Sparse Estimation with Math and R: 100 Exercises for Building Logic

✍ Scribed by Joe Suzuki

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 241
• Edition: 1st ed. 2021
• Category: Library

✦ Synopsis

The most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of sparse estimation by considering math problems and building R programs.  

Each chapter introduces the notion of sparsity and provides procedures followed by mathematical derivations and source programs with examples of execution. To maximize readers’ insights into sparsity, mathematical proofs are presented for almost all propositions, and programs are described without depending on any packages. The book is carefully organized to provide the solutions to the exercises in each chapter so that readers can solve the total of 100 exercises by simply following the contents of each chapter.

This textbook is suitable for an undergraduate or graduate course consisting of about 15 lectures (90 mins each). Written in an easy-to-follow and self-contained style, this book will also be perfect material for independent learning by data scientists, machine learning engineers, and researchers interested in linear regression, generalized linear lasso, group lasso, fused lasso, graphical models, matrix decomposition, and multivariate analysis.

This book is one of a series of textbooks in machine learning by the same author. Other titles are: 

- Statistical Learning with Math and R (https://www.springer.com/gp/book/9789811575679)

- Statistical Learning with Math and Python (https://www.springer.com/gp/book/9789811578762)

- Sparse Estimation with Math and Python

✦ Table of Contents

Preface
What Makes SEMR Unique?
Contents
1 Linear Regression
1.1 Linear Regression
1.2 Subderivative
1.3 Lasso
1.4 Ridge
1.5 A Comparison Between Lasso and Ridge
1.6 Elastic Net
1.7 About How to Set the Value of λ
2 Generalized Linear Regression
2.1 Generalization of Lasso in Linear Regression
2.2 Logistic Regression for Binary Values
2.3 Logistic Regression for Multiple Values
2.4 Poisson Regression
2.5 Survival Analysis
3 Group Lasso
3.1 When One Group Exists
3.2 Proximal Gradient Method
3.3 Group Lasso
3.4 Sparse Group Lasso
3.5 Overlap Lasso
3.6 Group Lasso with Multiple Responses
3.7 Group Lasso via Logistic Regression
3.8 Group Lasso for the Generalized Additive Models
4 Fused Lasso
4.1 Applications of Fused Lasso
4.2 Solving Fused Lasso via Dynamic Programming
4.3 LARS
4.4 Dual Lasso Problem and Generalized Lasso
4.5 ADMM
5 Graphical Models
5.1 Graphical Models
5.2 Graphical Lasso
5.3 Estimation of the Graphical Model based on the Quasi-likelihood
5.4 Joint Graphical Lasso
6 Matrix Decomposition
6.1 Singular Decomposition
6.2 Eckart-Young's Theorem
6.3 Norm
6.4 Sparse Estimation for Low-Rank Estimations
7 Multivariate Analysis
7.1 Principal Component Analysis (1): SCoTLASS
7.2 Principle Component Analysis (2): SPCA
7.3 K-Means Clustering
7.4 Convex Clustering
Appendix Bibliography