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.
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 2009and read a paper to the Royal Statistical Society in 2010.
Sara van de Geerhas beena full professor at the ETH in Zürich since 2005. Her main areas of research are empirical process theory, statistical learning theory, and nonparametric and high-dimensional statistics. She is an associate editor of Probability Theory and Related Fields, The Scandinavian Journal of Statistics and Statistical Surveys and a member of the Swiss National Science Foundation and correspondent of the Dutch Royal Academy of Sciences.
She received the IMS medal in 2003 and the ISI award in 2005, and was an invited speaker at the International Conference of Mathematicians in 2010.
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.