Opis: Estimation and Testing Under Sparsity 2016 - Sara van de Geer

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.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.

Szczegóły: Estimation and Testing Under Sparsity 2016 - Sara van de Geer

Tytuł: Estimation and Testing Under Sparsity 2016
Autor: Sara van de Geer
Wydawnictwo: Springer Verlag
ISBN: 9783319327730
Rok wydania: 2016
Ilość stron: 287
Oprawa: Miękka
Waga: 0.45 kg

Recenzje: Estimation and Testing Under Sparsity 2016 - Sara van de Geer