Bayesian Circular Regression with von Mises Quasi-Processes
This work addresses the need for regression models in scientific fields dealing with circular data, such as meteorology and biomechanics, by providing a novel Bayesian approach that is more interpretable and efficient than existing methods, though it is incremental in advancing circular regression techniques.
The paper tackles the problem of regression for circular data by introducing a Bayesian model based on von Mises quasi-processes, which offers an expressive and interpretable distribution over circle-valued functions with a simple, maximum-entropy density. It demonstrates the model's effectiveness through experiments on wind direction prediction and gait cycle analysis, achieving competitive results with improved computational efficiency via a new Gibbs sampling scheme.
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.