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

## TL;DR

This paper introduces heteroscedastic Gaussian processes tailored for modeling the variable uncertainty in large-scale crowdsourced traffic data, improving speed prediction accuracy by accounting for measurement noise variability.

## Contribution

It proposes a novel heteroscedastic Gaussian process model conditioned on sample size and traffic regime, enhancing uncertainty modeling in crowdsourced traffic speed data.

## Key findings

- HGP models outperform existing methods in predictive accuracy.
- SRC-HGP effectively captures time-varying uncertainty.
- Significant improvements in speed imputation and forecasting tasks.

## Abstract

Accurately modeling traffic speeds is a fundamental part of efficient intelligent transportation systems. Nowadays, with the widespread deployment of GPS-enabled 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.