Peter B?hlmann在ETHZ是高維統計、因果推斷方面的知名專家。布爾曼、吉爾所著的《高維數據統計學(方法理論和應用)(英文版)》統計學的前沿之作。這本書所針對的高維數據，是理論研究的熱點，在實際中也有著廣泛的應用。這本書重點闡述了Lasso和其他L1方法的變體，也有boosting等內容。
作者介紹
(瑞士)布爾曼//吉爾
目錄
1 Introduction 1.1 The framework 1.2 The possibilities and challenges 1.3 About the book 1.3.1 Organization of the book 1.4 Some examples 1.4.1 Prediction and biomarker discovery in genomics 2 Lasso for linear models 2.1 Organization of the chapter 2.2 Introduction and preliminaries 2.2.1 The Lasso estimator 2.3 Orthonormal design 2.4 Prediction 2.4.1 Practical aspects about the Lasso for prediction 2.4.2 Some results from asymptotic theory 2.5 Variable screening and -norms 2.5.1 Tuning parameter selection for variable screening 2.5.2 Motif regression for DNA binding sites 2.6 Variable selection 2.6.1 Neighborhood stability and irrepresentable condition 2.7 Key properties and corresponding assumptions: a summary 2.8 The adaptive Lasso: a two-stage procedure 2.8.1 An illustration: simulated data and motif regression 2.8.2 Orthonormal design 2.8.3 The adaptive Lasso: variable selection under weak conditions 2.8.4 Computation 2.8.5 Multi-step adaptive Lasso 2.8.6 Non-convex penalty functions 2.9 Thresholding the Lasso 2.10 The relaxed Lasso 2.11 Degrees of freedom of the Lasso 2.12 Path-following algorithms 2.12.1 Coordinatewise optimization and shooting algorithms 2.13 Elastic net: an extension Problems 3 Generalized linear models and the Lasso 3.1 Organization of the chapter 3.2 Introduction and preliminaries 3.2.1 The Lasso estimator: penalizing the negative log-likelihood. 3.3 Important examples of generalized linear models 3.3.1 Binary response variable and logistic regression 3.3.2 Poisson regression 3.3.3 Multi-category response variable and multinomial distribution Problems 4 The group Lasso 4.1 Organization of the chapter 4.2 Introduction and preliminaries 4.2.1 The group Lasso penalty 4.3 Factor variables as covariates 4.3.1 Prediction of splice sites in DNA sequences
4.4 Properties of the group Lasso for generalized linear models 4.5 The generalized group Lasso penalty 4.5.1 Groupwise prediction penalty and parametrization invariance 4.6 The adaptive group Lasso 4.7 Algorithms for the group Lasso 4.7.1 Block coordinate descent 4.7.2 Block coordinate gradient descent Problems 5 Additive models and many smooth univariate functions 5.1 Organization of the chapter 5.2 Introduction and preliminaries 5.2.1 Penalized maximum likelihood for additive models 5.3 The sparsity-smoothness penalty 5.3.1 Orthogonal basis and diagonal smoothing matrices 5.3.2 Natural cubic splines and Sobolev spaces 5.3.3 Computation 5.4 A sparsity-smoothness penalty of group Lasso type 5.4.1 Computational algorithm 5.4.2 Alternative approaches 5.5 Numerical examples 5.5.1 Simulated example …… 6 Theory for the lasso 7 Variable selection with the lasso 8 Theory for -penalty procedures 9 Non-convex loss functions and -regularization 10 Stable solutions 11 P-values for linear models and beyond 12 Boosting and greedy algorithms 14 Probability and moment inequalities Author index Index References
[