🧠 Machine Learning from Scratch

"What I cannot create, I do not understand." — Richard Feynman

Pure Python/NumPy implementations of fundamental Machine Learning, Deep Learning, and Reinforcement Learning algorithms — built without Scikit-Learn, PyTorch, or any black-box library. The goal is to understand what happens beneath the abstractions: how gradients are derived, why optimizers converge, and what the math actually looks like in code.

In quantitative finance and AI research, knowing why a cost function behaves a certain way — or how a Q-Learning agent converges to an optimal policy — matters as much as knowing how to call the right API. This repository is an exercise in that kind of understanding.

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📊 Visualizations

Decision Trees

Decision boundary visualization: the recursive algorithm partitioning the feature space to classify complex regions.

Numerical Optimization — Gradient Descent

Smooth convergence of the Log-Loss cost function, confirming that gradients were derived and implemented correctly.

Deep Learning — Neural Networks

A Multilayer Perceptron trained from scratch (manual backpropagation, chain rule) classifying Fashion-MNIST items.

K-Means

Geometric cluster separation using vectorized Euclidean distances — no loops, pure linear algebra.

Reinforcement Learning — Q-Learning

Agent reward evolution showing the transition from exploration (noisy early phase) to exploitation (stable optimal policy).

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🛠️ Repository Contents

Supervised Learning

• 01 Logistic Regression — Binary classification with Sigmoid activation and Gradient Descent optimization (Log-Loss)
• 02 Linear Regression — OLS (Ordinary Least Squares) and Gradient Descent for continuous prediction
• 03 Decision Trees — Recursive CART/ID3 implementation with manual information gain and impurity computation

Unsupervised Learning

• 04 K-Means Clustering — Iterative Expectation-Maximization with fully vectorized distance computation

Deep Learning & NLP

• 05 Sentiment Analysis — Basic NLP pipeline for text classification, built from scratch
• 07 Neural Networks — MLP with manual backpropagation (chain rule) and configurable activation functions

Confusion matrix for sentiment classification

Applied AI Systems

• 06 Recommender System — Collaborative filtering / matrix factorization without black-box libraries
• 08 Reinforcement Learning — Q-Learning agent navigating a controlled environment via Bellman equations

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📐 The Mathematical Engine

The focus throughout is on deriving gradients correctly rather than relying on autodiff. Example for Logistic Regression:

Cost function (Log-Loss):

$$ J(\theta) = - \frac{1}{m} \sum_{i=1}^{m} [y^{(i)}\log(h_\theta(x^{(i)})) + (1 - y^{(i)})\log(1 - h_\theta(x^{(i)}))] $$

Vectorized gradient for weight update:

$$ \frac{\partial J(\theta)}{\partial \theta} = \frac{1}{m} X^T (h_\theta(X) - y) $$

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🚀 Getting Started

Minimal dependencies — only numpy for computation and matplotlib/pandas for data and plotting.

# Clone the repository
git clone https://github.com/cockles98/machine-learning-from-scratch.git

# Install dependencies
pip install numpy pandas matplotlib jupyter

# Run the notebooks
jupyter notebook

Open the numbered files (01_..., 02_...) to follow each implementation step by step.