标题： 多输出高斯过程后验均值的低秩计算 显示英文标题

标题： Low-rank computation of the posterior mean in Multi-Output Gaussian Processes

摘要： 高斯过程（GP）是机器学习和计算科学中的多功能工具。我们这里考虑多输出高斯过程（MOGP）的情况，并提出低秩方法以高效地计算MOGP的后验均值。从低秩时空数据出发，我们考虑一个结构化的协方差函数，假设空间和时间上具有可分离性。这种可分离性反过来又使得协方差矩阵分解为个体协方差矩阵的克罗内克积。将典型的噪声项纳入模型后，则需要求解大规模的Stein方程来计算后验均值。为此，我们提出了基于LRPCG方法与调整后的用于求解Stein方程的Sylvester方程求解器KPIK相结合的高效低秩方法。我们在真实世界街道网络图上通过使用图滤波器作为协方差矩阵来测试所开发的方法。此外，我们提出了一种度加权平均协方差矩阵，在特定假设下可以实现更高效的收敛。 显示英文摘要

摘要： Gaussian processes (GP) are a versatile tool in machine learning and computational science. We here consider the case of multi-output Gaussian processes (MOGP) and present low-rank approaches for efficiently computing the posterior mean of a MOGP. Starting from low-rank spatio-temporal data we consider a structured covariance function, assuming separability across space and time. This separability, in turn, gives a decomposition of the covariance matrix into a Kronecker product of individual covariance matrices. Incorporating the typical noise term to the model then requires the solution of a large-scale Stein equation for computing the posterior mean. For this, we propose efficient low-rank methods based on a combination of a LRPCG method with the Sylvester equation solver KPIK adjusted for solving Stein equations. We test the developed method on real world street network graphs by using graph filters as covariance matrices. Moreover, we propose a degree-weighted average covariance matrix, which can be employed under specific assumptions to achieve more efficient convergence.