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Statistics for High-Dimensional Data

Methods, Theory and Applications

By Peter Bühlmann , Sara van de Geer

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This valuable compendium of statistical methods features a unique combination of methodology, theory, algorithms and applications. It covers recently developed approaches to handling large and complex data sets, including the Lasso and boosting methods.

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  • ISBN13: 978-3-6422-0191-2
  • 573 Pages
  • Publication Date: June 8, 2011
  • Available eBook Formats: PDF
Full Description
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.
Table of Contents

Table of Contents

  1. Introduction.
  2. Lasso for linear models.
  3. Generalized linear models and the Lasso.
  4. The group Lasso.
  5. Additive models and many smooth univariate functions.
  6. Theory for the Lasso.
  7. Variable selection with the Lasso.
  8. Theory for l1/l2
  9. penalty procedures.
  10. Non
  11. convex loss functions and l1
  12. regularization.
  13. Stable solutions.
  14. P
  15. values for linear models and beyond.
  16. Boosting and greedy algorithms.
  17. Graphical modeling.
  18. Probability and moment inequalities.
  19. Author Index.
  20. Index.
  21. References.
  22. Problems at the end of each chapter.

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