We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued functions, as well as vector fields. We target data inherently supported on manifolds, which is too complex for shallow Gaussian processes thereon. For example, while the latter perform well on high-altitude wind data, they struggle with the more intricate, nonstationary patterns at low altitudes. Our models significantly improve performance in these settings, enhancing prediction quality and uncertainty calibration, and remain robust to overfitting, reverting to shallow models when additional complexity is unneeded. We further showcase our models on Bayesian optimisation problems on manifolds, using stylised examples motivated by robotics, and obtain substantial improvements in later stages of the optimisation process. Finally, we show our models to have potential for speeding up inference for non-manifold data, when, and if, it can be mapped to a proxy manifold well enough.

本文提出了一种实用的深高斯过程模型，适用于里曼流形，旨在解决传统浅层高斯过程在复杂数据上的性能不足。该模型通过流形到流形的隐层架构，显著提高了高复杂度数据的预测质量和不确定性校准能力，并在贝叶斯优化问题中表现出显著的改进。最终，该研究展示了在适当映射的情况下，这些模型在非流形数据推断上的潜在加速效果。

流形上的残差深高斯过程