Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations

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.

Decentralized Data Fusion and Active Sensing with Mobile Sensors for Modeling and Predicting Spatiotemporal Traffic Phenomena

The problem of modeling and predicting spatiotemporal traffic phenomena over an urban road network is important to many traffic applications such as detecting and forecasting congestion hotspots. This paper presents a decentralized data fusion and active sensing (D2FAS) algorithm for mobile sensors to actively explore the road network to gather and assimilate the most informative data for predicting the traffic phenomenon. We analyze the time and communication complexity of D2FAS and demonstrate that it can scale well with a large number of observations and sensors. We provide a theoretical guarantee on its predictive performance to be equivalent to that of a sophisticated centralized sparse approximation for the Gaussian process (GP) model: The computation of such a sparse approximate GP model can thus be parallelized and distributed among the mobile sensors (in a Google-like MapReduce paradigm), thereby achieving efficient and scalable prediction. We also theoretically guarantee its active sensing performance that improves under various practical environmental conditions. Empirical evaluation on real-world urban road network data shows that our D2FAS algorithm is significantly more time-efficient and scalable than state-oftheart centralized algorithms while achieving comparable predictive performance.

Gaussian Process-Based Decentralized Data Fusion and Active Sensing for Mobility-on-Demand System

Mobility-on-demand (MoD) systems have recently emerged as a promising paradigm of one-way vehicle sharing for sustainable personal urban mobility in densely populated cities. In this paper, we enhance the capability of a MoD system by deploying robotic shared vehicles that can autonomously cruise the streets to be hailed by users. A key challenge to managing the MoD system effectively is that of real-time, fine-grained mobility demand sensing and prediction. This paper presents a novel decentralized data fusion and active sensing algorithm for real-time, fine-grained mobility demand sensing and prediction with a fleet of autonomous robotic vehicles in a MoD system. Our Gaussian process (GP)-based decentralized data fusion algorithm can achieve a fine balance between predictive power and time efficiency. We theoretically guarantee its predictive performance to be equivalent to that of a sophisticated centralized sparse approximation for the GP model: The computation of such a sparse approximate GP model can thus be distributed among the MoD vehicles, hence achieving efficient and scalable demand prediction. Though our decentralized active sensing strategy is devised to gather the most informative demand data for demand prediction, it can achieve a dual effect of fleet rebalancing to service the mobility demands. Empirical evaluation on real-world mobility demand data shows that our proposed algorithm can achieve a better balance between predictive accuracy and time efficiency than state-of-the-art algorithms.