鲁棒且共轭的时空高斯过程
Robust and Conjugate Spatio-Temporal Gaussian Processes
AI总结：
本文将鲁棒且共轭的高斯过程（RCGP）框架特化至时空设置，提出一种计算成本与经典方法相当且抗异常值的时空GP，并克服了先验均值敏感、不确定性量化不足及需手动调参三大缺点。
摘要：
状态空间表示允许在时空设置中以线性时间计算成本进行高斯过程（GP）回归，但在存在异常值时，性能通常会受损。在本文中，我们将Altamirano等人（2024）的鲁棒且共轭的GP（RCGP）框架调整并特化到时空设置中。通过这样做，我们获得了一个具有与经典时空GP相当的计算成本的异常鲁棒时空GP。我们还克服了RCGP的三个主要缺点：当先验均值选择不当时性能不可靠、缺乏可靠的不确定性量化，以及需要手动仔细选择超参数。我们在金融和天气预报应用中广泛研究了我们的方法，证明它为存在异常值时的时空建模提供了一种可靠的方法。
英文摘要：
State-space formulations allow for Gaussian process (GP) regression with linear-in-time computational cost in spatio-temporal settings, but performance typically suffers in the presence of outliers. In this paper, we adapt and specialise the robust and conjugate GP (RCGP) framework of Altamirano et al. (2024) to the spatio-temporal setting. In doing so, we obtain an outlier-robust spatio-temporal GP with a computational cost comparable to classical spatio-temporal GPs. We also overcome the three main drawbacks of RCGPs: their unreliable performance when the prior mean is chosen poorly, their lack of reliable uncertainty quantification, and the need to carefully select a hyperparameter by hand. We study our method extensively in finance and weather forecasting applications, demonstrating that it provides a reliable approach to spatio-temporal modelling in the presence of outliers.
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