TY  - GEN
AU  - Hastie, Trevor
AU  - Tibshirani, Robert
AU  - Wainwright, Martin
TI  - Statistical learning with sparsity: the lasso and generalizations
SN  - 9781498712163
U1  - 519.5 
PY  - 2015///
CY  - Boca Raton
PB  - CRC Press
KW  - Mathematical statistics
KW  - Least squares
KW  - Linear models (Statistics)
KW  - Proof theory
N1  - Table of Contents:

1.	Introduction

2.	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 
ℓq Penalties and Bayes Estimates 
Some Perspective 

3.	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 

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

5.	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
 
6.	Statistical Inference 
The Bayesian Lasso 
The Bootstrap 
Post-Selection Inference for the Lasso 
Inference via a Debiased Lasso 
Other Proposals for Post-Selection Inference 

7.	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
 
8.	Sparse Multivariate Methods 
Introduction 
Sparse Principal Components Analysis 
Sparse Canonical Correlation Analysis 
Sparse Linear Discriminant Analysis 
Sparse Clustering 

9.	Graphs and Model Selection 
Introduction 
Basics of Graphical Models
Graph Selection via Penalized Likelihood 
Graph Selection via Conditional Inference 
Graphical Models with Hidden Variables
 
10.	Signal Approximation and Compressed Sensing 
Introduction 
Signals and Sparse Representations 
Random Projection and Approximation 
Equivalence between ℓ0 and ℓ1 Recovery
 
11.	Theoretical Results for the Lasso 
Introduction 
Bounds on Lasso ℓ2-error 
Bounds on Prediction Error 
Support Recovery in Linear Regression 
Beyond the Basic Lasso 


N2  - Discover New Methods for Dealing with High-Dimensional Data

A sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data.

Top experts in this rapidly evolving field, the authors describe the lasso for linear regression and a simple coordinate descent algorithm for its computation. They discuss the application of l1 penalties to generalized linear models and support vector machines, cover generalized penalties such as the elastic net and group lasso, and review numerical methods for optimization. They also present statistical inference methods for fitted (lasso) models, including the bootstrap, Bayesian methods, and recently developed approaches. In addition, the book examines matrix decomposition, sparse multivariate analysis, graphical models, and compressed sensing. It concludes with a survey of theoretical results for the lasso.

In this age of big data, the number of features measured on a person or object can be large and might be larger than the number of observations. This book shows how the sparsity assumption allows us to tackle these problems and extract useful and reproducible patterns from big datasets. Data analysts, computer scientists, and theorists will appreciate this thorough and up-to-date treatment of sparse statistical modeling.

(https://www.crcpress.com/Statistical-Learning-with-Sparsity-The-Lasso-and-Generalizations/Hastie-Tibshirani-Wainwright/p/book/9781498712163)
ER  -