Notes, examples, and Python demos for the textbook "Machine Learning Refined" (published by Cambridge University Press).
Learn machine learning from the ground up - using Python and a handful of fundamental tools.
This repository contains a range of resources associated with the 2nd edition of the university textbook Machine Learning Refined. Our pedagogical approach stresses intuition, visualization, and “getting your hands dirty” building real machine learning models from scratch. The only technical prerequisites is a basic understanding of Python and matrix maths.
Are you an independent learner aiming to build a solid foundation in machine learning?
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When you’re ready - follow our installation instructions to run the notes locally or get started on a range of exercises. Always feel free to reach out to us with questions by filing an issue in this repository. A physical copy of the text may be procured via online retailers like these.
Are you an instructor looking use the text in an upcoming course? You’re in good company!.
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Instructor requests are most easily answered by filing an issue in this repository.
Verified college and university instructors may request a free physical copy of the text for examination via the publisher’s website.
We believe mastery of a machine learning concept/topic is achieved only when the answer to each of the following three questions is affirmative.
Intuition Can you describe the idea with a simple picture?Mathematical derivation Can you express your intuition in mathematical notation and derive underlying models/cost functions?Implementation Can you code up your derivations in a programming language, say Python, without using high-level libraries?We wrote our text with the aim of empowering readers to grasp the concepts of classic machine learning at this high standard.
Early drafts of the 2nd edition were released as Jupyter / Collab notebooks and are shared below.
While these allow for interesting and unique interactivity, the final draft significantly expands on this content and is available for download as a PDF here.
