  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.
