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Mathematics for Machine Learning
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
398 pages, Hardcover
Published February 29, 2020
257 people are currently reading
1554 people want to read
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Displaying 1 - 30 of 33 reviews
April 28, 2021
Remarkable!
I don't treat this one as an introductory book, but rather a "refresher" on the mathematics required for machine learning. Most of the book was a delight to read, I liked the slow building up of ideas in first chapters such as vector spaces, linear independence, basis, rank, linear mapping, inner products, orthogonality, .., etc. to the point that you become comfortable with them when used in more complex chapters, even if you had little or no background on such topics.
There were so many "Wow!"(s) moments, like geometrical interpretation of singular value decomposition, treating correlation as an inner product between two random variables, principal components as the eigenvalues and eigenvectors of data covariance matrix, latent variable perspective and many more..
Not to mention the amazing formatting, beautiful LaTeX and gorgeous figures that made me envious sometimes, for example:
Yet, some parts were not easy to grasp (or I completely skipped, like dual Lagrange optimization), and the Probability and Distributions chapter will be very hard to read without prior "wink ;)" knowledge on probability.
In general I really liked it and very much recommend it!
I don't treat this one as an introductory book, but rather a "refresher" on the mathematics required for machine learning. Most of the book was a delight to read, I liked the slow building up of ideas in first chapters such as vector spaces, linear independence, basis, rank, linear mapping, inner products, orthogonality, .., etc. to the point that you become comfortable with them when used in more complex chapters, even if you had little or no background on such topics.
There were so many "Wow!"(s) moments, like geometrical interpretation of singular value decomposition, treating correlation as an inner product between two random variables, principal components as the eigenvalues and eigenvectors of data covariance matrix, latent variable perspective and many more..
Not to mention the amazing formatting, beautiful LaTeX and gorgeous figures that made me envious sometimes, for example:
Yet, some parts were not easy to grasp (or I completely skipped, like dual Lagrange optimization), and the Probability and Distributions chapter will be very hard to read without prior "wink ;)" knowledge on probability.
In general I really liked it and very much recommend it!
October 12, 2018
I'm so intimidated by the enormous amount of terms and symbols, and couldn't say it's a beginner friendly book. So i'm gonna let go of this and try other books
September 23, 2022
1. Why read this?
This work gives you bottom-up approach to Machine Learning
2. What is inside of this?
1. Introduction
2. Linear Algebra
3. Analytical Geometry
4. Matrix Decomposition
5. Vector Calculus
6. Probability & Distribution
7. Continuous Optimization
8. Machine Learning Problems
8.a Empirical Risk Minimization et al
9. Linear Regression
10. Dimension Reduction
11. Density Estimation
12. SVM
3. What are my thoughts on this?
This is a detailed, bottom-up approach work.
I'd suggest going through this couple of times, to understand.
I was able to gain insights into few topics, where I had gaps of knowledge.
I'd have to read this multiple times, to help me further my understanding.
How each topic is connected to each other gives me visual understanding
Notes from this work
Deus Vult
Gottfried
This work gives you bottom-up approach to Machine Learning
2. What is inside of this?
1. Introduction
2. Linear Algebra
3. Analytical Geometry
4. Matrix Decomposition
5. Vector Calculus
6. Probability & Distribution
7. Continuous Optimization
8. Machine Learning Problems
8.a Empirical Risk Minimization et al
9. Linear Regression
10. Dimension Reduction
11. Density Estimation
12. SVM
3. What are my thoughts on this?
This is a detailed, bottom-up approach work.
I'd suggest going through this couple of times, to understand.
I was able to gain insights into few topics, where I had gaps of knowledge.
I'd have to read this multiple times, to help me further my understanding.
How each topic is connected to each other gives me visual understanding
Notes from this work
Deus Vult
Gottfried
April 29, 2020
Brilliant and Precise
The book is the missing piece between books like Artificial Intelligence: A Modern Approach and mathematics. It is recommended that you've had exposure to the mathematical topics prior to reading the book, but let that stop you if you're a beginner. Having said that, a course on single variable calculus ought to be under your belt.
The book is the missing piece between books like Artificial Intelligence: A Modern Approach and mathematics. It is recommended that you've had exposure to the mathematical topics prior to reading the book, but let that stop you if you're a beginner. Having said that, a course on single variable calculus ought to be under your belt.
May 16, 2022
Just got it finished for university,and if it's not for bunch of YouTube teachers having my back i would have never understood the concepts and the way it's explained in this book. It's definitely not a beginner friendly maybe i would go back to it one day,who knows.
What i know now is that i need to pass this damn subject ,hell yeah.
What i know now is that i need to pass this damn subject ,hell yeah.
December 7, 2020
If there is a book to start your machine learning journey the right way, whether you are a mathematics or computer science student, this would be it.
