论文标题
大规模低级高斯流程预测和支持点
Large-Scale Low-Rank Gaussian Process Prediction with Support Points
论文作者
论文摘要
低级近似是解决与大规模高斯流程回归相关的“大N问题”的流行策略。开发低级结构的基础功能至关重要，应仔细指定。预测过程通过以协方差函数和一组结诱导基础函数来简化问题。现有的文献提出了结选择和协方差估计的某些实际实施；但是，缺乏解释这两个因素对预测过程的影响的理论基础。在本文中，得出了预测过程和高斯过程预测的渐近预测性能，并研究了所选结和估计协方差的影响。我们建议将支持点用作结，最能代表数据位置。广泛的仿真研究证明了支持点的优势并验证了我们的理论结果。降水和臭氧的实际数据被用作示例，并且我们方法比其他广泛使用的低级别近似方法的效率得到了验证。
Low-rank approximation is a popular strategy to tackle the "big n problem" associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified. Predictive processes simplify the problem by inducing basis functions with a covariance function and a set of knots. The existing literature suggests certain practical implementations of knot selection and covariance estimation; however, theoretical foundations explaining the influence of these two factors on predictive processes are lacking. In this paper, the asymptotic prediction performance of the predictive process and Gaussian process predictions is derived and the impacts of the selected knots and estimated covariance are studied. We suggest the use of support points as knots, which best represent data locations. Extensive simulation studies demonstrate the superiority of support points and verify our theoretical results. Real data of precipitation and ozone are used as examples, and the efficiency of our method over other widely used low-rank approximation methods is verified.
