A computational approach to statistical learning
- Boca Raton CRC Press 2019
- xiii, 361 p. Includes bibliographical references and index
- Chapman & hall/ CRC texts in statistical science .
Table of contents:
1. Introduction
Computational approach
Statistical learning
Example
Prerequisites
How to read this book
Supplementary materials
Formalisms and terminology
Exercises
2. Linear Models
Introduction
Ordinary least squares
The normal equations
Solving least squares with the singular value decomposition
Directly solving the linear system
(*) Solving linear models with orthogonal projection
(*) Sensitivity analysis
(*) Relationship between numerical and statistical error
Implementation and notes
Application: Cancer incidence rates
Exercises
3. Ridge Regression and Principal Component Analysis
Application: Classifying and visualizing fashion MNIST
Exercises
10. Computation in Practice
Reference implementations
Sparse matrices
Sparse generalized linear models
Computation on row chunks
Feature hashing
Data quality issues
Implementation and notes
Application
Exercises
A Matrix Algebra
A Vector spaces
A Matrices
A Other useful matrix decompositions
B Floating Point Arithmetic and Numerical Computation
B Floating point arithmetic
B Numerical sources of error
B Computational effort
A Computational Approach to Statistical Learning gives a novel introduction to predictive modeling by focusing on the algorithmic and numeric motivations behind popular statistical methods. The text contains annotated code to over 80 original reference functions. These functions provide minimal working implementations of common statistical learning algorithms. Every chapter concludes with a fully worked out application that illustrates predictive modeling tasks using a real-world dataset.
The text begins with a detailed analysis of linear models and ordinary least squares. Subsequent chapters explore extensions such as ridge regression, generalized linear models, and additive models. The second half focuses on the use of general-purpose algorithms for convex optimization and their application to tasks in statistical learning. Models covered include the elastic net, dense neural networks, convolutional neural networks (CNNs), and spectral clustering. A unifying theme throughout the text is the use of optimization theory in the description of predictive models, with a particular focus on the singular value decomposition (SVD). Through this theme, the computational approach motivates and clarifies the relationships between various predictive models.