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＜電子ブック＞
Estimation and Testing Under Sparsity : École d'Été de Probabilités de Saint-Flour XLV – 2015 / by Sara van de Geer
(École d'Été de Probabilités de Saint-Flour ; 2159)

版	1st ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2016
大きさ	XIII, 274 p : online resource
著者標目	*van de Geer, Sara author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Statistics  LCSH:Computer science—Mathematics LCSH:Mathematical statistics FREE:Probability Theory FREE:Statistical Theory and Methods FREE:Probability and Statistics in Computer Science
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-32774-7

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