Mathematics of Machine Learning: An Introduction

Over the course of just a few decades, machine learning has grown into a force which shapes modern life perhaps as much as the combustion engine or wireless communication. As we drive to work, machine learning algorithms extract license plate numbers from images captured by automatic cameras at busy intersections. At work, they measure our productivity and govern our supply chains. In our personal lives, they power product recommendations on online shopping sites and suggestions on social media. In our homes and on our devices, they recognize our voices and our faces. They process our loan applications and evaluate our medical images. More globally, they stabilize power grids and assist in planning flight routes. There is not a space in our public and personal lives which machine learning has not at least begun to affect. For a field as ubiquitous, it is fairly poorly represented in our common knowledge. This article aims at giving a high level introduction to some core tasks, ideas and methods of machine learning for readers who are familiar with at least some undergraduate mathematics. Advanced readers may get more from certain sections, but our goal is to present a self-contained picture which requires little knowledge beyond calculus in multiple variables and elementary linear algebra. For readers who have not taken many of the advanced classes, this may also motivate why certain fields of study are of interest in applications. One big omission in this article are deep neural networks, i.e. the models which underly 'deep learning.' Due to their special importance, they will be discussed in a separate companion article.