Estimation and testing under sparsity
著者
書誌事項
Estimation and testing under sparsity
（Lecture notes in mathematics, 2159 . École d'été de probabilités de Saint-Flour ; 45-2015）
Springer, c2016
- タイトル別名
-
Estimation and testing under sparsity : École d'été de probabilités de Saint-Flour XLV - 2015
大学図書館所蔵 件 / 全41件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 267-269) and index
内容説明・目次
内容説明
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.
目次
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.
「Nielsen BookData」 より