15 Books to Understand Mathematical Foundations of Machine Learning in April, 2023



It is fundamental to have a decent comprehension of the mathematical foundations to be capable with machine learning. In view of that, here are fifteen books that can help you to comprehend Maths of Machine learning.

The vast majority learn Machine Learning with an accentuation on Programming. Notwithstanding, to be really capable with Data Science (and Machine Learning), you can’t overlook the mathematical foundations behind Data Science and Machine Learning.

In this post, I introduce fifteen books that I delighted in taking in the mathematical foundations of Machine Learning. ‘Appreciate‘ is maybe not the best of words since this exertion is hard going!


15 Books to Understand Mathematical Foundations of Machine Learning


1.) The Nature Of Statistical Learning Theory


The book is about interpreting statistical data correctly to gain insights into the underlying process/ phenomena (call it what you will) that generated the data.

Challenges: One needs to have a taste for rigorous maths – in particular, if you are equation-phobic, you may find it a put-off.

Be prepared to see flying integrals, limits, etc.





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2.) Pattern Classification by Richard O Duda


Practitioners developing or investigating pattern recognition systems in such diverse application areas as speech recognition, optical character recognition, image processing, or signal analysis, often face the difficult task of having to decide among a bewildering array of available techniques.

This unique text/professional reference provides the information you need to choose the most appropriate method for a given class of problems, presenting an in–depth, systematic account of the major topics in pattern recognition today.

A new edition of a classic work that helped define the field for over a quarter century, this practical book updates and expands the original work, focusing on pattern classification and the immense progress it has experienced in recent years.


Pattern Classification


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3.) Machine Learning: An Algorithmic Perspective, Second Edition (Chapman & Hall/Crc Machine Learning & Pattern Recognition)


If you are interested in learning enough AI to understand the sort of new techniques being introduced into Web 2 applications, then this is a good place to start. … it covers the subject matter of many an introductory course on AI and it has references to the source material and further reading but it is written in a fairly casual style.

Overall it works and much of the mathematics is explained in ways that make it fairly clear what is going on … . This is a suitable introduction to AI if you are studying the subject on your own and it would make a good course text for an introduction and overview of AI.”




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4) The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition


The book would be ideal for statistics graduate students . This book really is the standard in the field, referenced in most papers and books on the subject, and it is easy to see why. The book is very well written, with informative graphics on almost every other page.

It looks great and inviting. You can flip the book open to any page, read a sentence or two and be hooked for the next hour or so.




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5.) Pattern Recognition and Machine Learning (Information Science and Statistics)


This beautifully produced book is intended for advanced undergraduates, PhD students, researchers and practitioners, primarily in the machine learning or allied areas…A strong feature is the use of geometric illustration and intuition…

This is an impressive and interesting book that might form the basis of several advanced statistics courses. It would be a good choice for a reading group.




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6.) Machine Learning: The Art and Science of Algorithms that Make Sense of Data


As one of the most comprehensive machine learning texts around, this book does justice to the field’s incredible richness, but without losing sight of the unifying principles. Peter Flach’s clear, example-based approach begins by discussing how a spam filter works, which gives an immediate introduction to machine learning in action, with a minimum of technical fuss.

Flach provides case studies of increasing complexity and variety with well-chosen examples and illustrations throughout. He covers a wide range of logical, geometric and statistical models and state-of-the-art topics such as matrix factorisation and ROC analysis. These features ensure Machine Learning will set a new standard as an introductory textbook.




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7.) The Drunkard’s Walk: How Randomness Rules Our Lives


The Drunkard’s Walk reveals the psychological illusions that prevent us understanding everything from stock-picking to wine-tasting – read it, or risk becoming another victim of chance.

‘A wonderfully readable guide to how the mathematical laws of randomness affect our lives’ – Hawking

Randomness and uncertainty surround everything we do.

So why are we so bad at understanding them?




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8.) The Signal and the Noise: Why So Many Predictions Fail-but Some Don’t


With everything from the health of the global economy to our ability to fight terrorism dependent on the quality of our predictions, Nate Silver’s insights are an essential read.

Nate Silver built an innovative system for predicting baseball performance, predicted the 2008 election within a hair’s breadth, and became a national sensation as a blogger.




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8.) Statistics for Experimenters: Design, Innovation, and Discovery




Rewritten and updated, this new edition of Statistics for Experimenters adopts the same approaches as the landmark First Edition by teaching with examples, readily understood graphics, and the appropriate use of computers. Catalyzing innovation, problem solving, and discovery.

The Second Edition provides experimenters with the scientific and statistical tools needed to maximize the knowledge gained from research data, illustrating how these tools may best be utilized during all stages of the investigative process.


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9.) All of Statistics: A Concise Course in Statistical Inference


Taken literally, the title “All of Statistics” is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly.

It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines.




