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 ma-
chines and engineering automated systems. As machine learning becomes
more ubiquitous and its software packages become easier to use, it is nat-
ural 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.
The enthusiastic practitioner who is interested to learn more about the
magic behind successful machine learning algorithms currently faces a
daunting set of pre-requisite knowledge:
Programming languages and data analysis tools
Large-scale computation and the associated frameworks
Mathematics and statistics and how machine learning builds on it
At universities, introductory courses on machine learning tend to spend
early parts of the course covering some of these pre-requisites. For histori-
cal reasons, courses in machine learning tend to be taught in the computer
science department, where students are often trained in the first two areas
of knowledge, but not so much in mathematics and statistics.
Current machine learning textbooks primarily focus on machine learn-
ing algorithms and methodologies and assume that the reader is com-
petent in mathematics and statistics. Therefore, these books only spend
one or two chapters on 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 strug-
gle with the mathematical knowledge required to read a machine learning
textbook. Having taught undergraduate and graduate courses at universi-
ties, we find that the gap between high school mathematics and the math-
ematics level required to read a standard machine learning textbook is too
big for many people.
This book brings the mathematical foundations of basic machine learn-
ing concepts to the fore and collects the information in a single place so
that this skills gap is narrowed or even closed.
Vector Calculus Probability & Distributions Optimization
Linear Algebra Analytic Geometry Matrix Decomposition
between the two parts of the book to link mathematical concepts with
machine learning algorithms.
Of course there are more than two ways to read this book. Most readers
learn using a combination of top-down and bottom-up approaches, some-
times building up basic mathematical skills before attempting more com-
plex concepts, but also choosing topics based on applications of machine
learning.
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