Graphical Models and Probabilistic Inference Projects

This repository presents three mini-projects in graphical models

The projects focus on:

• latent-variable sequence modeling
• exact and approximate inference
• message passing on graphical models
• numerical stability in probabilistic computation

Featured Projects

1. Mixture of Markov Chains with EM

A latent-variable model for identifying hidden weather stations from observed symbolic sequences.
This project implements a 3-component mixture of first-order Markov chains and estimates the model using the Expectation-Maximization (EM) algorithm. The implementation highlights non-convex optimization, initialization sensitivity, log-domain likelihood computation, and smoothing for stable estimation.

Keywords: EM, latent variables, sequence modeling, Markov chains, numerical stability

2. Exact Inference vs Mean Field vs Gibbs Sampling

A comparative study of exact and approximate inference on a binary lattice model.
This project contrasts transfer-matrix-based exact inference, fully factorized mean field, and checkerboard Gibbs sampling, with particular attention to symmetry breaking and mixing behavior under different coupling strengths.

Keywords: exact inference, variational inference, Gibbs sampling, Ising model, approximation error

3. LDPC Decoding with Loopy Belief Propagation

A factor-graph-based implementation of LDPC decoding.
This project constructs a systematic generator matrix and performs log-domain loopy belief propagation for decoding under noisy observations.

Keywords: factor graphs, belief propagation, LDPC, message passing, probabilistic decoding

Why this repository

Rather than presenting raw coursework chronologically, this repository reorganizes the material around methodological themes that are central to probabilistic machine learning:

• latent-variable estimation
• approximate inference
• structured probabilistic computation

Repository Structure

• weather-stations-em/: EM for a mixture of Markov chains
• exact-vs-approx-inference/: exact inference, mean field, and Gibbs sampling
• ldpc-belief-propagation/: belief propagation for LDPC decoding

Reproducibility

Each subproject contains:

• a short project-specific README
• a cleaned notebook
• project-specific code, outputs, and supporting materials where applicable

Install dependencies with:

pip install -r requirements.txt