revised and used in place of conventional statistical tools. Written by prominent researchers in the field, the book focuses on high-dimensional and large-scale approximations and details the many basic multivariate methods used to achieve high levels of accuracy. The authors begin with a fundamental presentation of the basic tools and exact distributional results of multivariate statistics, and, in addition, the derivations of most distributional results are provided. Statistical methods for high-dimensional data, such as curve data, spectra, images, and DNA microarrays, are discussed. Bootstrap approximations from a methodological point of view, theoretical accuracies in MANOVA tests, and model selection criteria are also presented. Subsequent chapters feature additional topical coverage including: High-dimensional approximations of various statistics High-dimensional statistical methods Approximations with computable error bound Selection of variables based on model selection approach Statistics with error bounds and their appearance in discriminant analysis, growth curve models, generalized linear models, profile analysis, and multiple comparison Each chapter provides real-world applications and thorough analyses of the real data. In addition, approximation formulas found throughout the book are a useful tool for both practical and theoretical statisticians, and basic results on exact distributions in multivariate analysis are included in a comprehensive, yet accessible, format. Multivariate Statistics is an excellent book for courses on probability theory in statistics at the graduate level. It is also an essential reference for both practical and theoretical statisticians who are interested in multivariate analysis and who would benefit from learning the applications of analytical probabilistic methods in statistics.

Big and Complex Data Analysis

Big and Complex Data Analysis
  • Author : S. Ejaz Ahmed
  • Publisher : Springer
  • Release Date : 2017-03-21
  • Total pages : 386
  • ISBN : 9783319415734
  • File Size : 12,9 Mb
  • Total Download : 845
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This volume conveys some of the surprises, puzzles and success stories in high-dimensional and complex data analysis and related fields. Its peer-reviewed contributions showcase recent advances in variable selection, estimation and prediction strategies for a host of useful models, as well as essential new developments in the field. The continued and rapid advancement of modern technology now allows scientists to collect data of increasingly unprecedented size and complexity. Examples include epigenomic data, genomic data, proteomic data, high-resolution image data, high-frequency financial data, functional and longitudinal data, and network data. Simultaneous variable selection and estimation is one of the key statistical problems involved in analyzing such big and complex data. The purpose of this book is to stimulate research and foster interaction between researchers in the area of high-dimensional data analysis. More concretely, its goals are to: 1) highlight and expand the breadth of existing methods in big data and high-dimensional data analysis and their potential for the advancement of both the mathematical and statistical sciences; 2) identify important directions for future research in the theory of regularization methods, in algorithmic development, and in methodologies for different application areas; and 3) facilitate collaboration between theoretical and subject-specific researchers.

High-dimensional Microarray Data Analysis

High-dimensional Microarray Data Analysis
  • Author : Shuichi Shinmura
  • Publisher : Springer
  • Release Date : 2019-05-24
  • Total pages : 419
  • ISBN : 9811359970
  • File Size : 51,6 Mb
  • Total Download : 221
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This book shows how to decompose high-dimensional microarrays into small subspaces (Small Matryoshkas, SMs), statistically analyze them, and perform cancer gene diagnosis. The information is useful for genetic experts, anyone who analyzes genetic data, and students to use as practical textbooks. Discriminant analysis is the best approach for microarray consisting of normal and cancer classes. Microarrays are linearly separable data (LSD, Fact 3). However, because most linear discriminant function (LDF) cannot discriminate LSD theoretically and error rates are high, no one had discovered Fact 3 until now. Hard-margin SVM (H-SVM) and Revised IP-OLDF (RIP) can find Fact3 easily. LSD has the Matryoshka structure and is easily decomposed into many SMs (Fact 4). Because all SMs are small samples and LSD, statistical methods analyze SMs easily. However, useful results cannot be obtained. On the other hand, H-SVM and RIP can discriminate two classes in SM entirely. RatioSV is the ratio of SV distance and discriminant range. The maximum RatioSVs of six microarrays is over 11.67%. This fact shows that SV separates two classes by window width (11.67%). Such easy discrimination has been unresolved since 1970. The reason is revealed by facts presented here, so this book can be read and enjoyed like a mystery novel. Many studies point out that it is difficult to separate signal and noise in a high-dimensional gene space. However, the definition of the signal is not clear. Convincing evidence is presented that LSD is a signal. Statistical analysis of the genes contained in the SM cannot provide useful information, but it shows that the discriminant score (DS) discriminated by RIP or H-SVM is easily LSD. For example, the Alon microarray has 2,000 genes which can be divided into 66 SMs. If 66 DSs are used as variables, the result is a 66-dimensional data. These signal data can be analyzed to find malignancy indicators by principal component analysis and cluster analysis.

