Estimation and Testing Under Sparsity
van de Geer, Sara.
Estimation and Testing Under Sparsity École d'Été de Probabilités de Saint-Flour XLV – 2015 / [electronic resource] : by Sara van de Geer. - XIII, 274 p. online resource. - École d'Été de Probabilités de Saint-Flour, 2159 0721-5363 ; . - École d'Été de Probabilités de Saint-Flour, 2159 .
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.
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.
9783319327747
10.1007/978-3-319-32774-7 doi
Distribution (Probability theory.
Mathematical statistics.
Computer science.
Probability Theory and Stochastic Processes.
Statistical Theory and Methods.
Probability and Statistics in Computer Science.
QA273.A1-274.9 QA274-274.9
519.2
Estimation and Testing Under Sparsity École d'Été de Probabilités de Saint-Flour XLV – 2015 / [electronic resource] : by Sara van de Geer. - XIII, 274 p. online resource. - École d'Été de Probabilités de Saint-Flour, 2159 0721-5363 ; . - École d'Été de Probabilités de Saint-Flour, 2159 .
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.
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.
9783319327747
10.1007/978-3-319-32774-7 doi
Distribution (Probability theory.
Mathematical statistics.
Computer science.
Probability Theory and Stochastic Processes.
Statistical Theory and Methods.
Probability and Statistics in Computer Science.
QA273.A1-274.9 QA274-274.9
519.2