Heteroscedastic Gaussian processes for uncertainty modeling in large-scale crowdsourced traffic data

Accurately modeling traffic speeds is a fundamental part of efficient intelligent transportation systems. Nowadays, with the widespread deployment of GPSenabled devices, it has become possible to crowdsource the collection of speed information to road users (e.g. through mobile applications or dedicated in-vehicle devices). Despite its rather wide spatial coverage, crowdsourced speed data also brings very important challenges, such as the highly variable measurement noise in the data due to a variety of driving behaviors and sample sizes. When not properly accounted for, this noise can severely compromise any application that relies on accurate traffic data. In this article, we propose the use of heteroscedastic Gaussian processes (HGP) to model the time-varying uncertainty in large-scale crowdsourced traffic data. Furthermore, we develop a HGP conditioned on sample size and traffic regime (SRC-HGP), which makes use of sample size information (probe vehicles per minute) as well as previous observed speeds, in order to more accurately model the uncertainty in observed speeds. Using 6 months of crowdsourced traffic data from Copenhagen, we empirically show that the proposed heteroscedastic models produce significantly better predictive distributions when compared to current state-of-the-art methods for both speed imputation and short-term forecasting tasks. Keywords: Gaussian processes, heteroscedastic models, traffic data, crowdsourcing, uncertainty modeling, forecasting, imputation, floating car data 1. Introduction Modeling traffic speeds is an essential task for developing intelligent transportation systems, because it provides real-time and anticipatory information about the performance of the network. This information is not only essential for traffic managers, since it allows them to properly allocate resources (e.g. The role of accurate traffic speed modeling is even more significant when we consider innovative car-sharing, autonomous vehicles and connected vehicles technologies (Tajalli & Hajbabaie, 2018), where inappropriate routing of vehicles and poor system-wide optimization and coordination can have severe adverse effects in the behavior of the road network (e.g., congestion and poor quality of service) and, ultimately, it can be decisive to the adoption of these technologies. There are two main sources of traffic speed data: static traffic sensors located at fixed location and GPS sensors from floating vehicles.