Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size. This paper presents two parallel GP regression methods that exploit low-rank covariance matrix approximations for distributing the computational load among parallel machines to achieve time efficiency and scalability. We theoretically guarantee the predictive performances of our proposed parallel GPs to be equivalent to that of some centralized approximate GP regression methods: The computation of their centralized counterparts can be distributed among parallel machines, hence achieving greater time efficiency and scalability. We analytically compare the properties of our parallel GPs such as time, space, and communication complexity. Empirical evaluation on two real-world datasets in a cluster of 20 computing nodes shows that our parallel GPs are significantly more time-efficient and scalable than their centralized counterparts and exact/full GP while achieving predictive performances comparable to full GP.

本文介绍了两种基于低秩协方差矩阵逼近的并行高斯过程回归方法，这两种方法可以将计算负载分布在并行机器之间以达到时间效率和可伸缩性，并经过理论分析证明了这些方法的预测性能等价于一些集中式的近似高斯过程回归方法，并且在两个真实数据集上的实证评估表明我们的并行高斯过程回归方法比其集中式对应物和全高斯过程方法具有更高的时间效率和可伸缩性，同时实现与全高斯过程方法相当的预测性能。