The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes (GPs) are candidate model choices for interpolation. However, due to their poor scalability, they usually rely on inducing points for inference, which restricts their expressivity. Moreover, commonly imposed assumptions such as stationarity prevents them from capturing complex patterns in the data. While deep GPs can overcome this issue, training and making inference with them are difficult, again requiring crude approximations via inducing points. In this work, we instead approach the problem through Bayesian deep learning, where spatiotemporal fields are represented by deep neural networks, whose layers share the inductive bias of stationary GPs on the plane/sphere via random feature expansions. This allows one to (1) capture high frequency patterns in the data, and (2) use mini-batched gradient descent for large scale training. We experiment on various remote sensing data at local/global scales, showing that our approach produce competitive or superior results to existing methods, with well-calibrated uncertainties.

翻译：地球观测系统的快速发展要求一种可扩展的方法来插值遥感观测数据。这些方法原则上应能随着数据增长获取更多关于观测场的信息。高斯过程（GPs）是插值任务的候选模型选择。然而，由于其较差的扩展性，它们通常依赖诱导点进行推断，这限制了其表达能力。此外，常用的平稳性等假设阻碍了它们捕捉数据中的复杂模式。虽然深度高斯过程可以克服这一问题，但其训练和推断过程较为困难，仍需通过诱导点进行粗略近似。在本研究中，我们转而通过贝叶斯深度学习来探讨该问题，其中时空场由深度神经网络表示，其各层通过随机特征展开共享平面/球面上平稳高斯过程的归纳偏置。这使得我们能够：（1）捕捉数据中的高频模式；（2）使用小批量梯度下降进行大规模训练。我们在局部/全球尺度的多种遥感数据上进行实验，结果表明该方法能产生优于或媲美现有方法的结果，且具有良好校准的不确定性。