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9.) A First Course in Machine Learning, Second Edition (Machine Learning & Pattern Recognition)


The book is the best introductory book for ML currently available. It combines rigor and precision with accessibility, starts from a detailed explanation of the basic foundations of Bayesian analysis in the simplest of settings, and goes all the way to the frontiers of the subject such as infinite mixture models, GPs, and MCMC.

The new edition of A First Course in Machine Learning by Rogers and Girolami is an excellent introduction to the use of statistical methods in machine learning. The book introduces concepts such as mathematical modeling, inference, and prediction, providing ‘just in time’ the essential background on linear algebra, calculus, and probability theory that the reader needs to understand these concepts.




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10.) Machine Learning: A Probabilistic Perspective by Kevin Murphy 


A comprehensive introduction to machine learning that uses probabilistic models and inference as a unifying approach. Today’s Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data.

This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning.




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11.) Naked Statistics — by Charles Wheelan


Once considered tedious, the field of statistics is rapidly evolving into a discipline Hal Varian, chief economist at Google, has actually called “sexy.” From batting averages and political polls to game shows and medical research, the real-world application of statistics continues to grow by leaps and bounds. 

For those who slept through Stats 101, this book is a lifesaver. Wheelan strips away the arcane and technical details and focuses on the underlying intuition that drives statistical analysis. He clarifies key concepts such as inference, correlation, and regression analysis, reveals how biased or careless parties can manipulate or misrepresent data.


Naked-Statistics — by-Charles-Wheelan


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12.) Innumeracy — by John Allen Paulos


This book covers a number of numerical fallacies and adds explanations, but often it feels like the explanation would come up short to anyone who really didn’t understand the particular issue being covered. I’m quite good with math myself so it was easy for me to follow everything, but parts of the book came off more as a “we smart people get why that’s so dumb

It goes through a large number of real-world examples of applied mathematics, that I (a retired engineer) had thought were like breathing out, breathing in.


Innumeracy — by-John-Allen-Paulos


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13.) Practical Statistics for Data Scientists — by Andrew & Peter Bruce


Statistical methods are a key part of data science, yet very few data scientists have any formal statistics training. Courses and books on basic statistics rarely cover the topic from a data science perspective. This practical guide explains how to apply various statistical methods to data science, tells you how to avoid their misuse and gives you advice on what’s important and what’s not.

Many data science resources incorporate statistical methods but lack a deeper statistical perspective. If you’re familiar with the R programming language and have some exposure to statistics, this quick reference bridges the gap in an accessible, readable format.


Practical-Statistics-for-Data-Scientists — by-Andrew-Peter-Bruce


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13.) Statistics in Plain English




This introductory textbook provides an inexpensive, brief overview of statistics to help readers gain a better understanding of how statistics work and how to interpret them correctly.

Each chapter describes a different statistical technique, ranging from basic concepts like central tendency and describing distributions to more advanced concepts such as t tests, regression, repeated measures ANOVA, and factor analysis.


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14.) Think Stats — by Allen B. Downey


If you know how to program, you have the skills to turn data into knowledge, using tools of probability and statistics. This concise introduction shows you how to perform statistical analysis computationally, rather than mathematically, with programs written in Python.

By working with a single case study throughout this thoroughly revised book, you’ll learn the entire process of exploratory data analysis—from collecting data and generating statistics to identifying patterns and testing hypotheses. You’ll explore distributions, rules of probability, visualization, and many other tools and concepts.


Think-Stats — by-Allen-B.-Downey


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14.) Empirical Methods for Artificial Intelligence




This book presents empirical methods for studying complex computer programs: exploratory tools to help find patterns in data, experiment designs and hypothesis-testing tools to help data speak convincingly, and modeling tools to help explain data.

Computer science and artificial intelligence in particular have no curriculum in research methods, as other sciences do.


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15.) Python for Data Analysis — McKinney

This book covers complete instructions for manipulating, processing, cleaning, and crunching datasets in Python. The second edition of this hands-on guide is packed with practical case studies that show you how to solve a broad set of data analysis problems effectively. Youíll learn the latest versions of pandas, NumPy, IPython, and Jupyter in the process.

Written by Wes McKinney, the creator of the Python pandas project, this book is a practical, modern introduction to data science tools in Python. It ís ideal for analysts new to Python and for Python programmers new to data science and scientific computing. Data files and related material are available on GitHub.


Python-for-Data-Analysis — McKinney


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Finishing up comments:

1. Aside from all the above books, I would not prescribe perusing the books cover to cover. I want to peruse the books by theme as required i.e. as a kind of perspective book.

2. I find that these books showed me a feeling of quietude i.e. How little we know and how immense and complex this field is.

3. These books are immortal.

4. It demonstrates the life span of the Maths based approach.



Start Understanding these books One by One. Perhaps, a $8-10 book can change your Career for eternity.

Books changed my life in recent years. I was forced to peruse books in my formal education and avoided from perusing books in my corporate activity.





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