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PRINTED BOOKS
Author Hastie, Trevor, author.

Title Statistical Learning with Sparsity : The Lasso and Generalizations / Trevor Hastie, Rob Tibshirani, Martin Wainwright.

Published Boca Raton Chapman & Hall/CRC, 2015.

Copies

Location Call No. Status
 UniM ERC  519.5 HAST    AVAILABLE
Physical description xv, 351 pages : illustrations (colour) ; 24 cm.
Series Chapman & Hall/CRC monographs on statistics & applied probability ; 143.
Chapman & Hall/CRC monographs on statistics & applied probability ; 143.
Notes Formerly CIP. Uk.
Bibliography Includes bibliographical references and index.
Contents 1 Introduction 1 -- 2 Lasso for Linear Models 7 -- 2.1 Introduction 7 -- 2.2 Lasso Estimator 8 -- 2.3 Cross-Validation and Inference 13 -- 2.4 Computation of the Lasso Solution 14 -- 2.5 Degrees of Freedom 17 -- 2.6 Uniqueness of the Lasso Solutions 19 -- 2.7 A Glimpse at the Theory 20 -- 2.8 Nonnegative Garrote 20 -- 2.9 l<sub>q</sub> Penalties and Bayes Estimates 22 -- 2.10 Some Perspective 23 -- 3 Generalized Linear Models 29 -- 3.1 Introduction 29 -- 3.2 Logistic Regression 31 -- 3.3 Multiclass Logistic Regression 36 -- 3.4 Log-Linear Models and the Poisson GLM 40 -- 3.5 Cox Proportional Hazards Models 42 -- 3.6 Support Vector Machines 46 -- 3.7 Computational Details and glmnet 50 -- 4 Generalizations of the Lasso Penalty 55 -- 4.1 Introduction 55 -- 4.2 Elastic Net 56 -- 4.3 Group Lasso 58 -- 4.4 Sparse Additive Models and the Group Lasso 69 -- 4.5 Fused Lasso 76 -- 4.6 Nonconvex Penalties 84 -- 5 Optimization Methods 95 -- 5.1 Introduction 95 -- 5.2 Convex Optimality Conditions 95 -- 5.3 Gradient Descent 100 -- 5.4 Coordinate Descent 109 -- 5.5 A Simulation Study 117 -- 5.6 Least Angle Regression 118 -- 5.7 Alternating Direction Method of Multipliers 121 -- 5.8 Mmomation-Maximization Algorithms 123 -- 5.9 Biconvexity and Alternating Minimization 124 -- 5.10 Screening Rules 127 -- 6 Statistical Inference 139 -- 6.1 Bayesian Lasso 139 -- 6.2 Bootstrap 142 -- 6.3 Post-Selection Inference for the Lasso 147 -- 6.1 Inference via a Debiased Lasso 158 -- 6.5 Other Proposals for Post-Selection Inference 160 -- 7 Matrix Decompositions, Approximations, and Completion 167 -- 7.1 Introduction 167 -- 7.2 Singular Value Decomposition 169 -- 7.3 Missing Data, and Matrix Completion 169 -- 7.4 Reduced-Hank Regression 184 -- 7.5 A General Matrix Regression Framework 185 -- 7.6 Penalized Matrix Decomposition 187 -- 7.7 Additive Matrix Decomposition 190 -- 8 Sparse Multivariate Methods 201 -- 8.1 Introduction 201 -- 8.2 Sparse Principal Components Analysis 202 -- 8.3 Sparse Canonical Correlation Analysis 213 -- 8.4 Sparse Linear Discriminant Analysis 217 -- 8.5 Sparse Clustering 227 -- 9 Graphs and Model Selection 241 -- 9.1 Introduction 241 -- 9.2 Basics of Graphical Models 241 -- 9.3 Graph Selection via Penalized Likelihood 246 -- 9.4 Graph Selection via Conditional Inference 254 -- 9.5 Graphical Models with Hidden Variables 261 -- 10 Signal Approximation and Compressed Sensing 269 -- 10.1 Introduction 269 -- 10.2 Signals and Sparse Representations 269 -- 10.3 Random Projection and Approximation 276 -- 10.4 Equivalence between l⁰ and l¹ Recovery 280 -- 11 Theoretical Results for the Lasso 289 -- 11.1 Introduction 289 -- 11.2 Bounds on Lasso l²Error 291 -- 11.3 Bounds on Prediction Error 299 -- 11.4 Support Recovery in Linear Regression 301 -- 11.5 Beyond the Basic Lasso 309.
Other author Tibshirani, Robert, author.
Wainwright, Martin (Martin J.), author.
Subject Mathematical statistics.
Least squares.
Linear models (Statistics)
Proof theory.
ISBN 9781498712163 (hbk.) £57.99
9781498712170 (PDF ebook) () £57.99