Stochasticity in Motion: An Information-Theoretic Approach to Trajectory Prediction

TL;DR

This work tackles uncertainty in probabilistic trajectory prediction for autonomous driving by introducing an information-theoretic framework that decomposes total predictive uncertainty into aleatoric $H(y|x,\mathcal{D})$ and epistemic $I(y;\mathcal{W}|x,\mathcal{D})$ components. It employs a Monte Carlo approach with an ensemble-approximate posterior $q({\mathcal{W}})$ to estimate entropy terms and uses a Gaussian Mixture Model to represent $p(y|x,{\mathcal{W}})$ for sampling. The method is validated on nuScenes, showing that ensembles improve calibration and robustness, with epistemic uncertainty providing strong signals for OOD detection and risk-aware planning. Overall, the framework enables principled, actionable uncertainty quantification in trajectory prediction, potentially informing safer planning decisions in real-world autonomous driving systems.

Abstract

In autonomous driving, accurate motion prediction is crucial for safe and efficient motion planning. To ensure safety, planners require reliable uncertainty estimates of the predicted behavior of surrounding agents, yet this aspect has received limited attention. In particular, decomposing uncertainty into its aleatoric and epistemic components is essential for distinguishing between inherent environmental randomness and model uncertainty, thereby enabling more robust and informed decision-making. This paper addresses the challenge of uncertainty modeling in trajectory prediction with a holistic approach that emphasizes uncertainty quantification, decomposition, and the impact of model composition. Our method, grounded in information theory, provides a theoretically principled way to measure uncertainty and decompose it into aleatoric and epistemic components. Unlike prior work, our approach is compatible with state-of-the-art motion predictors, allowing for broader applicability. We demonstrate its utility by conducting extensive experiments on the nuScenes dataset, which shows how different architectures and configurations influence uncertainty quantification and model robustness.

Figures (5)

• Figure 1: The predictive distribution $p(y|x,\mathcal{D})$ of future trajectories for three example scenarios. The first row shows in-distribution scenarios, while the second row presents OOD cases: in ① and ③, segments of the input history have been removed, while in ②, parts of lane information have been removed. Both alterations mimic perception malfunctions. Naturally, prediction error is higher in the second row, indicated by the higher minADE metric, see Sec. \ref{['sec:results']} for details. Generally, we observe a correlation between minADE and total uncertainty. In these examples, epistemic uncertainty serves as a useful indicator for detecting OOD scenarios.
• Figure 2: Generating samples for Monte Carlo approximation. We fit a GMM to the final positions of trajectories predicted by every member of our ensemble. Then, we sample from each GMM to obtain per-model samples $y_n^m$ for calculating the term of aleatoric uncertainty. Finally, samples originating from all GMMs are aggregated as $y_n$ for calculating the term of total uncertainty.
• Figure 3: Differences ($\Delta$) in $\text{MinADE}_5$ between the original dataset and the corresponding out-of-distribution dataset for baseline models (y-axis) and ensembles (x-axis). Different colors correspond to various baseline models, while different markers denote distinct dataset augmentations. Markers positioned in the red area (lower triangle) of each plot indicate that the ensemble exhibits a larger $\Delta \text{MinADE}_5$ compared to the baseline. Conversely, markers in the green area signify a smaller $\Delta \text{MinADE}_5$ for the ensemble. Percentages indicate how often the ensemble outperforms the baseline. Upper row represents deep ensembles and lower row Dropout ensembles.
• Figure 4: Pearson correlation coefficient $\rho$ between total uncertainty and $\text{MinADE}_5$ for baseline models ($y$-axis) and ensembles ($x$-axis) over the validation set. Different colors represent various baseline models, while different markers indicate distinct dataset augmentations. Markers located in the red area (upper triangle) of each plot signify that the ensemble shows a lower correlation $\rho_{total}$ compared to the baseline. Conversely, markers in the green area (lower triangle) indicate a higher correlation for the ensemble. The numerical value in the bottom right corner of each plot represents the fraction of data points that fall within the green area. Upper row represents deep ensembles and lower row Dropout ensembles.
• Figure 5: Total, aleatoric, and epistemic uncertainties for a mixed ensemble ($1{\times} \text{LP, LF, PGP}$) for the original dataset as well as all out-of-distribution datasets.