Introduction to High-Dimensional Statistics
- ISBN-10
- 1000408353
- ISBN-13
- 9781000408355
- Category
- Computers
- Pages
- 364
- Language
- English
- Published
- 2021-08-26
- Publisher
- CRC Press
- Author
- Christophe Giraud
Description
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.
Get the book
Other editions
Similar books
-
High-Dimensional Statistics: A Non-Asymptotic Viewpoint
By Martin J. WainwrightPROBABILISTIC MATHEMATICS Editorial Board Z. Ghahramani (Department of Engineering, University of Cambridge) R. Gill (Mathematical ... Shurong Zheng and Zhidong Bai Mathematical Foundations of Infinite-Dimensional Statistical Models, ...
-
High-Dimensional Probability: An Introduction with Applications in Data Science
By Roman VershyninHigh-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions.
-
Statistics for High-Dimensional Data: Methods, Theory and Applications
By Peter Bühlmann, Sara van de Geer(S)ts. Here, we applied the 6-uniform irrepresentable condition, and the condition ||6 || < L. Thus 1–6Ls –%t. XI.'(S)ts. Because 1–6L > 0 and t! XI.'(S)ts > 0, this implies that A ≤ 0, and in fact that (1–6L) < –Ws/A#,(X11(S)), ...
-
High-dimensional Statistics
By Johannes LedererThis book provides clear expositions, motivational introductions to each chapter, rigorous step-by-step proofs, and comprehensive exercise sets with fully worked out solutions. These features make this book ideal for graduate level courses.
-
Fundamentals of High-Dimensional Statistics: With Exercises and R Labs
By Johannes LedererThe 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.
-
High-Dimensional Data Analysis with Low-Dimensional Models: Principles, Computation, and Applications
By John Wright, Yi MaWith 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 ...
-
High-Dimensional Statistics: A Non-Asymptotic Viewpoint
By Martin J. WainwrightRaskutti, G., Wainwright, M. J., and Yu, B. 2010. Restricted eigenvalue conditions for correlated Gaussian designs. Journal of Machine Learning Research, 11(August), 2241–2259. Raskutti, G., Wainwright, M. J., and Yu, B. 2011.
-
Geometric Structure of High-Dimensional Data and Dimensionality Reduction
By Jianzhong WangMATLAB 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.
-
Statistical Foundations of Data Science
By Runze Li, Cun-Hui Zhang, Jianqing FanIt 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.
-
Large Sample Covariance Matrices and High-Dimensional Data Analysis
By Zhidong Bai, Jianfeng Yao, Shurong ZhengBased on the authors' own research, this book provides a first-hand introduction to new high-dimensional statistical methods derived from RMT.