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

TL;DR

This paper introduces a universal probabilistic modeling approach for traffic forecasting by replacing the output layer with a Gaussian Mixture Model, enhancing uncertainty quantification without altering existing models.

Contribution

It presents a simple yet effective method to convert deterministic traffic models into probabilistic ones using GMM layers, applicable across various architectures.

Findings

The approach improves accuracy over unimodal baselines.

It provides more informative uncertainty estimates.

The method is robust under imperfect data conditions.

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