Evidential Uncertainty Estimation for Multi-Modal Trajectory Prediction

TL;DR

Problem: uncertainty in multi-modal trajectory prediction for autonomous driving arises from human behavior and perception noise. Approach: an evidential deep learning framework combines a $NIG$ distribution for positional uncertainty and a $Dirichlet$ prior for mode probabilities, enabling real-time, single-pass uncertainty estimation within a HiVT-based architecture and an Uncertainty Aggregator. The method further employs uncertainty-driven importance sampling to improve training efficiency by prioritizing informative high-uncertainty samples. Results: on Argoverse 1 and 2, the approach achieves accurate multi-modal predictions with calibrated probabilities (low ECE) and fast inference around $5.6\times10^{-3}$ s per prediction, while maintaining competitive minADE/minFDE. Significance: this framework delivers robust uncertainty quantification suitable for safety-critical autonomous driving and enables data-efficient training on large-scale datasets.

Abstract

Accurate trajectory prediction is crucial for autonomous driving, yet uncertainty in agent behavior and perception noise makes it inherently challenging. While multi-modal trajectory prediction models generate multiple plausible future paths with associated probabilities, effectively quantifying uncertainty remains an open problem. In this work, we propose a novel multi-modal trajectory prediction approach based on evidential deep learning that estimates both positional and mode probability uncertainty in real time. Our approach leverages a Normal Inverse Gamma distribution for positional uncertainty and a Dirichlet distribution for mode uncertainty. Unlike sampling-based methods, it infers both types of uncertainty in a single forward pass, significantly improving efficiency. Additionally, we experimented with uncertainty-driven importance sampling to improve training efficiency by prioritizing underrepresented high-uncertainty samples over redundant ones. We perform extensive evaluations of our method on the Argoverse 1 and Argoverse 2 datasets, demonstrating that it provides reliable uncertainty estimates while maintaining high trajectory prediction accuracy.

Figures (5)

• Figure 1: Evidential priors are used for both positional and mode probability prediction. At each time step, a Normal Inverse Gamma distribution models a higher-order probability distribution over the mean ($\mu$) and variance ($\sigma^2$) of each predicted position component ($x$ or $y$) which means each sample from NIG distribution would be a Gaussian distribution over the ($x$ or $y$). For modes probability prediction, a Dirichlet distribution estimates the probabilities of different possible trajectories, quantifying uncertainty in decision-making.
• Figure 2: Overview of our evidential-based multi-modal trajectory prediction framework. (A) The trajectory prediction model consists of three stages: Local Context Extraction, Global Intercation Modeling, and Multi-modal future decoding, which predict the parameters distribution. (B) The evidential framework models position uncertainty using a NIG distribution, capturing a higher-order distribution over the mean and variance of future positions. This allows real-time estimation of both aleatoric and epistemic uncertainty at each timestep. (C) A Dirichlet distribution models the categorical probability distribution over trajectory modes. Finally, both positional and mode uncertainties are processed by the Uncertainty Aggregator module to compute a holistic uncertainty estimate for each agent.
• Figure 3: Our Importance sampling framework. A model is trained on an initial randomly selected dataset, then the trained model is used to select new samples from remaining data points to retrain.
• Figure 4: t-SNE plot of Argoverse 2 validation set. All the embeddings have been mapped to 2D and color-coded with uncertainty on the left and the density of samples on the right.
• Figure 5: Trajectory prediction results on Argoverse 2 validation set. Agent history is in black, ground truth in green, and predicted trajectories in red with opacity reflecting mode probability. Left: Agent colors encode uncertainty. Right: Colors encode prediction error.