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|a van de Geer, Sara.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a Estimation and Testing Under Sparsity
|h [electronic resource] :
|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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| 264 |
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|a Cham :
|b Springer International Publishing :
|b Imprint: Springer,
|c 2016.
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|a XIII, 274 p.
|b online resource.
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|a text
|b txt
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|a computer
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|a text file
|b PDF
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|a École d'Été de Probabilités de Saint-Flour,
|x 0721-5363 ;
|v 2159
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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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|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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|a Probabilities.
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|a Statistics .
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| 650 |
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|a Mathematical statistics.
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| 650 |
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|a Probability Theory and Stochastic Processes.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M27004
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|a Statistical Theory and Methods.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/S11001
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|a Probability and Statistics in Computer Science.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/I17036
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|a SpringerLink (Online service)
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|t Springer Nature eBook
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|i Printed edition:
|z 9783319327730
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| 776 |
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|i Printed edition:
|z 9783319327754
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|a École d'Été de Probabilités de Saint-Flour,
|x 0721-5363 ;
|v 2159
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|u https://doi.org/10.1007/978-3-319-32774-7
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|a Mathematics and Statistics (SpringerNature-11649)
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|a Mathematics and Statistics (R0) (SpringerNature-43713)
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