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Estimation and Testing Under Sparsity : École d'Été de Probabilités de Saint-Flour XLV – 2015 / by Sara van de Geer.
Springer Nature - Springer Mathematics and Statistics eBooks 2016 English International Available online
View online- Format:
- Book
- Author/Creator:
- van de Geer, Sara., Author.
- Series:
- École d'Été de Probabilités de Saint-Flour ; 2159
- Language:
- English
- Subjects (All):
- Probabilities.
- Statistics.
- Computer science--Mathematics.
- Computer science.
- Mathematical statistics.
- Probability Theory.
- Statistical Theory and Methods.
- Probability and Statistics in Computer Science.
- Local Subjects:
- Probability Theory.
- Statistical Theory and Methods.
- Probability and Statistics in Computer Science.
- Physical Description:
- 1 online resource (XIII, 274 p.)
- Edition:
- 1st ed. 2016.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2016.
- Summary:
- 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.
- Contents:
- 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.
- Notes:
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 9783319327747
- 3319327747
- OCLC:
- 952973013
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