Higher-Order Langevin Monte Carlo Algorithms

This repository contains the implementation and experimental evaluation of generalized Higher-Order Langevin Monte Carlo (HoLMC) algorithms for Bayesian inference. We focus on third- and fourth-order underdamped Langevin samplers and demonstrate their performance in both regression and classification tasks using real-world datasets.

The implementation is done by creating a Python package called holmc. The package is modular and reproducible, with symbolic derivations, numerical validation, and Wasserstein-2 distance–based performance evaluation. All code, figures, and notebooks are included for easy experimentation and extension.

Installation

To set up the environment and install dependencies:

1. Create a virtual environment:

python3 -m venv holmc_env

2. Activate the environment:

On macOS/Linux:

source holmc_env/bin/activate

On Windows:

holmc_env\Scripts\activate

3. Install required packages:

pip install -r requirements.txt
pip install -e .

4. (Optional) Create a new Jupyter kernel:

python -m ipykernel install --user --name=holmc_env --display-name "holmc_env"

Project Structure

.
├── docs/                   # Symbolic derivations (MATLAB, Mathematica, Jupyter)
├── experiments/            # Regression and classification notebooks
├── holmc/                  # Core package (samplers, utils, metrics)
├── requirements.txt        # Python dependencies
├── setup.py                # Package setup script
├── pyproject.toml          # Build configuration
├── README.md               # This file
└── LICENSE                 # License information

Citation

This repository contains the official implementation for the methods and experiments described in our forthcoming journal publication:

Higher-Order Langevin Monte Carlo Algorithms, by T.L. Dang, M. Gürbüzbalaban, M. R. Islam, N. Yao and L. Zhu

A full citation will be added upon publication.

If you use this code in your work, please cite this repository as:

@misc{islam2025holmc,
  author       = {Rafiq Islam},
  title        = {Codebase for Higher-Order Langevin Monte Carlo Algorithms},
  year         = {2025},
  howpublished = {\url{https://github.com/rispace/higher-order-Langevin-dynamics}}
}

License

This project is licensed under the MIT License. See the LICENSE file for details.