# The Multivariate Generalised von Mises distribution: Inference and applications

arXiv: https://arxiv.org/abs/1602.05003 · HTML: https://mlsanity.com/paper/1602.05003/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2016.

## Built on by (most cited first, 3 of 3)

- [Riemannian Score-Based Generative Modelling](https://mlsanity.com/paper/2202.02763/) (2022)
- [Memory as Resonance: A Biomimetic Architecture for Infinite Context Memory on Ergodic Phonetic Manifolds](https://mlsanity.com/paper/2512.20245/) (2025)
- [Bayesian Circular Regression with von Mises Quasi-Processes](https://mlsanity.com/paper/2406.13151/) (2024)

## Abstract (arXiv)

Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by extending some standard probabilistic modelling tools to the circular domain. First we introduce a new multivariate distribution over circular variables, called the multivariate Generalised von Mises (mGvM) distribution. This distribution can be constructed by restricting and renormalising a general multivariate Gaussian distribution to the unit hyper-torus. Previously proposed multivariate circular distributions are shown to be special cases of this construction. Second, we introduce a new probabilistic model for circular regression, that is inspired by Gaussian Processes, and a method for probabilistic principal component analysis with circular hidden variables. These models can leverage standard modelling tools (e.g. covariance functions and methods for automatic relevance determination). Third, we show that the posterior distribution in these models is a mGvM distribution which enables development of an efficient variational free-energy scheme for performing approximate inference and approximate maximum-likelihood learning.