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.
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 ...
(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)), ...
This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks.
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.
This modern approach integrates classical and contemporary methods, fusing theory and practice and bridging the gap to statistical learning.
If F is countable or separable, required in the definition of i. then sup f,g∈B i |f − g| is measurable, and the asterisk ... which means that the Gaussian exponential inequality is not available, and we must use Bernstein's instead.
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
This book presents some of the most important modeling and prediction techniques, along with relevant applications.
PROBABILISTIC 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, ...
In particular, the material in this text directly supports the mathematical analysis and design of old, new, and not-yet-invented nonlinear high-dimensional machine learning algorithms.