Introduction

This chapter describes popular statistical models in terms of their mathematical characteristics and the algorithms used to implement them. It provides a reference implementation, in the R programming environment, for each of the models. Understanding the computational details behind statistical modeling algorithms is an increasingly important skill for anyone who wants to apply modern statistical learning methods. Statistical learning is the process of teaching computers to “learn” by automatically extracting knowledge from available data. Domain-specific expertise is essential to the successful construction and deployment of statistical learning algorithms. The reference implementations accurately approximate the algorithms used to estimate parameters in the respective learning algorithms. Many of the algorithms are motivated by concepts in numerical analysis and the difficulties of working with floating point arithmetic. The chapter concludes by mathematically formalizing the central elements of supervised learning.