Overview
- Starting with the popular Lasso method as its prime example, the book then extends to a broad family of estimation methods for high-dimensional data
- A theoretical basis for sparsity-inducing methods is provided, together with ways to build confidence intervals and tests
- The focus is on common features of methods for high-dimensional data and, as such, a potential starting point is given for the analysis of other methods not treated in the book
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2159)
Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)
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About this book
Taking the Lasso method as its starting point, this book describes the main ingredients needed to study general loss functions and sparsity-inducing regularizers. It also provides a semi-parametric approach to establishing confidence intervals and tests. Sparsity-inducing methods have proven to be very useful in the analysis of high-dimensional data. Examples include the Lasso and group Lasso methods, and the least squares method with other norm-penalties, such as the nuclear norm. The illustrations provided include generalized linear models, density estimation, matrix completion and sparse principal components. Each chapter ends with a problem section. The book can be used as a textbook for a graduate or PhD course.
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Keywords
Table of contents (18 chapters)
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Front Matter
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Back Matter
Reviews
“This book is presented as a series of lecture notes on the theory of penalized estimators under sparsity. … The level of detail is high, and almost all proofs are given in full, with discussion. Each chapter ends with a section of problems, which could be used in a study setting to improve understanding of the proofs.” (Andrew Duncan A. C. Smith, Mathematical Reviews, August, 2017)
“The book provides several examples and illustrations of the methods presented and discussed, while each of its 17 chapters ends with a problem section. Thus, it can be used as textbook for students mainly at postgraduate level.” (Christina Diakaki, zbMATH 1362.62006, 2017)
Authors and Affiliations
Bibliographic Information
Book Title: Estimation and Testing Under Sparsity
Book Subtitle: École d'Été de Probabilités de Saint-Flour XLV – 2015
Authors: Sara van de Geer
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-32774-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-32773-0Published: 29 June 2016
eBook ISBN: 978-3-319-32774-7Published: 28 June 2016
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIII, 274
Topics: Probability Theory and Stochastic Processes, Statistical Theory and Methods, Probability and Statistics in Computer Science