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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.
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.