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Statistics - Statistical Theory and Methods | Statistics for High-Dimensional Data - Methods, Theory and Applications

Statistics for High-Dimensional Data

Methods, Theory and Applications

Bühlmann, Peter, van de Geer, Sara

2011, XVIII, 558 p.

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  • Contains the fundamentals of the recent research in a very timely area
  • Gives an overview of the area and adds many new insights
  • There is a unique mix of methodology, theory, algorithms and applications
  • The number of recent papers on the topic is huge
  • Is a welcome consolidation
  • Is an essential for the further development of theory and methods

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.

Content Level » Graduate

Keywords » L1-regularization - algorithms - oracle inequalities - sparsity - variable and feature selection

Related subjects » Statistical Theory and Methods - Theoretical Computer Science

Table of contents 

Introduction.- Lasso for linear models.- Generalized linear models and the Lasso.- The group Lasso.- Additive models and many smooth univariate functions.- Theory for the Lasso.- Variable selection with the Lasso.- Theory for l1/l2-penalty procedures.- Non-convex loss functions and l1-regularization.- Stable solutions.- P-values for linear models and beyond.- Boosting and greedy algorithms.- Graphical modeling.- Probability and moment inequalities.- Author Index.- Index.- References.- Problems at the end of each chapter.

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