Estimation and Testing Under Sparsity

École d'Été de Probabilités de Saint-Flour XLV – 2015

Nonfiction, Science & Nature, Mathematics, Statistics, Computers, Application Software
Cover of the book Estimation and Testing Under Sparsity by Sara van de Geer, Springer International Publishing
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Author: Sara van de Geer ISBN: 9783319327747
Publisher: Springer International Publishing Publication: June 28, 2016
Imprint: Springer Language: English
Author: Sara van de Geer
ISBN: 9783319327747
Publisher: Springer International Publishing
Publication: June 28, 2016
Imprint: Springer
Language: English

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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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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