Statistics For High Dimensional Data

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Statistics for High-Dimensional Data

Peter Bühlmann,Sara van de Geer
Statistics for High Dimensional Data Book PDF

Author : Peter Bühlmann,Sara van de Geer
Publisher : Springer Science & Business Media
Page : 558 pages
File Size : 48,5 Mb
Release : 2011-06-08
Category : Mathematics
ISBN : 9783642201929

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Statistics for High-Dimensional Data by Peter Bühlmann,Sara van de Geer Pdf

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.

High-Dimensional Statistics

Martin J. Wainwright
High Dimensional Statistics Book PDF

Author : Martin J. Wainwright
Publisher : Cambridge University Press
Page : 571 pages
File Size : 44,5 Mb
Release : 2019-02-21
Category : Business & Economics
ISBN : 9781108498029

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High-Dimensional Statistics by Martin J. Wainwright Pdf

A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.

Fundamentals of High-Dimensional Statistics

Johannes Lederer
Fundamentals of High Dimensional Statistics Book PDF

Author : Johannes Lederer
Publisher : Springer Nature
Page : 355 pages
File Size : 47,8 Mb
Release : 2021-11-16
Category : Mathematics
ISBN : 9783030737924

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Fundamentals of High-Dimensional Statistics by Johannes Lederer Pdf

This textbook provides a step-by-step introduction to the tools and principles of high-dimensional statistics. Each chapter is complemented by numerous exercises, many of them with detailed solutions, and computer labs in R that convey valuable practical insights. The book covers the theory and practice of high-dimensional linear regression, graphical models, and inference, ensuring readers have a smooth start in the field. It also offers suggestions for further reading. Given its scope, the textbook is intended for beginning graduate and advanced undergraduate students in statistics, biostatistics, and bioinformatics, though it will be equally useful to a broader audience.

Statistical Analysis for High-Dimensional Data

Arnoldo Frigessi,Peter Bühlmann,Ingrid Glad,Mette Langaas,Sylvia Richardson,Marina Vannucci
Statistical Analysis for High Dimensional Data Book PDF

Author : Arnoldo Frigessi,Peter Bühlmann,Ingrid Glad,Mette Langaas,Sylvia Richardson,Marina Vannucci
Publisher : Springer
Page : 306 pages
File Size : 49,8 Mb
Release : 2016-02-16
Category : Mathematics
ISBN : 9783319270999

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Statistical Analysis for High-Dimensional Data by Arnoldo Frigessi,Peter Bühlmann,Ingrid Glad,Mette Langaas,Sylvia Richardson,Marina Vannucci Pdf

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.

Introduction to High-Dimensional Statistics

Christophe Giraud
Introduction to High Dimensional Statistics Book PDF

Author : Christophe Giraud
Publisher : CRC Press
Page : 410 pages
File Size : 53,6 Mb
Release : 2021-08-25
Category : Computers
ISBN : 9781000408355

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Introduction to High-Dimensional Statistics by Christophe Giraud Pdf

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

Inge Koch
Analysis of Multivariate and High Dimensional Data Book PDF

Author : Inge Koch
Publisher : Cambridge University Press
Page : 531 pages
File Size : 41,9 Mb
Release : 2014
Category : Business & Economics
ISBN : 9780521887939

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Analysis of Multivariate and High-Dimensional Data by Inge Koch Pdf

This modern approach integrates classical and contemporary methods, fusing theory and practice and bridging the gap to statistical learning.

High-Dimensional Probability

Roman Vershynin
High Dimensional Probability Book PDF

Author : Roman Vershynin
Publisher : Cambridge University Press
Page : 299 pages
File Size : 52,6 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9781108415194

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High-Dimensional Probability by Roman Vershynin Pdf

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

High-Dimensional Data Analysis with Low-Dimensional Models

John Wright,Yi Ma
High Dimensional Data Analysis with Low Dimensional Models Book PDF

Author : John Wright,Yi Ma
Publisher : Cambridge University Press
Page : 717 pages
File Size : 41,8 Mb
Release : 2022-01-13
Category : Computers
ISBN : 9781108489737

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High-Dimensional Data Analysis with Low-Dimensional Models by John Wright,Yi Ma Pdf

Connects fundamental mathematical theory with real-world problems, through efficient and scalable optimization algorithms.

