Learning Car-Following Behaviors Using Bayesian Matrix Normal Mixture Regression

TL;DR

This work addresses the challenge of modeling car-following behaviors with both predictive accuracy and interpretability under uncertainty. It introduces Bayesian Matrix Normal Mixture Regression (MNMR), built atop a matrix-normal mixture (MNMM) that uses separable row ($\boldsymbol{U}$) and column ($\boldsymbol{V}$) covariances to capture feature correlations and temporal dynamics, respectively. The framework yields a sequence-to-sequence predictive model via conditional and marginal Gaussian mixtures, with priors that promote interpretability of components through mean matrices and covariance structures. Evaluations on the HighD dataset show MNMR effectively captures CF dynamics, and the accompanying case study demonstrates its ability to identify distinct driving conditions through learned components, highlighting practical benefits for traffic simulations and autonomous driving systems.

Abstract

Learning and understanding car-following (CF) behaviors are crucial for microscopic traffic simulation. Traditional CF models, though simple, often lack generalization capabilities, while many data-driven methods, despite their robustness, operate as "black boxes" with limited interpretability. To bridge this gap, this work introduces a Bayesian Matrix Normal Mixture Regression (MNMR) model that simultaneously captures feature correlations and temporal dynamics inherent in CF behaviors. This approach is distinguished by its separate learning of row and column covariance matrices within the model framework, offering an insightful perspective into the human driver decision-making processes. Through extensive experiments, we assess the model's performance across various historical steps of inputs, predictive steps of outputs, and model complexities. The results consistently demonstrate our model's adeptness in effectively capturing the intricate correlations and temporal dynamics present during CF. A focused case study further illustrates the model's outperforming interpretability of identifying distinct operational conditions through the learned mean and covariance matrices. This not only underlines our model's effectiveness in understanding complex human driving behaviors in CF scenarios but also highlights its potential as a tool for enhancing the interpretability of CF behaviors in traffic simulations and autonomous driving systems.

Figures (4)

• Figure 1: Probabilistic graphical model of MNMM.
• Figure 2: Two illustrative cases to understand the dominant components (i.e., $\#6$, $\#7$, $\#14$, $\#41$, and $\#59$ in these cases) and the transitioning among them.
• Figure 3: The mean matrix $\boldsymbol{M}_k$ of the dominant components.
• Figure 4: The correlation matrices of the dominant components.