Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations
Jie Chen, Nannan Cao, Kian Hsiang Low, Ruofei Ouyang, Colin Keng-Yan Tan, Patrick Jaillet
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.
PDF Link: /papers/13/p152-chen.pdf
AUTHOR = "Jie Chen
and Nannan Cao and Kian Hsiang Low and Ruofei Ouyang and Colin Keng-Yan Tan and Patrick Jaillet",
TITLE = "Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations",
BOOKTITLE = "Proceedings of the Twenty-Ninth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-13)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2013",
PAGES = "152--161"