The Multivariate Generalised von Mises: Inference and applications

Circular variables arise in a multitude of data-modelling contexts ranging from robots to the social sciences. To correctly predict and analyse circular data, the field of circular and directional statistics has developed a range of MCMC methods for low-dimensional problems and small-to-medium-sized datasets. In this paper, we extend the toolbox of circular statistics to higher dimensions as a first step towards bringing this field and probabilistic machine learning closer together. To achieve this task, we introduce the multivariate Generalised von Mises (mGvM) distribution, a Gaussian Process analogue for circular variables, and demonstrate how this model naturally occurs as the posterior in regression and latent variable modelling with circular variables. We also outline how to perform variational inference for this model and present experimental results where the mGvM out-performs standard probabilistic machine learning approaches that do not account for the topological properties of circular variables.