A piece of advice: I would not recommend reading this book if you did not have exposure to calculus, introductory linear algebra and probability theory. You should view the first part of the book as a quick refresher, and not as an introduction to these subjects.
A piece of advice: I would not recommend reading this book if you did not have exposure to calculus, introductory linear algebra and probability theory. You should view the first part of the book as a quick refresher, and not as an introduction to these subjects.
July 7, 2021
Ideal as a reference for machine learning practitioners. Basic familiarity with the topics is recommended (otherwise, it is pretty dense), though a good book to identify gaps in one's knowledge. Also useful for general scientists who want to reorient into mathematical modelling.
August 24, 2022
Good refresher on mathematics for ML and how they relate to ML applications. Definitely not a great way to learn the material for the first time, but good if you've read other books on mathematics and ML tools and want to get a better understanding of how they come together.
September 15, 2021
I loved this book, and how it is written. I have strong mathematical background, so the initial chapters were rather unnecessary, although I read them and I really enjoyed re-learning some mathematical details with some intuition I had lost. Then, the machine learning examples, including regression and Bayesian perspectives, is really good and complete, and it is really helpful to have a strong basis on the mathematics behind most popular models. Usually people that use these models don't stop to think on these details, but once you get them, you have a better perspective of what the models are doing. Also, pictures and examples are very nice.
In summary, it is a good book, gives strong mathematical and Bayesian perspective, good basis to explain how models work to others, but the initial chapters are too hard for someone without mathematical background, and at the same time, they are sometimes dull for someone that already knows them. Specially because it hops from very basic stuff in linear algebra, to complex optimization results. They are definitely not for someone that do not know them previously.
In summary, it is a good book, gives strong mathematical and Bayesian perspective, good basis to explain how models work to others, but the initial chapters are too hard for someone without mathematical background, and at the same time, they are sometimes dull for someone that already knows them. Specially because it hops from very basic stuff in linear algebra, to complex optimization results. They are definitely not for someone that do not know them previously.
November 20, 2024
*** Second read***
The first time I read this I thought it was too terse/uncomprehensive but this second time around I found it particularly helpful. Initially the LA material is a bit too light but as you get to the Eigenstuff it improves vastly. I also really enjoyed the later chapters on linear regression (max likelihood, max a posteriori, and Bayesian approaches), on support vector machines (they have a nice derivation of the dual optimisation problem), and lastly on gaussian mixture models. Can highly recommend this as a supplement to other ML textbooks.
*** First read***
Not a fan. Didn’t like the notation and on top of that they barely proved any theorems. Felt like I was mindlessly going through a long chain of meaningless theorem. Personally think that the only way to learn this stuff properly is by doing a deep dive into linear algebra (Axler’s Linear Algebra Done Right or MIT OCW), multi-variable calculus (MIT OCW), probability theory (Ross?) and a proper ML textbook like Bishop’s Pattern Recognition and Machine Learning.
The first time I read this I thought it was too terse/uncomprehensive but this second time around I found it particularly helpful. Initially the LA material is a bit too light but as you get to the Eigenstuff it improves vastly. I also really enjoyed the later chapters on linear regression (max likelihood, max a posteriori, and Bayesian approaches), on support vector machines (they have a nice derivation of the dual optimisation problem), and lastly on gaussian mixture models. Can highly recommend this as a supplement to other ML textbooks.
*** First read***
Not a fan. Didn’t like the notation and on top of that they barely proved any theorems. Felt like I was mindlessly going through a long chain of meaningless theorem. Personally think that the only way to learn this stuff properly is by doing a deep dive into linear algebra (Axler’s Linear Algebra Done Right or MIT OCW), multi-variable calculus (MIT OCW), probability theory (Ross?) and a proper ML textbook like Bishop’s Pattern Recognition and Machine Learning.
May 9, 2022
This text is crucial for mathematical intuition mental-building for machine learning. Though concepts like linear algebra, probability theory, statistics, calculus and other fundamental math concepts need to be understood before you touch this book; for novices. (Otherwise this text will be a tough read, if you comprehend anything from it at all later absconding that precept.)
Nonetheless, for the concepts you're well prepared for; this book explains them dutifully and diligently.
Nonetheless, for the concepts you're well prepared for; this book explains them dutifully and diligently.
January 24, 2019
Very difficult mathematics book. However, I feel like I came out the other side with some new mathemetical skills in my toolbox and a better understanding of the theory behind many machine learning algrorithms. However, this book is definitely a very tough read.
January 4, 2021
Perfect and free, what else do you want?
June 26, 2021
An incredibly useful collection of—not just methods—but explanations, context and motivation for modern machine learning, accessible to advanced undergraduate and beginning graduate level.
May 11, 2024
Lots of helpful content & very dense.
