稀疏统计模型只具有少数非零参数或权重，经典地体现了化繁为简的理念，因而广泛应用于诸多领域。本书就稀疏性统计学习做出总结，以LASSO方法为中心，层层推进，逐渐囊括其他方法，深入探讨诸多稀疏性问题的求解和应用；不仅包含大量的例子和清晰的图表，还附有文献注释和课后练习，是深入学习统计学知识的参考。本书适合计算机科学、统计学和机器学习的学生和研究人员。

Preface
1 Introduction
2 The Lasso for Linear Models
2.1 Introduction
2.2 The Lasso Estimator
2.3 Cross-Validation and Inference
2.4 Computation of the Lasso Solution
2.4.1 Single Predictor: Soft Thresholding
2.4.2 Multiple Predictors: Cyclic Coordinate Descent
2.4.3 Soft-Thresholding and Orthogonal Bases
2.5 Degrees of Freedom
2.6 Uniqueness of the Lasso Solutions
2.7 A Glimpse at the Theory
2.8 The Nonnegative Garrote
2.9 lq Penalties and Bayes Estimates
2.10 Some Perspective
Exercises
3 Generalized Linear Models
3.1 Introduction
3.2 Logistic Regression
3.2.1 Example: Document Classification
3.2.2 Algorithms
3.3 Multiclass Logistic Regression
3.3.1 Example: Handwritten Digits
3.3.2 Algorithms
3.3.3 Grouped-Lasso Multinomial
3.4 Log-Linear Models and the Poisson GLM
3.4.1 Example: Distribution Smoothing
3.5 Cox Proportional Hazards Models
3.5.1 Cross-Validation
3.5.2 Pre-Validation
3.6 Support Vector Machines
3.6.1 Logistic Regression with Separable Data
3.7 Computational Details and glmnet
Bibliographic Notes
Exercises
4 Generalizations of the Lasso Penalty
4.1 Introduction
4.2 The Elastic Net
4.3 The Group Lasso
4.3.1 Computation for the Group Lasso
4.3.2 Sparse Group Lasso
4.3.3 The Overlap Group Lasso
4.4 Sparse Additive Models and the Group Lasso
4.4.1 Additive Models and Backfitting
4.4.2 Sparse Additive Models and Backfitting
4.4.3 Approaches Using Optimization and the Group Lasso
4.4.4 Multiple Penalization for Sparse Additive Models
4.5 The Fused Lasso
4.5.1 Fitting the Fused Lasso
4.5.1.1 Reparametrization
4.5.1.2 A Path Algorithm
4.5.1.3 A Dual Path Algorithm
4.5.1.4 Dynamic Programming for the Fused Lasso
4.5.2 Trend Filtering
4.5.3 Nearly Isotonic Regression
4.6 Nonconvex Penalties
Bibliographic Notes
Exercises
5 Optimization Methods
5.1 Introduction
5.2 Convex Optimality Conditions
5.2.1 Optimality for Differentiable Problems
5.2.2 Nondifferentiable Functions and Subgradients
5.3 Gradient Descent
5.3.1 Unconstrained Gradient Descent
5.3.2 Projected Gradient Methods
5.3.3 Proximal Gradient Methods
5.3.4 Accelerated Gradient Methods
5.4 Coordinate Descent
5.4.1 Separability and Coordinate Descent
5.4.2 Linear Regression and the Lasso
5.4.3 Logistic Regression and Generalized Linear Models
5.5 A Simulation Study
5.6 Least Angle Regression
5.7 Alternating Direction Method of Multipliers
5.8 Minorization-Maximization Algorithms
5.9 Biconvexity and Alternating Minimization
5.10 Screening Rules
Bibliographic Notes
Appendix
Exercises
6 Statistical Inference
6.1 The Bayesian Lasso
6.2 The Bootstrap
6.3 Post-Selection Inference for the Lasso
6.3.1 The Covariance Test
6.3.2 A General Scheme for Post-Selection Inference
6.3.2.1 Fixed-入 Inference for the Lasso
6.3.2.2 The Spacing Test for LAR
6.3.3 What Hypothesis Is Being Tested?
6.3.4 Back to Forward Stepwise Regression
6.4 Inference via a Debiased Lasso
6.5 Other Proposals for Post-Selection Inference
Bibliographic Notes
Exercises
7 Matrix Decompositions, Approximations, and Completion
7.1 Introduction
7.2 The Singular Value Decomposition
7.3 Missing Data and Matrix Completion
7.3.1 The Netflix Movie Challenge
7.3.2 Matrix Completion Using Nuclear Norm
7.3.3 Theoretical Results for Matrix Completion
7.3.4 Maximum Margin Factorization and Related Methods
7.4 Reduced-Rank Regression
7.5 A General Matrix Regression Framework
7.6 Penalized Matrix Decomposition
7.7 Additive Matrix Decomposition
Bibliographic Notes
Exercises
8 Sparse Multivariate Methods
8.1 Introduct