Gaussian Mixture Models (GMM) Exploration Lab

Project Overview

This project implements a comprehensive analysis of Gaussian Mixture Models (GMMs) using Python and the scikit-learn library. The goal is to explore key properties of GMMs, including:

• Data Generation: Synthetic 2D datasets from multiple Gaussian components with configurable means, covariances, and mixing weights.
• Model Fitting: EM algorithm convergence via GaussianMixture.
• Parameter Estimation: Visualization of learned means, covariances, and component weights.
• Model Selection: BIC and AIC criteria for optimal number of components.
• Visualization: 2D contour plots with 95% confidence ellipses and ground-truth vs. predicted clustering.

Features

• Clean Project Structure: src/ for code, results/ for outputs, .venv/ isolated via uv.
• Modern Tooling:
  • Dependency management with uv
  • Code formatting with black
  • Environment reproducibility via pyproject.toml and uv.lock
• One-Click Execution: Run uv run python main.py to generate plots and save results.

Results Figure

Figure: Ground truth (left) vs. GMM fit using EM algorithm (right). Ellipses represent 2σ confidence regions.

---

Author: Zhixi Hu
Email: [email protected]
Python: 3.11 | Managed with: uv