Computational Intelligence and Healthcare Informatics

Computational Intelligence and Healthcare Informatics
  • Author : Om Prakash Jena,Alok Ranjan Tripathy,Ahmed A. Elngar,Zdzislaw Polkowski
  • Publisher : John Wiley & Sons
  • Release Date : 2021-10-19
  • Total pages : 434
  • ISBN : 9781119818687
  • File Size : 33,9 Mb
  • Total Download : 167
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COMPUTATIONAL INTELLIGENCE and HEALTHCARE INFORMATICS The book provides the state-of-the-art innovation, research, design, and implements methodological and algorithmic solutions to data processing problems, designing and analysing evolving trends in health informatics, intelligent disease prediction, and computer-aided diagnosis. Computational intelligence (CI) refers to the ability of computers to accomplish tasks that are normally completed by intelligent beings such as humans and animals. With the rapid advance of technology, artificial intelligence (AI) techniques are being effectively used in the fields of health to improve the efficiency of treatments, avoid the risk of false diagnoses, make therapeutic decisions, and predict the outcome in many clinical scenarios. Modern health treatments are faced with the challenge of acquiring, analyzing and applying the large amount of knowledge necessary to solve complex problems. Computational intelligence in healthcare mainly uses computer techniques to perform clinical diagnoses and suggest treatments. In the present scenario of computing, CI tools present adaptive mechanisms that permit the understanding of data in difficult and changing environments. The desired results of CI technologies profit medical fields by assembling patients with the same types of diseases or fitness problems so that healthcare facilities can provide effectual treatments. This book starts with the fundamentals of computer intelligence and the techniques and procedures associated with it. Contained in this book are state-of-the-art methods of computational intelligence and other allied techniques used in the healthcare system, as well as advances in different CI methods that will confront the problem of effective data analysis and storage faced by healthcare institutions. The objective of this book is to provide researchers with a platform encompassing state-of-the-art innovations; research and design; implementation of methodological and algorithmic solutions to data processing problems; and the design and analysis of evolving trends in health informatics, intelligent disease prediction and computer-aided diagnosis. Audience The book is of interest to artificial intelligence and biomedical scientists, researchers, engineers and students in various settings such as pharmaceutical & biotechnology companies, virtual assistants developing companies, medical imaging & diagnostics centers, wearable device designers, healthcare assistance robot manufacturers, precision medicine testers, hospital management, and researchers working in healthcare system.

Statistical Inference from High Dimensional Data

Statistical Inference from High Dimensional Data
  • Author : Carlos Fernandez-Lozano
  • Publisher : MDPI
  • Release Date : 2021-04-28
  • Total pages : 314
  • ISBN : 9783036509440
  • File Size : 50,8 Mb
  • Total Download : 897
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• Real-world problems can be high-dimensional, complex, and noisy • More data does not imply more information • Different approaches deal with the so-called curse of dimensionality to reduce irrelevant information • A process with multidimensional information is not necessarily easy to interpret nor process • In some real-world applications, the number of elements of a class is clearly lower than the other. The models tend to assume that the importance of the analysis belongs to the majority class and this is not usually the truth • The analysis of complex diseases such as cancer are focused on more-than-one dimensional omic data • The increasing amount of data thanks to the reduction of cost of the high-throughput experiments opens up a new era for integrative data-driven approaches • Entropy-based approaches are of interest to reduce the dimensionality of high-dimensional data

