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 resulting 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 Markov Chain Monte
Carlo sampling. We argue that transductive learning in these models favors a
Bayesian approach to the parameters. 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.

本文介绍了一种用于预测圆形值的回归模型，探讨了与高斯过程相关的一族表达且可解释的分布。该模型密度简单，具有最大熵，通过引入一种新的 Stratonovich-like augmentation，可以进行快速的 Markov Chain Monte Carlo 采样。同时，本文论证了在这些模型中采用贝叶斯方法进行参数的转导学习，通过适用于单位圆的两个欧几里得维度的概率模型，对风向和运动步态周期百分比进行了实验证明。