# Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations

arXiv: https://arxiv.org/abs/1305.5826 · HTML: https://mlsanity.com/paper/1305.5826/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2013.

## Built on by (most cited first, 5 of 5)

- [Bayesian Optimization under Stochastic Delayed Feedback](https://mlsanity.com/paper/2206.09341/) (2022)
- [Low-Precision Arithmetic for Fast Gaussian Processes](https://mlsanity.com/paper/2207.06856/) (2022)
- [Convolutional Normalizing Flows for Deep Gaussian Processes](https://mlsanity.com/paper/2104.08472/) (2021)
- [Safe and Adaptive Decision-Making for Optimization of Safety-Critical Systems: The ARTEO Algorithm](https://mlsanity.com/paper/2211.05495/) (2022)
- [Bayesian Optimization for Dynamic Pricing and Learning](https://mlsanity.com/paper/2510.12447/) (2025)

## Abstract (arXiv)

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.