Analyzing High-Dimensional Gene Expression and DNA Methylation Data with R

Analyzing High-Dimensional Gene Expression and DNA Methylation Data with R
  • Author : Hongmei Zhang
  • Publisher : CRC Press
  • Release Date : 2020-05-14
  • Total pages : 200
  • ISBN : 9781498772600
  • File Size : 32,9 Mb
  • Total Download : 379
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Analyzing high-dimensional gene expression and DNA methylation data with R is the first practical book that shows a ``pipeline" of analytical methods with concrete examples starting from raw gene expression and DNA methylation data at the genome scale. Methods on quality control, data pre-processing, data mining, and further assessments are presented in the book, and R programs based on simulated data and real data are included. Codes with example data are all reproducible. Features: • Provides a sequence of analytical tools for genome-scale gene expression data and DNA methylation data, starting from quality control and pre-processing of raw genome-scale data. • Organized by a parallel presentation with explanation on statistical methods and corresponding R packages/functions in quality control, pre-processing, and data analyses (e.g., clustering and networks). • Includes source codes with simulated and real data to reproduce the results. Readers are expected to gain the ability to independently analyze genome-scaled expression and methylation data and detect potential biomarkers. This book is ideal for students majoring in statistics, biostatistics, and bioinformatics and researchers with an interest in high dimensional genetic and epigenetic studies.

Geometric Structure of High-Dimensional Data and Dimensionality Reduction

Geometric Structure of High-Dimensional Data and Dimensionality Reduction
  • Author : Jianzhong Wang
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-04-28
  • Total pages : 356
  • ISBN : 9783642274978
  • File Size : 50,7 Mb
  • Total Download : 722
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"Geometric Structure of High-Dimensional Data and Dimensionality Reduction" adopts data geometry as a framework to address various methods of dimensionality reduction. In addition to the introduction to well-known linear methods, the book moreover stresses the recently developed nonlinear methods and introduces the applications of dimensionality reduction in many areas, such as face recognition, image segmentation, data classification, data visualization, and hyperspectral imagery data analysis. Numerous tables and graphs are included to illustrate the ideas, effects, and shortcomings of the methods. MATLAB code of all dimensionality reduction algorithms is provided to aid the readers with the implementations on computers. The book will be useful for mathematicians, statisticians, computer scientists, and data analysts. It is also a valuable handbook for other practitioners who have a basic background in mathematics, statistics and/or computer algorithms, like internet search engine designers, physicists, geologists, electronic engineers, and economists. Jianzhong Wang is a Professor of Mathematics at Sam Houston State University, U.S.A.

Statistical Foundations of Data Science

Statistical Foundations of Data Science
  • Author : Jianqing Fan,Runze Li,Cun-Hui Zhang,Hui Zou
  • Publisher : CRC Press
  • Release Date : 2020-09-21
  • Total pages : 752
  • ISBN : 9781466510852
  • File Size : 43,5 Mb
  • Total Download : 468
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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.

