The Mathematics of Machine Learning

This book is an introduction to machine learning, with a strong focus on the mathematics behind the standard algorithms and techniques in the field, aimed at senior undergraduates and early graduate students of Mathematics.

There is a focus on well-known supervised machine learning algorithms, detailing the existing theory to provide some theoretical guarantees, featuring intuitive proofs and exposition of the material in a concise and precise manner. A broad set of topics is covered, giving an overview of the field. A summary of the topics covered is: statistical learning theory, approximation theory, linear models, kernel methods, Gaussian processes, deep neural networks, ensemble methods and unsupervised learning techniques, such as clustering and dimensionality reduction.

This book is suited for students who are interested in entering the field, by preparing them to master the standard tools in Machine Learning. The reader will be equipped to understand the main theoretical questions of the current research and to engage with the field.

Table of Contents

Part I: Introduction and preliminaries

1 Int roduction to machine learning

2 Pro bability review

3 Optimization

Part II: Supervised learning

4 Statistical learning theory

5 Linear models

6 Kernel methods

7 Gaussian processes

8 Deep learning

9 Ensemble methods

Part Ill: Beyond supervised learning

10 Topics in unsupervised learning

11 Reinforcement learning

About the Authors

Maria Han Veiga

Assistant professor of mathematics, Ohio State University, Ohio, USA

Prior to joining Ohio State, she was a postdoctoral fellow at the University of Michigan in Mathematics and Data Science (MIDAS). She obtained her PhD at the University of Zurich. Her research focuses on numerical analysis for hyperbolic partial differential equations and scientific machine learning.

François Ged

Postdoctoral fellow, University of Vienna, Austria

He obtained his PhD in Mathematics at the University of Zurich, Switzerland, after which he was a postdoc fellow at the École Polytechnique Fédérale de Lausanne. His research interests gravitate around the theory of deep learning and reinforcement learning, as well as mathematical population genetics and growth-fragmentation processes.