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.

• Exposition of machine learning suited for mathematics students

• Broad and concise introduction of some of the main topics in machine learning

• Based on lecture notes that have been used to teach undergraduate students in mathematics.

Dr. 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.

Dr. 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.