1.1 Introduction
1.2 Distinguishing Cats from Dogs: a Machine Learning Approach
1.3 The Basic Taxonomy of Machine Learning Problems
1.4 Mathematical Optimization
1.5 Conclusion
2.1 Introduction 
\
2.2 The Zero-Order Optimality Condition \
2.3 Global Optimization Methods \
2.4 Local Optimization Methods \
2.5 Random Search \
2.6 Coordinate Search and Descent \
2.7 Conclusion
2.8 Exercises
3.1 Introduction \
3.2 The First-Order Optimality Condition \
3.3 The Geometry of First-Order Taylor Series \
3.4 Computing Gradients Efficiently
3.5 Gradient Descent \
3.6 Two Natural Weaknesses of Gradient Descent \
3.7 Conclusion
3.8 Exercises
4.1 The Second-Order Optimality Condition \
4.2 The Geometry of Second-Order Taylor Series \
4.3 Newton’s Method \
4.4 Two Natural Weaknesses of Newton’s Method \
4.5 Conclusion
4.6 Exercises
5.1 Introduction
5.2 Least Squares Linear Regression \
5.3 Least Absolute Deviations \
5.4 Regression Quality Metrics \
5.5 Weighted Regression \
5.6 Multi-Output Regression \
5.7 Conclusion
5.8 Exercises
5.9 Endnotes: Probabilistic interpretation of linear regression \
6.1 Introduction
6.2 Logistic Regression and the Cross Entropy Cost \
6.3 Logistic Regression and the Softmax Cost \
6.4 The Perceptron \
6.5 Support Vector Machines \
6.6 Which Approach Produces the Best Results? \
6.7 The Categorical Cross Entropy Cost \
6.8 Classification Quality Metrics \
6.9 Weighted Two-Class Classification \
6.10 Conclusion
6.11 Exercises
7.1 Introduction
7.2 One-versus-All Multi-Class Classification \
7.3 Multi-Class Classification and the Perceptron \
7.4 Which Approach Produces the Best Results? \
7.5 The Categorical Cross Entropy Cost Function \
7.6 Classification Quality Metrics \
7.7 Weighted Multi-Class Classification
7.8 Stochastic and Mini-Batch Learning \
7.9 Conclusion
7.10 Exercises
8.1 Introduction
8.2 Fixed Spanning Sets, Orthonormality, and Projections \
8.3 The Linear Autoencoder and Principal Component Analysis \
8.4 Recommender Systems \
8.5 K-Means Clustering \
8.6 General Matrix Factorization Techniques \
8.7 Conclusion
8.8 Exercises
8.9 Endnotes
9.1 Introduction
9.2 Histogram Features \
9.3 Feature Scaling via Standard Normalization \
9.4 Imputing Missing Values in a Dataset \
9.5 Feature Scaling via PCA-Sphering \
9.6 Feature Selection via Boosting \
9.7 Feature Selection via Regularization \
9.8 Conclusion
9.9 Exercises
10.1 Introduction \ \
10.2 Nonlinear Regression \
10.3 Nonlinear Multi-Output Regression \
10.4 Nonlinear Two-Class Classification \
10.5 Nonlinear Multi-Class Classification \
10.6 Nonlinear Unsupervised Learning \
10.7 Conclusion
10.8 Exercises
11.1 Introduction \
11.2 Universal Approximators \
11.3 Universal Approximation of Real Data \
11.4 Naive Cross-Validation \
11.5 Efficient Cross-Validation via Boosting \
11.6 Efficient Cross-Validation via Regularization \
11.7 Testing Data
11.8 Which Universal Approximator Works Best in Practice?
11.9 Bagging Cross-Validated Models \
11.10 K-Fold Cross-Validation \
11.11 When Feature Learning Fails
11.12 Conclusion
11.13 Exercises
12.1 Introduction
12.2 Fixed-Shape Universal Approximators
12.3 The Kernel Trick
12.4 Kernels as Measures of Similarity
12.5 Optimization of Kernelized Models
12.6 Cross-Validating Kernelized Learners
12.7 Conclusion
12.8 Exercises
13.1 Introduction
13.2 Fully Connected Neural Networks \
13.3 Activation Functions \
13.4 The Backpropagation Algorithm
13.5 Optimization of Neural Network Models \
13.6 Batch Normalization \
13.7 Cross-Validation via Early Stopping \
13.8 Conclusion
13.9 Exercises
14.1 Introduction
14.2 From Stumps to Deep Trees
14.3 Regression Trees
14.4 Classification Trees
14.5 Gradient Boosting
14.6 Random Forests
14.7 Cross-Validation Techniques for Recursively Defined Trees
14.8 Conclusion
14.9 Exercises
A.1 Introduction
A.2 Momentum-Accelerated Gradient Descent \
A.3 Normalized Gradient Descent \
A.4 Advanced Gradient-Based Methods \
A.5 Mini-Batch Optimization \
A.6 Conservative Steplength Rules \
A.7 General Steepest Descent \
A.8 Newton’s Method, Regularization, and Nonconvex Functions \
A.9 Hessian-Free Methods
B.1 Introduction
B.2 The Derivative
B.3 Derivative Rules for Elementary Functions and Operations
B.4 The Gradient
B.5 The Computation Graph
B.6 The Forward Mode of Automatic Differentiation
B.7 The Reverse Mode of Automatic Differentiation
B.8 Higher-Order Derivatives
B.9 Taylor Series
B.10 Using the autograd Library
C.1 Introduction
C.2 Vectors and Vector Operations \
C.3 Matrices and Matrix Operations \
C.4 Eigenvalues and Eigenvectors \
C.5 Vector and Matrix Norms
Example ”roadmaps” shown below provide suggested paths
for navigating the text based on a variety of learning outcomes and university
courses taught using the present book.
To make full use of the text one needs only a basic understanding of vector algebra (mathematical
functions, vector arithmetic, etc.) and computer programming (for example,
basic proficiency with a dynamically typed language like Python). We provide
complete introductory treatments of other prerequisite topics including linear
algebra, vector calculus, and automatic differentiation in the appendices of the
text.
The majority of the notes and exercise wrappers in this repository can be run without the need to install anything locally - for free on Google Collab. Click the Collab sticker at the top of a notebook to open it in Collab.
After cloning this repository and entering the directory we recommend one of three methods for successfully running the Jupyter notebooks contained therein.
