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Estimation and testing under sparsit...

Geer, Sara van de.

Estimation and testing under sparsityEcole d'Ete de probabilites de Saint-Flour XLV - 2015 /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Estimation and testing under sparsityby Sara van de Geer.
Reminder of title:	Ecole d'Ete de probabilites de Saint-Flour XLV - 2015 /
Author:	Geer, Sara van de.
Published:	Cham :Springer International Publishing :2016.
Description:	xiii, 274 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Estimation theory.
Online resource:	http://dx.doi.org/10.1007/978-3-319-32774-7
ISBN:	9783319327747$q(electronic bk.)

Estimation and testing under sparsityEcole d'Ete de probabilites de Saint-Flour XLV - 2015 /
Geer, Sara van de.

Estimation and testing under sparsityEcole d'Ete de probabilites de Saint-Flour XLV - 2015 /[electronic resource] :by Sara van de Geer. - Cham :Springer International Publishing :2016. - xiii, 274 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21590075-8434 ;. - Lecture notes in mathematics ;2035..

1 Introduction -- The Lasso -- 3 The square-root Lasso -- 4 The bias of the Lasso and worst possible sub-directions -- 5 Confidence intervals using the Lasso -- 6 Structured sparsity -- 7 General loss with norm-penalty -- 8 Empirical process theory for dual norms -- 9 Probability inequalities for matrices -- 10 Inequalities for the centred empirical risk and its derivative -- 11 The margin condition -- 12 Some worked-out examples -- 13 Brouwer's fixed point theorem and sparsity -- 14 Asymptotically linear estimators of the precision matrix -- 15 Lower bounds for sparse quadratic forms -- 16 Symmetrization, contraction and concentration -- 17 Chaining including concentration -- 18 Metric structure of convex hulls.

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.

ISBN: 9783319327747$q(electronic bk.)

Standard No.: 10.1007/978-3-319-32774-7doiSubjects--Topical Terms:

181864
Estimation theory.

LC Class. No.: QA276.8

Dewey Class. No.: 519.544

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505 0 $a 1 Introduction -- The Lasso -- 3 The square-root Lasso -- 4 The bias of the Lasso and worst possible sub-directions -- 5 Confidence intervals using the Lasso -- 6 Structured sparsity -- 7 General loss with norm-penalty -- 8 Empirical process theory for dual norms -- 9 Probability inequalities for matrices -- 10 Inequalities for the centred empirical risk and its derivative -- 11 The margin condition -- 12 Some worked-out examples -- 13 Brouwer's fixed point theorem and sparsity -- 14 Asymptotically linear estimators of the precision matrix -- 15 Lower bounds for sparse quadratic forms -- 16 Symmetrization, contraction and concentration -- 17 Chaining including concentration -- 18 Metric structure of convex hulls.
520 $a 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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