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Providing both point estimation and uncertainty quantification for traffic forecasting is crucial for supporting accurate and reliable services in intelligent transportation systems. However, the majority of existing traffic forecasting works mainly focus on point estimation without quantifying the uncertainty of predictions. Meanwhile, existing uncertainty quantification (UQ) methods fail to capture the inherent static characteristics of traffic uncertainty along both the spatial and temporal dimensions. Directly equipping the traffic forecasting works with uncertainty quantification techniques may even damage the prediction accuracy. In this paper, we propose a novel traffic forecasting model aiming at providing point estimation and uncertainty quantification simultaneously, called STUP. Compared to the traditional graph convolution networks (GCNs), our framework is able to incorporate uncertainty quantification into traffic forecasting to further improve forecasting performance. Specifically, we first develop an adaptive strategy to initialize uncertainty distribution. Then a kind of spatial–temporal uncertainty layer is carefully designed to model the evolution process of both the traffic state and its corresponding uncertainty, along with a gated adjusting unit to avoid error information propagation. Finally, we propose a novel constraint loss to further help improve the forecasting accuracy and to alleviate the training difficulty caused by the lack of uncertainty labels. Experiments on five real-world traffic datasets demonstrate that STUP outperforms the state-of-the-art baselines on both the traffic prediction task and uncertainty quantification task. [Display omitted] • A spatial–temporal traffic forecasting method considering uncertainty is proposed. • Discovering the relationship between traffic data and factors of uncertainty. • Balancing the accuracy and reliability on traffic forecasting. [ABSTRACT FROM AUTHOR]

Accurate forecasting of time series mitigates the uncertainty of future outlooks and is a great help in reducing errors in decisions. Despite years of researches, there are still some challenges to accurate forecasting of time series, including the difficulty of dynamic modeling, the problem of capturing short-term correlations, and the conundrum of long-term forecasting. This paper offers an A dversarial Truncated Cauchy S elf- A ttentive T ime- V ariant Neural N etwork (ASATVN) for multi-step ahead time series forecasting. Specifically, the proposed model builds on Generative Adversarial Networks, in which the generator is composed of a novel time-variant model. The time-variant model contributes to learning dynamic time-series changes with its time-variant architecture and employs a newly proposed Truncated Cauchy Self-Attention block to capture the local sequential dependencies better. For the discriminator, two self-attentive discriminators are presented to regularize predictions with fidelity and continuity, which is beneficial to predicting sequence over longer time horizons. Our proposed ASATVN model outperforms the state-of-the-art predictive models on eleven real-world benchmark datasets, demonstrating its effectiveness. • A time-variant network learns various dynamics across multiple time steps. • A new self-attention are more sensitive to the local context of time series. • Two discriminators regularize predictor to offer realistic and continuous forecasts. [ABSTRACT FROM AUTHOR]