# A Bayesian approach to quantifying uncertainties and improving generalizability in traffic prediction models

arXiv: https://arxiv.org/abs/2307.05946 · HTML: https://mlsanity.com/paper/2307.05946/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 12 Jul 2023.

## Builds on (most cited first, 17 of 17)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Understanding and Improving Layer Normalization](https://mlsanity.com/paper/1911.07013/) (2019)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](https://mlsanity.com/paper/1512.05287/) (2015)
- [Deep and Confident Prediction for Time Series at Uber](https://mlsanity.com/paper/1709.01907/) (2017)
- [Robustness of Bayesian Neural Networks to Gradient-Based Attacks](https://mlsanity.com/paper/2002.04359/) (2020)
- [Stacked Bidirectional and Unidirectional LSTM Recurrent Neural Network for Forecasting Network-wide Traffic State with Missing Values](https://mlsanity.com/paper/2005.11627/) (2020)
- [Recurrent Dropout without Memory Loss](https://mlsanity.com/paper/1603.05118/) (2016)
- [Uncertainty Quantification for Traffic Forecasting: A Unified Approach](https://mlsanity.com/paper/2208.05875/) (2022)
- [Deep-Ensemble-Based Uncertainty Quantification in Spatiotemporal Graph Neural Networks for Traffic Forecasting](https://mlsanity.com/paper/2204.01618/) (2022)

## Built on by (most cited first, 5 of 5)

- [Deploying scalable traffic prediction models for efficient management in real-world large transportation networks during hurricane evacuations](https://mlsanity.com/paper/2406.12119/) (2024)
- [Unveiling Stochasticity: Universal Multi-modal Probabilistic Modeling for Traffic Forecasting](https://mlsanity.com/paper/2604.16084/) (2026)
- [Causally-Aware Spatio-Temporal Multi-Graph Convolution Network for Accurate and Reliable Traffic Prediction](https://mlsanity.com/paper/2408.13293/) (2024)
- [CONTINA: Confidence Interval for Traffic Demand Prediction with Coverage Guarantee](https://mlsanity.com/paper/2504.13961/) (2025)
- [MMCAformer: Macro-Micro Cross-Attention Transformer for Traffic Speed Prediction with Microscopic Connected Vehicle Driving Behavior](https://mlsanity.com/paper/2602.16730/) (2026)

## Abstract (arXiv)

Deep-learning models for traffic data prediction can have superior performance in modeling complex functions using a multi-layer architecture. However, a major drawback of these approaches is that most of these approaches do not offer forecasts with uncertainty estimates, which are essential for traffic operations and control. Without uncertainty estimates, it is difficult to place any level of trust to the model predictions, and operational strategies relying on overconfident predictions can lead to worsening traffic conditions. In this study, we propose a Bayesian recurrent neural network framework for uncertainty quantification in traffic prediction with higher generalizability by introducing spectral normalization to its hidden layers. In our paper, we have shown that normalization alters the training process of deep neural networks by controlling the model's complexity and reducing the risk of overfitting to the training data. This, in turn, helps improve the generalization performance of the model on out-of-distribution datasets. Results demonstrate that spectral normalization improves uncertainty estimates and significantly outperforms both the layer normalization and model without normalization in single-step prediction horizons. This improved performance can be attributed to the ability of spectral normalization to better localize the feature space of the data under perturbations. Our findings are especially relevant to traffic management applications, where predicting traffic conditions across multiple locations is the goal, but the availability of training data from multiple locations is limited. Spectral normalization, therefore, provides a more generalizable approach that can effectively capture the underlying patterns in traffic data without requiring location-specific models.