论文标题
空间高斯流程回归及其应用的有效实施
An Efficient Implementation for Spatial-Temporal Gaussian Process Regression and Its Applications
论文作者
论文摘要
时空高斯过程回归是一种空间数据建模的流行方法。 Its state-of-art implementation is based on the state-space model realization of the spatial-temporal Gaussian process and its corresponding Kalman filter and smoother, and has computational complexity $\mathcal{O}(NM^3)$, where $N$ and $M$ are the number of time instants and spatial input locations, respectively, and thus can only be applied to data with large $N$ but relatively small $M$.在本文中，我们的主要目标是表明，通过探索空间空间模型实现的Kronecker结构，可以将计算复杂性进一步降低到$ \ Mathcal {o}（M^3+Nm^2）$，因此可以将拟议的实施应用于大型$ N $ $ M和Modersery $ M $ M $ M $ M。在天气数据预测中的应用和空间分布的系统识别中说明了所提出的实施。我们的次要目标是为科罗拉多降水数据和GHCN温度数据设计一个内核，以便在实施更有效的情况下，也可以实现更好的预测性能。
Spatial-temporal Gaussian process regression is a popular method for spatial-temporal data modeling. Its state-of-art implementation is based on the state-space model realization of the spatial-temporal Gaussian process and its corresponding Kalman filter and smoother, and has computational complexity $\mathcal{O}(NM^3)$, where $N$ and $M$ are the number of time instants and spatial input locations, respectively, and thus can only be applied to data with large $N$ but relatively small $M$. In this paper, our primary goal is to show that by exploring the Kronecker structure of the state-space model realization of the spatial-temporal Gaussian process, it is possible to further reduce the computational complexity to $\mathcal{O}(M^3+NM^2)$ and thus the proposed implementation can be applied to data with large $N$ and moderately large $M$. The proposed implementation is illustrated over applications in weather data prediction and spatially-distributed system identification. Our secondary goal is to design a kernel for both the Colorado precipitation data and the GHCN temperature data, such that while having more efficient implementation, better prediction performance can also be achieved than the state-of-art result.
