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.

翻译：在许多科学领域中，均需要回归模型来预测循环值。本研究探索了一类表达性强且可解释的圆值随机函数分布族，其与针对两个欧几里得维度并以单位圆为条件的高斯过程相关。所得概率模型与统计物理学中的连续自旋模型存在关联。此外，其密度函数非常简洁且具有最大熵特性，这与先前基于高斯过程并采用环绕或径向边缘化的方法不同。对于后验推断，我们引入了一种新的类Stratonovich增广方法，该方法适用于快速马尔可夫链蒙特卡洛采样。我们认为，在这些模型中进行转导学习更倾向于对参数采用贝叶斯方法。我们通过实验将该模型应用于（i）风向预测以及（ii）跑步步态周期百分比随关节角度变化的预测。