# Bayesian Circular Regression with von Mises Quasi-Processes

arXiv: https://arxiv.org/abs/2406.13151 · HTML: https://mlsanity.com/paper/2406.13151/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 73 references that are in the map.
- First posted on arXiv 19 Jun 2024.

## Builds on (most cited first, 6 of 6)

- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Pathwise Conditioning of Gaussian Processes](https://mlsanity.com/paper/2011.04026/) (2020)
- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [Recent advances in directional statistics](https://mlsanity.com/paper/2005.06889/) (2020)
- [The Multivariate Generalised von Mises distribution: Inference and applications](https://mlsanity.com/paper/1602.05003/) (2016)
- [The projected dynamic linear model for time series on the sphere](https://mlsanity.com/paper/2308.14996/) (2023)

## Abstract (arXiv)

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.