Deisenroth M.P. Faisal A.A., Cheng S.O. Mathematics for Machine Learning

Cambridge: Cambridge University Press, 2020. — 398 p. — ISBN 110845514X.Machine learning is the latest in a long line of attempts to distill human knowledge and reasoning into a form that is suitable for constructing machines and engineering automated systems. As machine learning becomes more ubiquitous and its software packages become easier to use, it is natural and desirable that the low-level technical details are abstracted away and hidden from the practitioner. However, this brings with it the danger that a practitioner becomes unaware of the design decisions and, hence, the limits of machine learning algorithms. Current machine learning textbooks primarily focus on machine learning algorithms and methodologies and assume that the reader is competent in mathematics and statistics. Therefore, these books only spend one or two chapters of background mathematics, either at the beginning of the book or as appendices. We have found many people who want to delve into the foundations of basic machine learning methods who struggle with the mathematical knowledge required to read a machine learning textbook. Having taught undergraduate and graduate courses at universities, we find that the gap between high school mathematics and the mathematics level required to read a standard machine learning textbook is too big for many people. This book brings the mathematical foundations of basic machine learning concepts to the fore and collects the information in a single place so that this skills gap is narrowed or even closed. This book is intended to be a guidebook to the vast mathematical literature that forms the foundations of modern machine learning. We motivate the need for mathematical concepts by directly pointing out their usefulness in the context of fundamental machine learning problems. In the interest of keeping the book short, many details and more advanced concepts have been left out. Equipped with the basic concepts presented here, and how they fit into the larger context of machine learning, the reader can find numerous resources for further study, which we provide at the end of the respective chapters. For readers with a mathematical background, this book provides a brief but precisely stated glimpse of machine learning. We do not aim to write a classical machine learning book. Instead, our intention is to provide the mathematical background, applied to four central machine learning problems, to make it easier to read other machine learning textbooks.Who Is the Target Audience ?This book is written in an academic mathematical style, which enables us to be precise about the concepts behind machine learning. We sprinkle comments and remarks throughout the text, in the hope that it provides useful guidance with respect to the big picture. The book assumes the reader to have mathematical knowledge commonly covered in high school mathematics and physics. For example, the reader should have seen derivatives and integrals before, and geometric vectors in two or three dimensions. Starting from there, we generalize these concepts. Therefore, the target audience of the book includes undergraduate university students, evening learners and learners participating in online machine learning courses.Mathematical Foundations
Introduction and Motivation.
Linear Algebra.
Analytic Geometry.
Matrix Decompositions.
Vector Calculus.
Probability and Distributions.
Continuous Optimization.
Central Machine Learning Problems
When Models Meet Data.
Linear Regression.
Dimensionality Reduction with Principal Component Analysis.
Density Estimation with Gaussian Mixture Models.
Classification with Support Vector Machines.
References.
Index.Latest revision: 15.10.2019True PDF (A4 format)