Statistical Learning with Sparsity: The Lasso and Generalizations (Hardcover)

Introduction

The Lasso for Linear Models
Introduction
The Lasso Estimator
Cross-Validation and Inference
Computation of the Lasso Solution
Degrees of Freedom
Uniqueness of the Lasso Solutions
A Glimpse at the Theory
The Nonnegative Garrote
ℓ_q Penalties and Bayes Estimates
Some Perspective

Generalized Linear Models
Introduction
Logistic Regression
Multiclass Logistic Regression
Log-Linear Models and the Poisson GLM
Cox Proportional Hazards Models
Support Vector Machines
Computational Details and glmnet

Generalizations of the Lasso Penalty
Introduction
The Elastic Net
The Group Lasso
Sparse Additive Models and the Group Lasso
The Fused Lasso
Nonconvex Penalties

Optimization Methods
Introduction
Convex Optimality Conditions
Gradient Descent
Coordinate Descent
A Simulation Study
Least Angle Regression
Alternating Direction Method of Multipliers
Minorization-Maximization Algorithms
Biconvexity and Alternating Minimization
Screening Rules

Statistical Inference
The Bayesian Lasso
The Bootstrap
Post-Selection Inference for the Lasso
Inference via a Debiased Lasso
Other Proposals for Post-Selection Inference

Matrix Decompositions, Approximations, and Completion
Introduction
The Singular Value Decomposition
Missing Data and Matrix Completion
Reduced-Rank Regression
A General Matrix Regression Framework
Penalized Matrix Decomposition
Additive Matrix Decomposition

Sparse Multivariate Methods
Introduction
Sparse Principal Components Analysis
Sparse Canonical Correlation Analysis
Sparse Linear Discriminant Analysis
Sparse Clustering

Graphs and Model Selection
Introduction
Basics of Graphical Models
Graph Selection via Penalized Likelihood
Graph Selection via Conditional Inference
Graphical Models with Hidden Variables

Signal Approximation and Compressed Sensing
Introduction
Signals and Sparse Representations
Random Projection and Approximation
Equivalence between ℓ₀ and ℓ₁ Recovery

Theoretical Results for the Lasso
Introduction
Bounds on Lasso ℓ₂-error
Bounds on Prediction Error
Support Recovery in Linear Regression
Beyond the Basic Lasso

Bibliographic Notes and Exercises appear at the end of each chapter.