A Computational Approach to Statistical Learning

A Computational Approach to Statistical Learning gives a novel introduction to predictive modelling 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 modelling 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.

1. Introduction
2. Linear Models
3. Ridge Regression and Principal Component Analysis
4. Linear Smoothers
5. Generalized Linear Models
6. Additive Models
7. Penalized Regression Models
8. Neural Networks
9. Dimensionality Reduction
10. Computation in Practice

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