将残差结构引入流形上的深度高斯过程，提升复杂数据建模能力。
Residual Deep Gaussian Processes on Manifolds
- 在流形间构建残差型深层高斯过程，支持向量场与标量函数建模。
- 在低空风速等非平稳数据上显著提升预测精度与不确定性校准效果。
- 适用于机器人优化等流形贝叶斯优化任务，且能自动简化避免过拟合。
我们提出了一种实用的流形上的深度高斯过程模型，其设计思想类似残差神经网络。通过流形到流形的隐藏层和任意输出层，可建模流形值或标量值函数，以及向量场。针对固有定义在流形上的复杂数据，传统浅层高斯过程表现不足；例如，浅层模型在高层风速数据上表现良好，但在低层更复杂的非平稳模式中表现不佳。我们的模型在此类场景下显著提升性能，改善预测质量与不确定性校准，并对过拟合保持鲁棒性，在无需额外复杂度时可退化为浅层模型。进一步在机器人启发的流形贝叶斯优化问题上展示模型效果，优化后期性能大幅提升。最后，我们表明当非流形数据可映射到足够好的代理流形时，该模型有望加速推理。
原文摘要 · Abstract (English)
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.
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