Geometric Structure of High-Dimensional Data and Dimensionality Reduction

Jianzhong Wang
Geometric Structure of High Dimensional Data and Dimensionality Reduction Book PDF

Author : Jianzhong Wang
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 46,9 Mb
Release : 2012-04-28
Category : Computers
ISBN : 9783642274978

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Geometric Structure of High-Dimensional Data and Dimensionality Reduction by Jianzhong Wang Pdf

"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.

High-dimensional Data Analysis

Tianwen Tony Cai,Xiaotong Shen
High dimensional Data Analysis Book PDF

Author : Tianwen Tony Cai,Xiaotong Shen
Publisher : World Scientific Publishing Company Incorporated
Page : 307 pages
File Size : 42,6 Mb
Release : 2011
Category : Mathematics
ISBN : 981432485X

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High-dimensional Data Analysis by Tianwen Tony Cai,Xiaotong Shen Pdf

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.

Clustering High--Dimensional Data

Francesco Masulli,Alfredo Petrosino,Stefano Rovetta
Clustering High Dimensional Data Book PDF

Author : Francesco Masulli,Alfredo Petrosino,Stefano Rovetta
Publisher : Springer
Page : 149 pages
File Size : 45,8 Mb
Release : 2015-11-24
Category : Computers
ISBN : 9783662485774

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Clustering High--Dimensional Data by Francesco Masulli,Alfredo Petrosino,Stefano Rovetta Pdf

This book constitutes the proceedings of the International Workshop on Clustering High-Dimensional Data, CHDD 2012, held in Naples, Italy, in May 2012. The 9 papers presented in this volume were carefully reviewed and selected from 15 submissions. They deal with the general subject and issues of high-dimensional data clustering; present examples of techniques used to find and investigate clusters in high dimensionality; and the most common approach to tackle dimensionality problems, namely, dimensionality reduction and its application in clustering.

Multivariate Statistics

Yasunori Fujikoshi,Vladimir V. Ulyanov,Ryoichi Shimizu
Multivariate Statistics Book PDF

Author : Yasunori Fujikoshi,Vladimir V. Ulyanov,Ryoichi Shimizu
Publisher : John Wiley & Sons
Page : 564 pages
File Size : 43,8 Mb
Release : 2011-08-15
Category : Mathematics
ISBN : 9780470539866

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Multivariate Statistics by Yasunori Fujikoshi,Vladimir V. Ulyanov,Ryoichi Shimizu Pdf

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.

High-Dimensional Covariance Estimation

Mohsen Pourahmadi
High Dimensional Covariance Estimation Book PDF

Author : Mohsen Pourahmadi
Publisher : John Wiley & Sons
Page : 204 pages
File Size : 50,8 Mb
Release : 2013-06-24
Category : Mathematics
ISBN : 9781118034293

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High-Dimensional Covariance Estimation by Mohsen Pourahmadi Pdf

Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.

Large Sample Covariance Matrices and High-Dimensional Data Analysis

Jianfeng Yao,Shurong Zheng,Zhidong Bai
Large Sample Covariance Matrices and High Dimensional Data Analysis Book PDF

Author : Jianfeng Yao,Shurong Zheng,Zhidong Bai
Publisher : Cambridge University Press
Page : 0 pages
File Size : 50,8 Mb
Release : 2015-03-26
Category : Mathematics
ISBN : 1107065178

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Large Sample Covariance Matrices and High-Dimensional Data Analysis by Jianfeng Yao,Shurong Zheng,Zhidong Bai Pdf

High-dimensional data appear in many fields, and their analysis has become increasingly important in modern statistics. However, it has long been observed that several well-known methods in multivariate analysis become inefficient, or even misleading, when the data dimension p is larger than, say, several tens. A seminal example is the well-known inefficiency of Hotelling's T2-test in such cases. This example shows that classical large sample limits may no longer hold for high-dimensional data; statisticians must seek new limiting theorems in these instances. Thus, the theory of random matrices (RMT) serves as a much-needed and welcome alternative framework. Based on the authors' own research, this book provides a first-hand introduction to new high-dimensional statistical methods derived from RMT. The book begins with a detailed introduction to useful tools from RMT, and then presents a series of high-dimensional problems with solutions provided by RMT methods.

Statistical Inference from High Dimensional Data

Carlos Fernandez-Lozano
Statistical Inference from High Dimensional Data Book PDF

Author : Carlos Fernandez-Lozano
Publisher : MDPI
Page : 314 pages
File Size : 52,8 Mb
Release : 2021-04-28
Category : Science
ISBN : 9783036509440

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Statistical Inference from High Dimensional Data by Carlos Fernandez-Lozano Pdf

• 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