# Deep-Ensemble-Based Uncertainty Quantification in Spatiotemporal Graph Neural Networks for Traffic Forecasting

arXiv: https://arxiv.org/abs/2204.01618 · HTML: https://mlsanity.com/paper/2204.01618/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 44 references that are in the map.
- First posted on arXiv 4 Apr 2022.

## Builds on (most cited first, 14 of 14)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [Hyperparameter Ensembles for Robustness and Uncertainty Quantification](https://mlsanity.com/paper/2006.13570/) (2020)
- [A Complete Recipe for Stochastic Gradient MCMC](https://mlsanity.com/paper/1506.04696/) (2015)
- [Neural Ensemble Search for Uncertainty Estimation and Dataset Shift](https://mlsanity.com/paper/2006.08573/) (2020)
- [Deep and Confident Prediction for Time Series at Uber](https://mlsanity.com/paper/1709.01907/) (2017)
- [Quantifying Uncertainty in Deep Spatiotemporal Forecasting](https://mlsanity.com/paper/2105.11982/) (2021)
- [AutoDEUQ: Automated Deep Ensemble with Uncertainty Quantification](https://mlsanity.com/paper/2110.13511/) (2021)
- [Graph-Partitioning-Based Diffusion Convolutional Recurrent Neural Network for Large-Scale Traffic Forecasting](https://mlsanity.com/paper/1909.11197/) (2019)

## Built on by (most cited first, 10 of 10)

- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Uncertainty Quantification for Hallucination Detection in Large Language Models: Foundations, Methodology, and Future Directions](https://mlsanity.com/paper/2510.12040/) (2025)
- [A Bayesian approach to quantifying uncertainties and improving generalizability in traffic prediction models](https://mlsanity.com/paper/2307.05946/) (2023)
- [Evidential Uncertainty Estimation for Multi-Modal Trajectory Prediction](https://mlsanity.com/paper/2503.05274/) (2025)
- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [Credal Graph Neural Networks](https://mlsanity.com/paper/2512.02722/) (2025)
- [Uncertainty Quantification for Image-based Traffic Prediction across Cities](https://mlsanity.com/paper/2308.06129/) (2023)
- [A Comparative Study of Loss Functions: Traffic Predictions in Regular and Congestion Scenarios](https://mlsanity.com/paper/2308.15464/) (2023)
- [Mesoscale Traffic Forecasting for Real-Time Bottleneck and Shockwave Prediction](https://mlsanity.com/paper/2402.05663/) (2024)
- [Uncertainty separation via ensemble quantile regression](https://mlsanity.com/paper/2412.13738/) (2024)

## Abstract (arXiv)

Deep-learning-based data-driven forecasting methods have produced impressive results for traffic forecasting. A major limitation of these methods, however, is that they provide forecasts without estimates of uncertainty, which are critical for real-time deployments. We focus on a diffusion convolutional recurrent neural network (DCRNN), a state-of-the-art method for short-term traffic forecasting. We develop a scalable deep ensemble approach to quantify uncertainties for DCRNN. Our approach uses a scalable Bayesian optimization method to perform hyperparameter optimization, selects a set of high-performing configurations, fits a generative model to capture the joint distributions of the hyperparameter configurations, and trains an ensemble of models by sampling a new set of hyperparameter configurations from the generative model. We demonstrate the efficacy of the proposed methods by comparing them with other uncertainty estimation techniques. We show that our generic and scalable approach outperforms the current state-of-the-art Bayesian and a number of other commonly used frequentist techniques.