Unveiling Stochasticity: Universal Multi-modal Probabilistic Modeling for Traffic Forecasting

2026-04-17

AI Summary

This work addresses the limitation of existing traffic forecasting methods, which are predominantly deterministic and thus struggle to effectively capture the inherent uncertainty in traffic dynamics. To overcome this, the authors propose a general, plug-and-play probabilistic framework that transforms any pre-existing model into a probabilistic one by replacing its output layer with a Gaussian Mixture Model (GMM) layer and training end-to-end using negative log-likelihood loss—without altering the original model architecture or training pipeline. The approach enables, for the first time in traffic forecasting, a systematic evaluation of cumulative distribution functions and prediction intervals, substantially improving uncertainty quantification accuracy. Experiments on multiple real-world datasets demonstrate that the method preserves the original deterministic performance while outperforming both unimodal probabilistic and deterministic baselines, and exhibits enhanced robustness under low-quality data conditions.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Planning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Web traffic and log analysis
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Traffic forecasting is a challenging spatio-temporal modeling task and a critical component of urban transportation management. Current studies mainly focus on deterministic predictions, with limited considerations on the uncertainty and stochasticity in traffic dynamics. Therefore, this paper proposes an elegant yet universal approach that transforms existing models into probabilistic predictors by replacing only the final output layer with a novel Gaussian Mixture Model (GMM) layer. The modified model requires no changes to the training pipeline and can be trained using only the Negative Log-Likelihood (NLL) loss, without any auxiliary or regularization terms. Experiments on multiple traffic datasets show that our approach generalizes from classic to modern model architectures while preserving deterministic performance. Furthermore, we propose a systematic evaluation procedure based on cumulative distributions and confidence intervals, and demonstrate that our approach is considerably more accurate and informative than unimodal or deterministic baselines. Finally, a more detailed study on a real-world dense urban traffic network is presented to examine the impact of data quality on uncertainty quantification and to show the robustness of our approach under imperfect data conditions. Code available at https://github.com/Weijiang-Xiong/OpenSkyTraffic

Problem

• traffic forecasting
• uncertainty
• stochasticity
• probabilistic modeling
• spatio-temporal modeling

Innovation

• probabilistic modeling
• Gaussian Mixture Model
• traffic forecasting
• uncertainty quantification
• spatio-temporal modeling