Estimation and testing under sparsity [e-book] : École d'Été de Probabilités de Saint-Flour XLV – 2015 / by Sara van de Geer

• Autore: Geer, Sara A. van de
• Descrizione fisica: 1 online resource (xiii, 274 p.)
• Disciplina: 519.2
• Soggetto topico: Mathematical statistics; Probabilities
• Classificazione: AMS 62J07
• Nota di contenuto: 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
• Sommario/riassunto: 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
• ISBN: 9783319327730 (alk. paper)
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 991003507699707536
• Lo trovi qui: Univ. del Salento
• Localizzazioni e accesso elettronico: https://link.springer.com/book/10.1007/978-3-319-32774-7
• Serie: Lecture Notes in Mathematics, 0075-8434 ; 2159