Time-efficient Bayesian Inference for a (Skewed) Von Mises Distribution on the Torus in a Deep Probabilistic Programming Language

Abstract

Probabilistic programming languages (PPLs) are at the interface between statistics and the theory of programming languages. PPLs formulate statistical models as stochastic programs that enable automatic inference algorithms and optimization. Pyro and its sibling NumPyro are PPLs built on top of the deep learning frameworks PyTorch and Jax, respectively, providing simple interfaces for inference using efficient implementations of Hamiltonian Monte Carlo (HMC), the No-U-Turn Sampler (NUTS), and Stochastic Variational Inference (SVI). The Sine von Mises distribution and its skewed variant are toroidal distributions relevant to protein bioinformatics. We demonstrate the use of the skewed Sine von Mises distribution by modeling dihedral angles of proteins using a Bayesian mixture model inferred using NUTS, exploiting NumPyro's facilities for automatic enumeration.

BibTeX

@inproceedings{
 ronning2021time,
 title={Time-efficient Bayesian Inference for a (Skewed) Von Mises Distribution on the Torus in a Deep Probabilistic Programming Language},
 author={Ola Rønning and Christophe Ley and Kanti V. Mardia and Thomas Hamelryck},
 booktitle={2021 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI)},
 pages={1--8},
 year={2021},
 doi={10.1109/MFI52462.2021.9591184}
}