Bayesian Circular Regression with von Mises Quasi-Processes

TL;DR

This paper introduces a novel Bayesian circular regression model based on von Mises quasi-processes, offering a simple, interpretable, and high-entropy alternative to existing methods, with efficient inference via Gibbs sampling.

Contribution

It develops a new family of Gaussian process-like models for circular data with a simple density and maximum-entropy property, along with a fast Gibbs sampling inference scheme.

Findings

Effective prediction of wind directions.

Accurate modeling of gait cycle percentages.

Demonstrated computational efficiency of the sampling method.

Abstract

The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes targeting two Euclidean dimensions conditioned on the unit circle. The probability model has connections with continuous spin models in statistical physics. Moreover, its density is very simple and has maximum-entropy, unlike previous Gaussian process-based approaches, which use wrapping or radial marginalization. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling. We argue that transductive learning in these models favors a Bayesian approach to the parameters and apply our sampling scheme to the Double Metropolis-Hastings algorithm. We present experiments applying this model to the prediction of (i) wind directions and (ii) the percentage of the running gait cycle as a function of joint angles.