# Probabilistic Traffic Forecasting with Dynamic Regression

arXiv: https://arxiv.org/abs/2301.06650 · HTML: https://mlsanity.com/paper/2301.06650/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 52 references that are in the map.
- First posted on arXiv 17 Jan 2023.

## Builds on (most cited first, 20 of 20)

- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Temporal Pattern Attention for Multivariate Time Series Forecasting](https://mlsanity.com/paper/1809.04206/) (2018)
- [Decoupled Dynamic Spatial-Temporal Graph Neural Network for Traffic Forecasting](https://mlsanity.com/paper/2206.09112/) (2022)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [How to Build a Graph-Based Deep Learning Architecture in Traffic Domain: A Survey](https://mlsanity.com/paper/2005.11691/) (2020)
- [TACTiS: Transformer-Attentional Copulas for Time Series](https://mlsanity.com/paper/2202.03528/) (2022)
- [Autoregressive Models for Matrix-Valued Time Series](https://mlsanity.com/paper/1812.08916/) (2018)
- [Adjusting for Autocorrelated Errors in Neural Networks for Time Series](https://mlsanity.com/paper/2101.12578/) (2021)
- [Residual Correction in Real-Time Traffic Forecasting](https://mlsanity.com/paper/2209.05406/) (2022)
- [Incorporating travel behavior regularity into passenger flow forecasting](https://mlsanity.com/paper/2004.00992/) (2020)

## Built on by (most cited first, 4 of 4)

- [Learning with Calibration: Exploring Test-Time Computing of Spatio-Temporal Forecasting](https://mlsanity.com/paper/2506.00635/) (2025)
- [Better Batch for Deep Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2305.17028/) (2023)
- [Do Time Series Foundation Model Benchmarks Hide Regime-Dependent Failures? Evidence from Traffic Speed Forecasting](https://mlsanity.com/paper/2606.18367/) (2026)
- [Frequency-Constrained Learning for Long-Term Forecasting](https://mlsanity.com/paper/2508.01508/) (2025)

## Abstract (arXiv)

This paper proposes a dynamic regression (DR) framework that enhances existing deep spatiotemporal models by incorporating structured learning for the error process in traffic forecasting. The framework relaxes the assumption of time independence by modeling the error series of the base model (i.e., a well-established traffic forecasting model) using a matrix-variate autoregressive (AR) model. The AR model is integrated into training by redesigning the loss function. The newly designed loss function is based on the likelihood of a non-isotropic error term, enabling the model to generate probabilistic forecasts while preserving the original outputs of the base model. Importantly, the additional parameters introduced by the DR framework can be jointly optimized alongside the base model. Evaluation on state-of-the-art (SOTA) traffic forecasting models using speed and flow datasets demonstrates improved performance, with interpretable AR coefficients and spatiotemporal covariance matrices enhancing the understanding of the model.