Statistics for High-Dimensional Data
Methods, Theory and Applications
(Sprache: Englisch)
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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Produktinformationen zu „Statistics for High-Dimensional Data “
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.
Klappentext zu „Statistics for High-Dimensional Data “
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.
Inhaltsverzeichnis zu „Statistics for High-Dimensional Data “
From the 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.
Autoren-Porträt von Peter Bühlmann, Sara van de Geer
Peter Bühlmann and Sara van de Geer are professors in statistics at the ETH Zürich. Their recent scientific contributions are in high-dimensional statistical inference and statistical learning. They are both member of various editorial boards, fellows of the Institute of Mathematical Statistics (IMS) and have been elected as IMS Medallion lecturers.
Bibliographische Angaben
- Autoren: Peter Bühlmann , Sara van de Geer
- 2011, 2011, XVIII, 558 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3642201911
- ISBN-13: 9783642201912
- Erscheinungsdatum: 28.06.2011
Sprache:
Englisch
Rezension zu „Statistics for High-Dimensional Data “
From the reviews:"This book is a complete study of l1-penalization based statistical methods for high-dimensional data ... . Definitely, this book is useful. ... its strong level in mathematics makes it more suitable to researchers and graduate students who already have a strong background in statistics. ... it gives the state-of-the-art of the theory, and therefore can be used for an advanced course on the topic. ... the last part of the book is an exciting introduction to new research perspectives provided by l1-penalized methods." (Pierre Alquier, Mathematical Reviews, Issue 2012 e)
"All Classical Statisticians interested in the very popular but a bit old methodologies like the Lasso (Tibshirani, 1996), its modifications like adaptive Lasso (Zou, 2006), and their theory, computational algorithms, applications to bioinformatics and other high dimensional applications. All such researchers would find this book worth buying. It is written by two outstanding theoreticians with flair for clear writing and excellent applications. ... theory depends a lot on new concentration inequalities coming from the French probabilists. The book has good collection of these, with proofs." (Jayanta K. Ghosh, International Statistical Review, Vol. 80 (3), 2012)
Pressezitat
From the reviews:"This book is a complete study of 1-penalization based statistical methods for high-dimensional data ... . Definitely, this book is useful. ... its strong level in mathematics makes it more suitable to researchers and graduate students who already have a strong background in statistics. ... it gives the state-of-the-art of the theory, and therefore can be used for an advanced course on the topic. ... the last part of the book is an exciting introduction to new research perspectives provided by 1-penalized methods." (Pierre Alquier, Mathematical Reviews, Issue 2012 e)
"All Classical Statisticians interested in the very popular but a bit old methodologies like the Lasso (Tibshirani, 1996), its modifications like adaptive Lasso (Zou, 2006), and their theory, computational algorithms, applications to bioinformatics and other high dimensional applications. All such researchers would find this book worth buying. It is written by two outstanding theoreticians with flair for clear writing and excellent applications. ... theory depends a lot on new concentration inequalities coming from the French probabilists. The book has good collection of these, with proofs." (Jayanta K. Ghosh, International Statistical Review, Vol. 80 (3), 2012)
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