Machine Learning, Mathematics
Some Maths Resources to Help You in Your ML Journey
I have been looking for content to improve my maths skills for ML. I have also noticed when scrolling a few threads many people did not find content that explains maths in an intuitive manner. Leading to a lack of belief in learning ML. But this does not have to be.
I’m with you, odd-looking characters and Greek letters don’t look welcoming. But they are some good teachers online that can demystify that experience.
Some of those materials are below:
General Maths Videos Series
3blue1brown Calculus and Linear Algebra series
I remember watching both of these series a while ago and I will be watching them again. The narrator explores the topic without getting bogged down in the details. Feels like you’re discovering the maths with the original people who made calculus. In the linear algebra series, he does such a great job visualising vector space. You can see the various operations done to vectors and matrices in picture form. Allowing you to understand the need of various operations and what they do.
I’m sure you know about Sal Kahn by now. As you watched a couple of his videos. His videos intuitively explain various topics. Also, show you the various hand-by-hand actions you need to take to do various calculations. Like matrix multiplication and calculating derivatives.
For maths topics relevant to ML check out:
The practice questions allow you to test your knowledge with quick feedback. This should help cement what you just learnt in the videos.
Understand Calculus in 35 Minutes — The Organic Chemistry Tutor
A general overview of the subject. So, you can be familiar with the concepts for deep learning later on. If you have no clue about calculus and don’t know where to start. Then video should be the one for you. As it’s only less than an hour and learn the gist of what calculus is. And take the knowledge into further study.
NOTE: you won’t learn all of calculus in 30 minutes. But the video will help you get accustomed to the main ideas of the subject.
Deep Learning Specific Maths
3blue1brown Deep Learning series
Taking the concepts from the previous series and applying them to deep learning. 3blue1brown does a wonderful job visualizing neural networks and explaining what they are.
An absolute beginner would find the series useful as it introduces what neural networks are. A more knowledgeable ML user may also find it helpful. It has an insightful way of showing fundamental concepts like gradient descent and Linear algebra used in a neural network.
Mathematics for Machine Learning book
I tend to use this book as a reference guide if it’s a concept I want to check out. This book goes through the most important subjects relevant to machine learning and goes in-depth.
Example of the notation page:
Mathematics for Machine Learning — Multivariate Calculus — Imperial College London
A multi-hour series explaining how calculus is used in deep learning. The material comes at the subject with a high-level view. But goes into sufficient enough detail to help you learn a lot. This series should spike your interest in learning calculus more thoroughly. Without getting lost in the details.
Other Noteworthy Materials
Now, these are resources that I have not used or have used very lightly but gotten good recommendations from various people.
So check them out:
This course teaches Linear algebra from a top-down perspective. Linear algebra in the context being used in real deep learning applications. While you learn maths, it won’t be as theory-heavy. So, you will be playing with a lot of code.
From their website:
[the course is] completely centered around practical applications and to use cutting edge algorithms and tools, including PyTorch, Numba, and randomized SVD. It also covers foundational numerical linear algebra concepts such as floating point arithmetic, machine epsilon, singular value decomposition, eigen decomposition, and QR decomposition.
This course talks about the linear algebra used in real computation. Not just Linear algebra done by hand.
…
A typical first linear algebra course focuses on how to solve matrix problems by hand, for instance, spending time using Gaussian Elimination with pencil and paper to solve a small system of equations manually. However, it turns out that the methods and concerns for solving larger matrix problems via a computer are often drastically different
NOTE: As the course was made a while ago. I don’t know if the code is still in-date. But the concepts still seem fine.
Deep Learning book by Ian Goodfellow and Yoshua Bengio and Aaron Courville
From their website:
The Deep Learning textbook is a resource intended to help students and practitioners enter the field of machine learning in general and deep learning in particular.
I have not thoroughly read all of the book. But I have used the notation page to understand maths symbols in various deep learning work.
These are experts in the deep learning field. Trust me, they know what they are talking about.
Ian Goodfellow, the creator of GANs.
Yoshua Bengio, one of the godfathers of deep learning.
An Introduction to Statistical Learning
A few people in the ML scene have recommended this book. Statistics is a pretty important topic. Helping you work out how to improve and analyse your datasets. So learning more about the topic should not hurt.
If you found this article interesting, then check out my mailing list. Where I write more stuff like this
