  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.
