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160701 ||| eng |
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|a 9783319327747
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| 100 |
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|a van de Geer, Sara
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| 245 |
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|a Estimation and Testing Under Sparsity
|h Elektronische Ressource
|b École d'Été de Probabilités de Saint-Flour XLV – 2015
|c by Sara van de Geer
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| 250 |
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|a 1st ed. 2016
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| 260 |
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|a Cham
|b Springer International Publishing
|c 2016, 2016
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| 300 |
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|a XIII, 274 p
|b online resource
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| 505 |
0 |
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|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
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| 653 |
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|a Mathematical statistics
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| 653 |
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|a Statistical Theory and Methods
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| 653 |
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|a Statistics
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| 653 |
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|a Probability and Statistics in Computer Science
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| 653 |
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|a Probability Theory and Stochastic Processes
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| 653 |
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|a Probabilities
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
0 |
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|a École d'Été de Probabilités de Saint-Flour
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| 856 |
4 |
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|u https://doi.org/10.1007/978-3-319-32774-7?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 519.2
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| 520 |
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|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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