Introduction to High-Dimensional Statistics

2021-08-25
Introduction to High-Dimensional Statistics

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  • Author: Christophe Giraud
  • Publisher: CRC Press
  • ISBN: 1000408353
  • Category : Computers
  • Languages : en
  • Pages : 410

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.

High-Dimensional Statistics

2019-02-21
High-Dimensional Statistics

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  • Author: Martin J. Wainwright
  • Publisher: Cambridge University Press
  • ISBN: 1108498027
  • Category : Business & Economics
  • Languages : en
  • Pages : 571

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

High-Dimensional Probability

2018-09-27
High-Dimensional Probability

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  • Author: Roman Vershynin
  • Publisher: Cambridge University Press
  • ISBN: 1108415199
  • Category : Business & Economics
  • Languages : en
  • Pages : 299

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

Statistics for High-Dimensional Data

2011-06-08
Statistics for High-Dimensional Data

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  • Author: Peter Bühlmann
  • Publisher: Springer Science & Business Media
  • ISBN: 364220192X
  • Category : Mathematics
  • Languages : en
  • Pages : 558

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.

Fundamentals of High-Dimensional Statistics

2021-11-16
Fundamentals of High-Dimensional Statistics

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  • Author: Johannes Lederer
  • Publisher: Springer Nature
  • ISBN: 3030737926
  • Category : Mathematics
  • Languages : en
  • Pages : 355

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.

High-Dimensional Data Analysis with Low-Dimensional Models

2022-01-13
High-Dimensional Data Analysis with Low-Dimensional Models

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  • Author: John Wright
  • Publisher: Cambridge University Press
  • ISBN: 1108805558
  • Category : Computers
  • Languages : en
  • Pages : 718

Connecting theory with practice, this systematic and rigorous introduction covers the fundamental principles, algorithms and applications of key mathematical models for high-dimensional data analysis. Comprehensive in its approach, it provides unified coverage of many different low-dimensional models and analytical techniques, including sparse and low-rank models, and both convex and non-convex formulations. Readers will learn how to develop efficient and scalable algorithms for solving real-world problems, supported by numerous examples and exercises throughout, and how to use the computational tools learnt in several application contexts. Applications presented include scientific imaging, communication, face recognition, 3D vision, and deep networks for classification. With code available online, this is an ideal textbook for senior and graduate students in computer science, data science, and electrical engineering, as well as for those taking courses on sparsity, low-dimensional structures, and high-dimensional data. Foreword by Emmanuel Candès.

Geometric Structure of High-Dimensional Data and Dimensionality Reduction

2012-04-28
Geometric Structure of High-Dimensional Data and Dimensionality Reduction

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  • Author: Jianzhong Wang
  • Publisher: Springer Science & Business Media
  • ISBN: 3642274978
  • Category : Computers
  • Languages : en
  • Pages : 356

"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.

Analysis of Multivariate and High-Dimensional Data

2014
Analysis of Multivariate and High-Dimensional Data

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  • Author: Inge Koch
  • Publisher: Cambridge University Press
  • ISBN: 0521887933
  • Category : Business & Economics
  • Languages : en
  • Pages : 531

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

Statistical Foundations of Data Science

2020-09-21
Statistical Foundations of Data Science

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  • Author: Jianqing Fan
  • Publisher: CRC Press
  • ISBN: 1466510854
  • Category : Mathematics
  • Languages : en
  • Pages : 752

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.

Statistical Analysis for High-Dimensional Data

2016-02-16
Statistical Analysis for High-Dimensional Data

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  • Author: Arnoldo Frigessi
  • Publisher: Springer
  • ISBN: 3319270990
  • Category : Mathematics
  • Languages : en
  • Pages : 306

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.