Bayesian Circular Regression with von Mises Quasi-Processes

Yarden Cohen, Alexandre Khae Wu Navarro, Jes Frellsen, Richard E. Turner, Raziel Riemer, Ari Pakman
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:1693-1701, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-cohen25a, title = {Bayesian Circular Regression with von Mises Quasi-Processes}, author = {Cohen, Yarden and Navarro, Alexandre Khae Wu and Frellsen, Jes and Turner, Richard E. and Riemer, Raziel and Pakman, Ari}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {1693--1701}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/cohen25a/cohen25a.pdf}, url = {https://proceedings.mlr.press/v258/cohen25a.html}, 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.} }
Endnote
%0 Conference Paper %T Bayesian Circular Regression with von Mises Quasi-Processes %A Yarden Cohen %A Alexandre Khae Wu Navarro %A Jes Frellsen %A Richard E. Turner %A Raziel Riemer %A Ari Pakman %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-cohen25a %I PMLR %P 1693--1701 %U https://proceedings.mlr.press/v258/cohen25a.html %V 258 %X 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.
APA
Cohen, Y., Navarro, A.K.W., Frellsen, J., Turner, R.E., Riemer, R. & Pakman, A.. (2025). Bayesian Circular Regression with von Mises Quasi-Processes. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:1693-1701 Available from https://proceedings.mlr.press/v258/cohen25a.html.

Related Material