The Multivariate Generalised von Mises: Inference and applications

Circular variables arise in a multitude of data-modelling contexts ranging from robots to 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 step towards bringing this field and probabilistic machine learning together. To achieve this task, we introduce a Gaussian Process analogue for circular variables and outline how to perform variational inference for this model. We demonstrate how this model naturally occurs in the contexts of regression and latent variable modelling and present experimental results where this model overperforms standard probabilistic machine learning approaches that do not account for the topological properties of circular variables.