Probabilistic Graphical Models & Gaussian Mixture Models

This repository summaries basic principles and technologies in Probabilistic Graphical Models and uses Gaussian Mixture Models as an example to illustrate these basic ideas. Comments and discussion are highly appreciated!

Notes of Probabilistic Graphical Models

• Representation
• Inference
• Learning

Learning & Inference in Gaussian Mixture Models Implemented in Python

with NumPy & SciPy:

• Maximize Likelihood Estimation by EM Algorithm
• Maximize Likelihood Estimation by Stochastic EM Algorithm
• Data Augmentation Algorithm
• Mean Field Variational Inference
• Gibbs Sampling
• Metropolis-Hastings Sampling

with PyTorch & Pyro:

• [PyTorch] Maximize Likelihood Estimation by Gradient Descent
• [PyTorch] Hamiltonian Monte Carlo
• [Pyro] Stochastic Variational Inference