This paper studies the traffic state estimation (TSE) problem using sparse observations from mobile sensors. Most existing TSE methods either rely on well-defined physical traffic flow models or require large amounts of simulation data as input to train learning algorithms. Different from previous studies, in this paper we propose a purely data-driven and model-free solution. We consider TSE as a spatiotemporal matrix completion/interpolation problem and apply spatiotemporal delay embedding to transform the original incomplete matrix into a fourth-order Hankel structured tensor. By imposing a low-rank assumption on this tensor structure, we can approximate and characterize both global patterns and local patterns in a data-driven manner. We use a truncated nuclear norm of a balanced spatiotemporal unfolding to approximate the tensor rank and develop an efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve the problem. The proposed framework only involves two hyperparameters, spatial and temporal window lengths, which are easy to set given the degree of data sparsity. To validate the effectiveness of our proposed method, we conducted numerical experiments on real-world high-resolution trajectory data, which demonstrated its superiority in some challenging scenarios. The proposed method shows great potential for solving the TSE problem using sparse observations from mobile sensors and can be applied in various traffic applications.

Recent studies have significantly improved the prediction accuracy of travel demand using graph neural networks. However, these studies largely ignored uncertainty that inevitably exists in travel demand prediction. To fill this gap, this study proposes a framework of probabilistic graph neural networks (Prob-GNN) to quantify the spatiotemporal uncertainty of travel demand. This Prob-GNN framework is substantiated by deterministic and probabilistic assumptions, and empirically applied to the task of predicting the transit and ridesharing demand in Chicago. We found that the probabilistic assumptions (e.g. distribution tail, support) have a greater impact on uncertainty prediction than the deterministic ones (e.g. deep modules, depth). Among the family of Prob-GNNs, the GNNs with truncated Gaussian and Laplace distributions achieve the highest performance in transit and ridesharing data. Even under significant domain shifts, Prob-GNNs can predict the ridership uncertainty in a stable manner, when the models are trained on pre-COVID data and tested across multiple periods during and after the COVID-19 pandemic. Prob-GNNs also reveal the spatiotemporal pattern of uncertainty, which is concentrated on the afternoon peak hours and the areas with large travel volumes. Overall, our findings highlight the importance of incorporating randomness into deep learning for spatiotemporal ridership prediction. Future research should continue to investigate versatile probabilistic assumptions to capture behavioral randomness, and further develop methods to quantify uncertainty to build resilient cities.

Yihong Tang, Zhaokai Wang, Ao Qu, Yihao Yan, Zhaofeng Wu, Dingyi Zhuang, Jushi Kai, Kebing Hou, Xiaotong Guo, Jinhua Zhao, Zhan Zhao, Wei Ma. Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing: Industry Track. 2024.

Traffic crashes present substantial challenges to human safety and socio-economic development in urban areas. Developing a reliable and responsible traffic crash prediction model is crucial to address growing public safety concerns and improve the safety of urban mobility systems. Traditional methods face limitations at fine spatiotemporal scales due to the sporadic nature of high-risk crashes and the predominance of non-crash characteristics. Furthermore, while most current models show promising occurrence prediction, they overlook the uncertainties arising from the inherent nature of crashes, and then fail to adequately map the hierarchical ranking of crash risk values for more precise insights. To address these issues, we introduce the Spatiotemporal Zero-Inflated Tweedie Graph Neural Networks (STZITD-GNN), the first uncertainty-aware probabilistic graph deep learning model in road-level daily-basis traffic crash prediction for multi-steps. Our model combines the interpretability of the statistical Tweedie family with the predictive power of graph neural networks, excelling in predicting a comprehensive range of crash risks. The decoder employs a compound Tweedie model, handling the non-Gaussian distribution inherent in crash data, with a zero-inflated component for accurately identifying non-crash cases and low-risk roads. The model accurately predicts and differentiates between high-risk, low-risk, and no-risk scenarios, providing a holistic view of road safety that accounts for the full spectrum of probability and severity of crashes. Empirical tests using real-world traffic data from London, UK, demonstrate that the STZITD-GNN surpasses other baseline models across multiple benchmarks, including a reduction in regression error of up to 34.60% in point estimation metrics and an improvement of above 47% in interval-based uncertainty metrics.

Understanding Origin-Destination (O-D) travel demand is crucial for transportation management. However, traditional spatial-temporal deep learning models grapple with addressing the sparse and long-tail characteristics in high-resolution O-D matrices and quantifying prediction uncertainty. This dilemma arises from the numerous zeros and over-dispersed demand patterns within these matrices, which challenge the Gaussian assumption inherent to deterministic deep learning models. To address these challenges, we propose a novel approach: the Spatial-Temporal Tweedie Graph Neural Network (STTD). The STTD introduces the Tweedie distribution as a compelling alternative to the traditional 'zero-inflated' model and leverages spatial and temporal embeddings to parameterize travel demand distributions. Our evaluations using real-world datasets highlight STTD's superiority in providing accurate predictions and precise confidence intervals, particularly in high-resolution scenarios. GitHub code is available online(https://github.com/STTDAnonymous/STTD).