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...
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| Language: | English |
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Cham :
Springer International Publishing : Imprint: Springer,
2016.
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| Edition: | 1st ed. 2016. |
| Series: | École d'Été de Probabilités de Saint-Flour,
2159 |
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| Online Access: | https://doi.org/10.1007/978-3-319-32774-7 |
Table of 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.