High-dimensional Microarray Data Analysis

High-dimensional Microarray Data Analysis
  • Author : Shuichi Shinmura
  • Publisher : Springer
  • Release Date : 2019-05-14
  • Total pages : 419
  • ISBN : 9789811359989
  • File Size : 21,8 Mb
  • Total Download : 476
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This book shows how to decompose high-dimensional microarrays into small subspaces (Small Matryoshkas, SMs), statistically analyze them, and perform cancer gene diagnosis. The information is useful for genetic experts, anyone who analyzes genetic data, and students to use as practical textbooks. Discriminant analysis is the best approach for microarray consisting of normal and cancer classes. Microarrays are linearly separable data (LSD, Fact 3). However, because most linear discriminant function (LDF) cannot discriminate LSD theoretically and error rates are high, no one had discovered Fact 3 until now. Hard-margin SVM (H-SVM) and Revised IP-OLDF (RIP) can find Fact3 easily. LSD has the Matryoshka structure and is easily decomposed into many SMs (Fact 4). Because all SMs are small samples and LSD, statistical methods analyze SMs easily. However, useful results cannot be obtained. On the other hand, H-SVM and RIP can discriminate two classes in SM entirely. RatioSV is the ratio of SV distance and discriminant range. The maximum RatioSVs of six microarrays is over 11.67%. This fact shows that SV separates two classes by window width (11.67%). Such easy discrimination has been unresolved since 1970. The reason is revealed by facts presented here, so this book can be read and enjoyed like a mystery novel. Many studies point out that it is difficult to separate signal and noise in a high-dimensional gene space. However, the definition of the signal is not clear. Convincing evidence is presented that LSD is a signal. Statistical analysis of the genes contained in the SM cannot provide useful information, but it shows that the discriminant score (DS) discriminated by RIP or H-SVM is easily LSD. For example, the Alon microarray has 2,000 genes which can be divided into 66 SMs. If 66 DSs are used as variables, the result is a 66-dimensional data. These signal data can be analyzed to find malignancy indicators by principal component analysis and cluster analysis.

Applied Biclustering Methods for Big and High-Dimensional Data Using R

Applied Biclustering Methods for Big and High-Dimensional Data Using R
  • Author : Adetayo Kasim,Ziv Shkedy,Sebastian Kaiser,Sepp Hochreiter,Willem Talloen
  • Publisher : CRC Press
  • Release Date : 2016-10-03
  • Total pages : 407
  • ISBN : 9781482208245
  • File Size : 52,9 Mb
  • Total Download : 667
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Proven Methods for Big Data Analysis As big data has become standard in many application areas, challenges have arisen related to methodology and software development, including how to discover meaningful patterns in the vast amounts of data. Addressing these problems, Applied Biclustering Methods for Big and High-Dimensional Data Using R shows how to apply biclustering methods to find local patterns in a big data matrix. The book presents an overview of data analysis using biclustering methods from a practical point of view. Real case studies in drug discovery, genetics, marketing research, biology, toxicity, and sports illustrate the use of several biclustering methods. References to technical details of the methods are provided for readers who wish to investigate the full theoretical background. All the methods are accompanied with R examples that show how to conduct the analyses. The examples, software, and other materials are available on a supplementary website.

Statistical Analysis for High-Dimensional Data

Statistical Analysis for High-Dimensional Data
  • Author : Arnoldo Frigessi,Peter Bühlmann,Ingrid Glad,Mette Langaas,Sylvia Richardson,Marina Vannucci
  • Publisher : Springer
  • Release Date : 2018-03-30
  • Total pages : 306
  • ISBN : 3319800736
  • File Size : 42,8 Mb
  • Total Download : 323
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This book features research contributions from The Abel Symposium on Statistical Analysis for High Dimensional Data, held in Nyvågar, Lofoten, Norway, in May 2014. The focus of the symposium was on statistical and machine learning methodologies specifically developed for inference in “big data” situations, with particular reference to genomic applications. The contributors, who are among the most prominent researchers on the theory of statistics for high dimensional inference, present new theories and methods, as well as challenging applications and computational solutions. Specific themes include, among others, variable selection and screening, penalised regression, sparsity, thresholding, low dimensional structures, computational challenges, non-convex situations, learning graphical models, sparse covariance and precision matrices, semi- and non-parametric formulations, multiple testing, classification, factor models, clustering, and preselection. Highlighting cutting-edge research and casting light on future research directions, the contributions will benefit graduate students and researchers in computational biology, statistics and the machine learning community.

Geometric and Topological Inference

Geometric and Topological Inference
  • Author : Jean-Daniel Boissonnat,Frédéric Chazal,Mariette Yvinec
  • Publisher : Cambridge University Press
  • Release Date : 2018-09-27
  • Total pages : 247
  • ISBN : 9781108419390
  • File Size : 53,8 Mb
  • Total Download : 642
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A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.