SNL Directional

Self-normalized likelihood for directional statistics -- density estimation on spheres and tori.

Overview

This repository applies the self-normalized likelihood (SNL) framework to directional distributions, where the normalisation constant is particularly challenging to compute. It includes implementations and experiments for:

• Von Mises distributions (circular data)
• Von Mises-Fisher distributions (spherical data, 2D and 3D)
• Kent distributions (spherical data with anisotropy)
• Bivariate sine von Mises distributions (toroidal data)
• Truncated Gaussians and mixtures
• Application to protein dihedral angles

Related paper: "Learning Energy-Based Models by Self-normalising the Likelihood" (TMLR 2026) [paper]

Structure

SNLDirectional/       # Core package (models, distributions, training)
Data/                 # Datasets (including protein dihedrals)
tests/                # Unit tests
main_trainer.py       # Main training script
test_*.ipynb          # Jupyter notebooks for each distribution type

Usage

# Run the main trainer
python main_trainer.py

# Or explore individual distribution experiments via the notebooks
jupyter notebook test_von_mises.ipynb

Citation

@article{senetaire2026snl,
  title={Learning Energy-Based Models by Self-normalising the Likelihood},
  author={Senetaire, Hugo and Jeha, Paul and Mattei, Pierre-Alexandre and Frellsen, Jes},
  journal={Transactions on Machine Learning Research},
  year={2026}
}