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dair-ai/Mathematics-for-ML

Source: https://github.com/dair-ai/Mathematics-for-ML

Mathematics for Machine Learning

A collection of resources to learn and review mathematics for machine learning.

:book: Books

Algebra, Topology, Differential Calculus, and Optimization Theory For Computer Science and Machine Learning

by Jean Gallier and Jocelyn Quaintance

Includes mathematical concepts for machine learning and computer science.

Book: https://www.cis.upenn.edu/~jean/math-deep.pdf

Applied Math and Machine Learning Basics

by Ian Goodfellow and Yoshua Bengio and Aaron Courville

This includes the math basics for deep learning from the Deep Learning book.

Chapter: https://www.deeplearningbook.org/contents/part_basics.html

Mathematics for Machine Learning

by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong

This is probably the place you want to start. Start slowly and work on some examples. Pay close attention to the notation and get comfortable with it.

Book: https://mml-book.github.io

Probabilistic Machine Learning: An Introduction

by Kevin Patrick Murphy

This book contains a comprehensive overview of classical machine learning methods and the principles explaining them.

Book: https://probml.github.io/pml-book/book1.html

Mathematics for Deep Learning

by Brent Werness, Rachel Hu et al.

This reference contains some mathematical concepts to help build a better understanding of deep learning.

Chapter: https://d2l.ai/chapter_appendix-mathematics-for-deep-learning/index.html

The Mathematical Engineering of Deep Learning

by Benoit Liquet, Sarat Moka and Yoni Nazarathy

This book provides a complete and concise overview of the mathematical engineering of deep learning. In addition to overviewing deep learning foundations, the treatment includes convolutional neural networks, recurrent neural networks, transformers, generative adversarial networks, reinforcement learning, and multiple tricks of the trade. The focus is on the basic mathematical description of deep learning models, algorithms and methods.

Book: https://deeplearningmath.org

Bayes Rules! An Introduction to Applied Bayesian Modeling

by Alicia A. Johnson, Miles Q. Ott, Mine Dogucu

Great online book covering Bayesian approaches.

Book: https://www.bayesrulesbook.com/index.html

📄 Papers

The Matrix Calculus You Need For Deep Learning

by Terence Parr & Jeremy Howard

In deep learning, you need to understand a bunch of fundamental matrix operations. If you want to dive deep into the math of matrix calculus this is your guide.

Paper: https://arxiv.org/abs/1802.01528

The Mathematics of AI

by Gitta Kutyniok

An article summarising the importance of mathematics in deep learning research and how it’s helping to advance the field.

Paper: https://arxiv.org/pdf/2203.08890.pdf

🎥 Video Lectures

Multivariate Calculus by Imperial College London

by Dr. Sam Cooper & Dr. David Dye

Backpropagation is a key algorithm for training deep neural nets that rely on Calculus. Get familiar with concepts like chain rule, Jacobian, gradient descent.

Video Playlist: https://www.youtube.com/playlist?list=PLiiljHvN6z193BBzS0Ln8NnqQmzimTW23

Mathematics for Machine Learning - Linear Algebra

by Dr. Sam Cooper & Dr. David Dye

A great companion to the previous video lectures. Neural networks perform transformations on data and you need linear algebra to get better intuitions of how that is done.

Video Playlist: https://www.youtube.com/playlist?list=PLiiljHvN6z1_o1ztXTKWPrShrMrBLo5P3

CS229: Machine Learning

by Anand Avati

Lectures containing mathematical explanations to many concepts in machine learning.

Course: https://www.youtube.com/playlist?list=PLoROMvodv4rNH7qL6-efu_q2_bPuy0adh

🧮 Math Basics

The Elements of Statistical Learning

by Jerome H. Friedman, Robert Tibshirani, and Trevor Hastie

Machine learning deals with data and in turn uncertainty which is what statistics aims to teach. Get comfortable with topics like estimators, statistical significance, etc.

Book: https://hastie.su.domains/ElemStatLearn/

If you are interested in an introduction to statistical learning, then you might want to check out “An Introduction to Statistical Learning”.

Probability Theory: The Logic of Science

by E. T. Jaynes

In machine learning, we are interested in building probabilistic models and thus you will come across concepts from probability theory like conditional probability and different probability distributions.

Source: https://bayes.wustl.edu/etj/prob/book.pdf

Information Theory, Inference and Learning Algorithms

by David J. C. MacKay

When you are applying machine learning you are dealing with information processing which in essence relies on ideas from information theory such as entropy and KL Divergence,…

Book: https://www.inference.org.uk/itprnn/book.html

Statistics and probability

by Khan Academy

A complete overview of statistics and probability required for machine learning.

Course: https://www.khanacademy.org/math/statistics-probability

Linear Algebra Done Right

by Sheldon Axler

Slides and video lectures on the popular linear algebra book Linear Algebra Done Right.

Lecture and Slides: https://linear.axler.net/LADRvideos.html

Linear Algebra

by Khan Academy

Vectors, matrices, operations on them, dot & cross product, matrix multiplication etc. is essential for the most basic understanding of ML maths.

Course: https://www.khanacademy.org/math/linear-algebra

Calculus

by Khan Academy

Precalculus, Differential Calculus, Integral Calculus, Multivariate Calculus

Course: https://www.khanacademy.org/math/calculus-home

This collection is far from exhaustive but it should provide a good foundation to start learning some of the mathematical concepts used in machine learning. Reach out on Twitter if you have any questions.