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Statistical Learning with Sparsity: The Lasso and Generalizations > 데이터마이닝

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Statistical Learning with Sparsity: The Lasso and Generalizations
히트도서
판매가격 89,000원
저자 Trevor Hastie
도서종류 외국도서
출판사 Chapman & Hall
발행언어 영어
발행일 2015-7
페이지수 367
ISBN 9781498712163
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  • 도서 정보

    도서 상세설명

    Table of Contents

    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
    ℓq 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

    Bibliography

    Author Index

    Index
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