Description
Book SynopsisModern 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.
Trade ReviewFrom 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)
Table of ContentsIntroduction.- 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.
