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Estimation and Testing Under Sparsity École d'Été de Probabilités de Saint-Flour XLV - 2015 /
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 v...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2016.
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| Edición: | 1st ed. 2016. |
| Colección: | École d'Été de Probabilités de Saint-Flour ;
2159 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 100 | 1 | |a van de Geer, Sara. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |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. |
| 250 | |a 1st ed. 2016. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2016. | |
| 300 | |a XIII, 274 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a École d'Été de Probabilités de Saint-Flour ; |v 2159 | |
| 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. | ||
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Statistics . | |
| 650 | 0 | |a Computer science-Mathematics. | |
| 650 | 0 | |a Mathematical statistics. | |
| 650 | 1 | 4 | |a Probability Theory. |
| 650 | 2 | 4 | |a Statistical Theory and Methods. |
| 650 | 2 | 4 | |a Probability and Statistics in Computer Science. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319327730 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319327754 |
| 830 | 0 | |a École d'Été de Probabilités de Saint-Flour ; |v 2159 | |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||