July 1, 2023
This is my favorite playbook on machine learning, and here's why. Recently, we were told at the machine learning specialization: "Do not bother if you don't understand any of the mathematics on the slides — you will not need it to do the practice labs". Perhaps, the trick works for the younger students who love lullabies, but I find it very strange because I have a different world view.
In fact, the reason I do math is that I need to understand what happens under the hood of all the AI bricks to be able to write a code for a real-world problem that would match a very complex system, such as a deep neural network. When I was reading this book, I have not just refreshed my linalg but also have got on track with the modern concepts in mathematics and found if very useful.
No matter how talented you are, you cannot build the next big thing without this hardcore fundamentals. And, by the way, I had 100/100 of points in my specialization thanks to this book.
In fact, the reason I do math is that I need to understand what happens under the hood of all the AI bricks to be able to write a code for a real-world problem that would match a very complex system, such as a deep neural network. When I was reading this book, I have not just refreshed my linalg but also have got on track with the modern concepts in mathematics and found if very useful.
No matter how talented you are, you cannot build the next big thing without this hardcore fundamentals. And, by the way, I had 100/100 of points in my specialization thanks to this book.
May 2, 2022
The book covers a lot of different topics in machine learning and math. The machine learning methods are mostly the traditional ones and there is no chapter for neural nets and deep learning and the authors are upfront about that. Nonetheless, the background math that the authors provide in this book is very useful.
P.S. I started a book club to read this book, and I think that is what kept me reading. I believe this is the first text book that I read completely, and I highly suggest to read not only this book but other reference books in groups.
P.S. I started a book club to read this book, and I think that is what kept me reading. I believe this is the first text book that I read completely, and I highly suggest to read not only this book but other reference books in groups.
Currently reading
May 30, 2021I'm half way through this book. It gives a very nice bird-eye overview of the main mathematical pillars often used in machine learning. Each chapter moves very fast and serves more as a dense summary of the main concepts rather than an introductory read. Overall, it’s a very helpful text for someone looking for an overview of what background knowledge is needed to understand the machine learning literature or a review for those who have had prior exposure to these topics.
April 24, 2021
I've been working as an engineer with data scientists for several years. Aurelien Geron's book is essential if you're new to the field. I picked this up to get a better understanding of the math behind some ML approaches. It does a good job connecting the dots between the various areas of math and ML problems.
August 31, 2021
3.5/5 stars, rounded up. The earlier parts on the core concepts of mathematics for ML are better seen as a refresher than as a stand-alone introduction. The latter chapters, however, make good use of the toolset introduced in Chapters 1-7 by showing how one can arrive at classical machine learning models, thus understanding their properties and shortcomings.
October 3, 2024
من افضل الكتب لتعلم الرياضيات في مجال الـML ، الكتاب يجمع لك الاحصاء و الاحتمالات و الجبر الخطي و التفاضل و التكامل في مكان واحد لكنه غير موجه للمبتدئين، لذلك لو قررت تقرأه حط في بالك انك راح تضطر تراجع المفاهيم الاساسية لفروع الرياضيات الي يتناولها الكتاب ، ايضا الكتاب معتمد على كورس الجبر الخطي من MIT لقيلبرت سترانق وهو الافضل في مجاله 🙏🏻
August 17, 2022
Nice exposition of mathematics required for machine learning.
September 12, 2022
They've done an amazing job bridging undergraduate mathematics with graduate level machine learning
September 13, 2022
Very useful for everyone who is interested in machine learning. However two or three of the formulas were transcribed incorrectly.
December 24, 2022
A well structured summary/recap for most of the underlying maths that you’ll need in a DS role. I found some of the non-standard used notations to be unnecessarily confusing.
August 13, 2025
Read for a project. Proud that I understood all of the math in this.
December 29, 2020
A must read for beginners in machine learning!
July 12, 2025
A modern theoretical book on collated mathematics with further reading section at the end of each chapter.
There is a strong negative correlation, in my experience, between books of similar genre and entertainment, but this book seemed to add quite a bit of positivity - maybe because most of it seemed like a refresher. Certain topics (such as calculus on matrices, tensors and density functions) gave me a hard time when I first studied them, and they haven't been any easier this time either. Visualisation helps.
Appreciate the authors for hosting the companion webpage for shameless people like myself.
There is a strong negative correlation, in my experience, between books of similar genre and entertainment, but this book seemed to add quite a bit of positivity - maybe because most of it seemed like a refresher. Certain topics (such as calculus on matrices, tensors and density functions) gave me a hard time when I first studied them, and they haven't been any easier this time either. Visualisation helps.
Appreciate the authors for hosting the companion webpage for shameless people like myself.
January 5, 2019
awesome
Displaying 1 - 30 of 33 reviews