*This textbook is a well-rounded, rigorous, and informative work presenting the mathematics behind modern machine learning techniques. It hits all the right notes: the choice of topics is up-to-date and perfect for a course on data science for mathematics students at the advanced undergraduate or early graduate level. This book fills a sorely-needed gap in the existing literature by not sacrificing depth for breadth, presenting proofs of major theorems and subsequent derivations, as well as providing a copious amount of Python code. I only wish a book like this had been around when I first began my journey!*

Nicholas Hoell, University of Toronto*This is a well-written book that provides a deeper dive into data-scientific methods than many introductory texts. The writing is clear, and the text logically builds up regularization, classification, and decision trees. Compared to its probable competitors, it carves out a unique niche.*

Adam Loy, Carleton College*The data is the fuel of the new industry of the future, and this new science based in statistic and mathematical modeling have a deep background that must be learnt to understand the gist this new technology and theirs applications. This year I have gotten a certificate in Machine Learning in the MIT and of course I studied from several excellent books, but just one cover all the fundamental knowledge in a clear, rigorous and elegant way. Even with phyton programming to test the algorithms and stay in touch in a real way with the mathematical technics required to learn in a professional way. The book have other important advantage, the format is big, clean and full of colour, more when one must understand an specific notation in a rigorous way. A great book really thought in the students who want to progress in this subject. A splendid job of professor Dirk P. Kroese and his colleagues.*

Marcelo Cortes*I'm very early on in the text, but the text is impressive in the breadth and depth of its coverage, along with its attention to the mathematical theory. The exercises are challenging, which makes the text a little tricky for self-study -- at least to the extent your self-study is enhanced by knowing if you got the problems right or wrong. If I ever make it through the whole text, and change my opinion, I'll come back and edit this review; but I think just getting through Chapter 2 will be a semester's worth of knowledge.*

Richard Rivero

*I really enjoyed working through this book. It is definitely mathematical and algorithmic in its treatment of the topics covered: Statistical "Learning", Monte Carlo Methods, Unsupervised "Learning", Regression Models, Regularization and Kernel Methods, Classification, Decision Trees and Ensemble Methods, Deep "Learning" ( Neural Networks ) As a statistician and data scientist, I find the convoluted "machine learning" terminology very affected and as helpful as trying to design a plane based on the flying dynamics of a bird. Sometimes the rigourous mathematical notation is difficult to follow on the initial reading. Most algorithms are implemented in Python but the code should be more clearly documented so that one can follow the implementation of the solution without getting stuck on coding issues as the book encourages the reader to focus on the algorithm and to not treat the python code as a black box. The list of references is quite complete and it was interesting to check my library to see just how many of the references I already had. If this book is to be used for training analysts then there should be more practical examples and code solutions available.*

Jon Dickens-
The first impression when handling and opening this book at a random page
is superb. A big format (A4) and heavy weight, because the paper quality is
high, along with a spectacular style and large font, much colour and many
plots, and blocks of python code enhanced in colour boxes. This makes the
book attractive and easy to study. There is an electronic version of the book
that I have not seen, but the hardback version is highly recommended. The
authors have also set up a GitHub page (https://github.com/DSML-book)
with all the code and data needed to reproduce the examples.
The Table of Contents is also superb, making the book a comprehensive
up-to-date excellent tool for self-learning or for graduate and masters courses
on data science. With those that may come from a different background,
the book has four appendices to level background knowledge before
starting the real study: A) Linear algebra and functional analysis; B)
Multivariate differentiation and optimization; C) Probability and statistics;
and D) Python primer. These appendices are extensive (140 pages, 27% of
the book) and have rigorous mathematical summaries of essential topics
needed to understand the machine learning techniques of the book. I found
these materials an excellent review of the required concepts, though they
obviously do not provide enough detail or simplicity to conquer everything.
Of course, it is recommended that students follow the book to capture the
definitions and not miss relevant concepts. The book is a very well-designed
data science course, with mathematical rigor in mind. Key concepts are
highlighted in red in the margins, often with links to other parts of
the book.
The first chapters are introductory, including one on Mote Carlo methods.
Readers with some previous experience in the field can skip the appendices
and introductory chapters and jump directly to their favourite machine
learning method.
I will review the chapters backwards. For example, deep learning is the last
one (Chapter 9). Neural networks are introduced in a formal mathematical
way, as are the optimization techniques required to fit them. I liked the
Algorithm blocks, which are all over the book, as a tool to summarize
methods that require looping and conditions. The chapter on decision trees
and ensemble methods covers random forests and boosting. Classical
regression and classification techniques are detailed in three chapters, one
of which is devoted to regularization and kernel methods. There is also a
chapter on unsupervised learning that covers density estimation, clustering,
and principal components. Each chapter ends with additional information
sources and exercises. The list of references generally contains other books
or review papers for further learning.
In summary, this book will be excellent for those that want to build a strong
mathematical foundation for their knowledge on the main machine learning
techniques, and at the same time get python recipes on how to perform the
analyses for worked examples.

Victor Moreno, Book review, ISCB News, December 2020.