Synopses & Reviews
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, such as the Lasso and boosting methods. It also provides the mathematical theory behind them, proving their great potential in a large number of settings. Both the methods and theory are then illustrated with real data examples.
Review
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)
Review
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)
Synopsis
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.
Synopsis
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.
About the Author
Peter Bühlmann is Professor of Statistics at ETH Zürich. His main research areas are high-dimensional statistical inference, machine learning, graphical modeling, nonparametric methods, and statistical modeling in the life sciences. He is currently editor of the Annals of Statistics. He was awarded a Medallion lecture by the Institute of Mathematical Statistics in 2009
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.