CUQDS: Conformal Uncertainty Quantification under Distribution Shift for Trajectory Prediction

TL;DR

CUQDS addresses trajectory prediction under distribution shift by jointly learning a Gaussian process based uncertainty model for a base predictor and a conformal P control calibration to maintain coverage online. The GP module models the conditional output distribution Y|x as N(mu(x), sigma^2(x)) with a learnable kernel and inducing variables, while the P control module updates the conformal quantile online to maintain long run coverage 1 - alpha. The approach yields narrower, calibrated uncertainty intervals and improves base model accuracy; experiments on Argoverse 1 report average 7.07% accuracy improvement, 25.41% NLL reduction, and 21.02% better coverage over strong baselines. This framework enables reliable online trajectory uncertainty quantification under distribution shift, with practical impact for autonomous vehicle planning.

Abstract

Trajectory prediction models that can infer both finite future trajectories and their associated uncertainties of the target vehicles in an online setting (e.g., real-world application scenarios) is crucial for ensuring the safe and robust navigation and path planning of autonomous vehicle motion. However, the majority of existing trajectory prediction models have neither considered reducing the uncertainty as one objective during the training stage nor provided reliable uncertainty quantification during inference stage under potential distribution shift. Therefore, in this paper, we propose the Conformal Uncertainty Quantification under Distribution Shift framework, CUQDS, to quantify the uncertainty of the predicted trajectories of existing trajectory prediction models under potential data distribution shift, while considering improving the prediction accuracy of the models and reducing the estimated uncertainty during the training stage. Specifically, CUQDS includes 1) a learning-based Gaussian process regression module that models the output distribution of the base model (any existing trajectory prediction or time series forecasting neural networks) and reduces the estimated uncertainty by additional loss term, and 2) a statistical-based Conformal P control module to calibrate the estimated uncertainty from the Gaussian process regression module in an online setting under potential distribution shift between training and testing data.

Figures (2)

• Figure 1: Illustration of the importance of a good uncertainty interval estimation for the predicted trajectories of the target vehicles.
• Figure 2: Our CUQDS models the conditional output distribution $\tilde{Y}|\tilde{x}, \mathcal{D} \sim \mathcal{N}\left(f_{\theta}\left(\tilde{x}\right), \tilde{{\sigma}}^{2}\left(\tilde{x}\right)\right)$ of base model $f_{\theta}$ by the Gaussian process regression (GPR) module, and provides the correspond calibrated uncertainty interval $\left[f_{\theta}\left(\tilde{x}\right)-\hat{q}^t\tilde{{\sigma}}\left(\tilde{x}\right), f_{\theta}\left(\tilde{x}\right)+\hat{q}^t\tilde{{\sigma}}\left(\tilde{x}\right)\right]$ for the predicted trajectories by the uncertainty calibration (UC) module.