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Estimation and testing under sparsity[electronic resource] :Ecole d'Ete de probabilites de Saint-Flour XLV - 2015 /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	519.544
書名/作者:	Estimation and testing under sparsity : Ecole d'Ete de probabilites de Saint-Flour XLV - 2015 // by Sara van de Geer.
作者:	Geer, Sara van de.
出版者:	Cham : : Springer International Publishing :, 2016.
面頁冊數:	xiii, 274 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Estimation theory.
標題:	Inequalities (Mathematics)
標題:	Mathematics.
標題:	Probability Theory and Stochastic Processes.
標題:	Statistical Theory and Methods.
標題:	Probability and Statistics in Computer Science.
ISBN:	9783319327747
ISBN:	9783319327730
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-32774-7

Estimation and testing under sparsity[electronic resource] :Ecole 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

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

184305
Estimation theory.

LC Class. No.: QA276.8

Dewey Class. No.: 519.544

Estimation and testing under sparsity[electronic resource] :Ecole d'Ete de probabilites de Saint-Flour XLV - 2015 /
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