ML Repository: In-depth Analysis of Core Machine Learning Concepts and Mathematical Principles

davidterroso's ML open-source project focuses on in-depth analysis of core machine learning concepts and mathematical principles, aiming to address the learning pitfalls of beginners who "know the what but not the why" (such as inability to diagnose model issues, difficulty customizing algorithms, etc.). The project covers a complete learning path from basic algorithms to advanced topics, helping to build a solid theoretical foundation and distinguish between machine learning engineers and tool users.

• Original author/maintainer: davidterroso
• Source platform: GitHub
• Original title: ML
• Original link: https://github.com/davidterroso/ML
• Update time: 2026-05-28T22:15:29Z

The project covers multiple core topics, forming a systematic learning path:

Supervised Learning Basics

Linear regression (least squares method, gradient descent, etc.), logistic regression (cross-entropy loss, Softmax), support vector machines (maximum margin, kernel methods)

Unsupervised Learning

Clustering (K-means, GMM, EM algorithm), dimensionality reduction (PCA, t-SNE, autoencoders)

Probability and Statistics Basics

Probability theory (Bayes' theorem, common distributions), estimation theory (MLE/MAP, information theory)

Optimization Theory

Convex optimization (gradient descent, adaptive optimizers), constrained optimization (Lagrange multipliers, KKT conditions)

Advanced Topics

Decision trees and ensemble learning (random forests, GBDT), neural network basics (backpropagation, regularization), deep learning extensions (CNN, RNN, Transformer)

Learners need to be familiar with the following mathematical tools: Linear Algebra: Vector/matrix operations, eigenvalue decomposition, orthogonal projection Calculus: Multivariate gradients, Hessian matrix, chain rule Probability and Statistics: Probability distributions, expectation, Bayesian inference The project uses a standard mathematical symbol system to ensure the rigor and consistency of derivations.

Learning paths are provided for readers with different backgrounds:

• Those with weak mathematical foundations: First supplement linear algebra (3Blue1Brown videos), calculus, and probability theory, then gradually read the project content
• Those with programming experience but weak theory: Reverse learning (select familiar algorithms → derivation → implementation from scratch → comparison)
• Those with mathematical foundations: Systematically learn in the project's order (topic reading + practice + code implementation + paper comparison)

The project helps build the connection between theory and practice:

• Hyperparameter understanding: Learning rate (convergence speed), regularization coefficient (bias-variance trade-off), kernel function parameters (feature complexity)
• Model diagnosis: Overfitting (complexity vs. data volume), underfitting (insufficient capacity), gradient vanishing/explosion (activation functions and initialization)
• Algorithm selection: Data scale (time complexity), feature type (continuous/discrete), problem nature (convex/non-convex optimization)

Resource Type	Representative	Advantages	Limitations
Online course	Coursera ML course	Systematic, with exercises	Limited mathematical depth
Textbook	Statistical Learning Methods	Comprehensive, rigorous	Long length, high threshold
Code tutorial	scikit-learn documentation	Practical, easy to get started	Lack of theoretical depth
This project	davidterroso/ML	Moderate mathematical depth	Requires certain mathematical foundations
This project is positioned between theory and practice, suitable for learners who want to deeply understand the principles.

Summary: The ML Repository fills the key link of mathematical principles in machine learning education, helping learners master stable underlying principles and cultivate independent analysis abilities, which is a necessary path for excellent engineers. Extended Directions:

• Classic textbooks: Pattern Recognition and Machine Learning, Deep Learning
• Specialized in-depth: Convex optimization (Boyd), probabilistic graphical models (Koller), reinforcement learning (Sutton)
• Cutting-edge directions: Causal inference, Bayesian deep learning, Neural Tangent Kernel (NTK)