Uncertainty Quantification for Traffic Forecasting Using Deep-Ensemble-Based Spatiotemporal Graph Neural Networks

Deep-learning-based data-driven forecasting methods have achieved impressive results for traffic forecasting. Specifically, spatiotemporal graph neural networks have emerged as a promising class of approaches because of their ability to model both spatial and temporal patterns in traffic data. A major limitation of these methods, however, is that they provide forecasts without estimates of data and model uncertainty, which are critical for understanding inherent variations of the data and forecast limitations due to a lack of training data. We develop a scalable deep ensemble approach to quantify data and model uncertainties for spatiotemporal graph neural networks. Our approach consists of four stages: 1) using a Gaussian-assumption-free simultaneous quantile regression loss for training a spatiotemporal graph neural network to model the traffic distribution; 2) applying a scalable Bayesian optimization method to tune the hyperparameters of the spatiotemporal graph neural network; 3) fitting a Gaussian copula generative model to capture the joint distributions of the high-performing hyperparameter configurations, and training an ensemble of models by sampling a new set of hyperparameter configurations from the generative model; and 4) decomposing the data and model uncertainties from the spatiotemporal graph neural network ensembles. We illustrate the effectiveness of our approach on a diffusion convolutional recurrent neural network, a state-of-the-art method for short-term traffic forecasting. We demonstrate the efficacy of our ensemble-based uncertainty quantification method by comparing it with other uncertainty estimation techniques. We show that our generic and scalable approach outperforms the current state-of-the-art Bayesian and a number of other commonly used frequentist uncertainty estimation techniques. The code is available on GitHub: https://github.com/tanwimallick/DESQRUQ.