After installing docker and docker-compose on your machine
traverse to this repo at your terminal and type
docker-compose up -d
When running this command the first time an associated docker image is pulled from DockerHub.
Then in any web browser go to
localhost:8888
to view the repository contents - including jupyter notebooks.
After installing Anaconda Python 3 distribution on your machine, cd into this repo’s directory and follow these steps to create a conda virtual environment to view its contents and notebooks. Python 3.10 and up is required.
First, create the environment
conda create python=3.10 --name mlr2 --file requirements.txt
Then activate it
conda activate mlr2
Run jupyter via the command below
jupyter notebook --port=8888 --ip=0.0.0.0 --allow-root --NotebookApp.token=''
And finally, open any web browser and traverse to
localhost:8888
to view the repository contents - including jupyter notebooks.
Using Python 3.10 or above and pip or uv on your machine, cd into this repo’s directory and follow these steps to install the required packages.
First create a virtual environment and activate it - for example with uv
uv venv --python 3.10.0 && source .venv/bin/activate
Then install Python requirements
uv pip install -r requirements.txt
Run jupyter via the command below
jupyter notebook --port=8888 --ip=0.0.0.0 --allow-root --NotebookApp.token=''
And finally, open any web browser and traverse to
localhost:8888
to view the repository contents - including jupyter notebooks.
An excellent book that treats the fundamentals of machine learning from basic principles to practical implementation. The book is suitable as a text for senior-level and first-year graduate courses in engineering and computer science. It is well organized and covers basic concepts and algorithms in mathematical optimization methods, linear learning, and nonlinear learning techniques. The book is nicely illustrated in multiple colors and contains numerous examples and coding exercises using Python.
John G. Proakis, University of California, San Diego
Some machine learning books cover only programming aspects, often relying on outdated software tools; some focus exclusively on neural networks; others, solely on theoretical foundations; and yet more books detail advanced topics for the specialist. This fully revised and expanded text provides a broad and accessible introduction to machine learning for engineering and computer science students. The presentation builds on first principles and geometric intuition, while offering real-world examples, commented implementations in Python, and computational exercises. I expect this book to become a key resource for students and researchers.
Osvaldo Simeone, King’s College, London
This book is great for getting started in machine learning. It builds up the tools of the trade from first principles, provides lots of examples, and explains one thing at a time at a steady pace. The level of detail and runnable code show what’s really going when we run a learning algorithm.
David Duvenaud, University of Toronto
This book covers various essential machine learning methods (e.g., regression, classification, clustering, dimensionality reduction, and deep learning) from a unified mathematical perspective of seeking the optimal model parameters that minimize a cost function. Every method is explained in a comprehensive, intuitive way, and mathematical understanding is aided and enhanced with many geometric illustrations and elegant Python implementations.
Kimiaki Sihrahama, Kindai University, Japan
Books featuring machine learning are many, but those which are simple, intuitive, and yet theoretical are extraordinary ‘outliers’. This book is a fantastic and easy way to launch yourself into the exciting world of machine learning, grasp its core concepts, and code them up in Python or Matlab. It was my inspiring guide in preparing my ‘Machine Learning Blinks’ on my BASIRA YouTube channel for both undergraduate and graduate levels.
Islem Rekik, Director of the Brain And SIgnal Research and Analysis (BASIRA) Laboratory
You’ll find a large number of intuitive animations in the notes of this repository.
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| Cross-validation (regression) | Cross-validation (two-class classification) | Cross-validation (multi-class classification) |
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| K-means clustering | Feature normalization | Normalized gradient descent |
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| Rotation | Convexification | Dogification! |
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| A nonlinear transformation | Weighted classification | The moving average |
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| Batch normalization | Logistic regression |
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| Polynomials vs. NNs vs. Trees (regression) | Polynomials vs. NNs vs. Trees (classification) |
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| Changing gradient descent’s steplength (1d) | Changing gradient descent’s steplength (2d) |
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| Convex combination of two functions | Taylor series approximation |
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| Feature selection via regularization | Secant planes |
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| Function approximation with a neural network | A regression tree |