Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
CUQDS: Conformal Uncertainty Quantification Under Distribution Shift for Trajectory Prediction
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Proposes CUQDS, a framework that adds a Gaussian process regression uncertainty module (with learnable RBF kernel and PCA-based inducing variables) to existing trajectory predictors and calibrates intervals online with a conformal P-control quantile under distribution shift.
Problem
Trajectory prediction models give overconfident uncertainty estimates and standard conformal prediction loses coverage guarantees when test data drifts from training data.
Approach
Model the base predictor's output distribution with a GP regression module trained with an extra NLL-style loss to shrink variance, then update the conformal quantile after each prediction via a P-control rule (initialized on validation data) so long-run miscoverage tends to the target error rate.
Key results
- Applying CUQDS improves minADE6/minFDE6/MR6 for base models, e.g. HiVT minADE6 0.692 to 0.682 and MR6 0.106 to 0.097, with about 7.07% average accuracy gain reported.
- Compared to SPCI-augmented base models, CUQDS reduces NLL by about 25.41% on average (e.g. HiVT 21.354 to 16.354).
- On LaneGCN, standard split conformal prediction achieves coverage 0.402 versus 0.746 for the P-control module.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add CUQDS to HiVT | HiVT · Argoverse 1 testing | minADE_6: 0.692 -> 0.682 | Helped |
| Add CUQDS to LaneGCN | LaneGCN · Argoverse 1 testing | minADE_6: 0.719 -> 0.704 | Helped |
| Add CUQDS to LBA | LBA · Argoverse 1 testing | minADE_6: 0.717 -> 0.705 | Helped |
| Add CUQDS to LBF | LBF · Argoverse 1 testing | minADE_6: 0.720 -> 0.714 | Helped |
| Add CUQDS to Trajectron++ | Trajectron++ · Argoverse 1 testing | minADE_6: 0.764 -> 0.693 | Helped |
| Add CUQDS instead of SPCI | HiVT, LaneGCN, LBA, and LBF · Argoverse 1 testing | NLL: reduces ... by 25.41% on average | Helped |
| Add CUQDS instead of SPCI | HiVT, LaneGCN, LBA, and LBF · Argoverse 1 testing | coverage rate: improves ... by 21.02% | Helped |
| Replace adaptive P control calibration with fixed split conformal prediction (ablation) | LaneGCN+CUQDS · Argoverse 1 testing | coverage rate: 0.746 vs 0.402 | Hurt |
| Add P control uncertainty calibration (ablation) | CUQDS · Argoverse 1 testing | coverage rate: 0.497 -> 0.746; 0.603 -> 0.832 | Helped |
| Replace Gaussian process regression with self-attention direct modeling (ablation) | HiVT+CUQDS · Argoverse 1 testing | minADE_6: 0.682 -> 0.694 | Hurt |
| Replace Gaussian process regression with self-attention direct modeling (ablation) | HiVT+CUQDS · Argoverse 1 testing | minFDE_6: 1.034 -> 1.047 | Hurt |
| Replace Gaussian process regression with self-attention direct modeling (ablation) | HiVT+CUQDS · Argoverse 1 testing | miss rate_6: 0.097 -> 0.107 | Hurt |
Surprising findings
- Table for coverage rates shows inconsistent numbers versus the text (e.g., HiVT coverage reported as 0.832 vs. the 0.603 'without UC' value), and Trajectron+++CUQDS minFDE6 (1.101) is worse than its SPCI variant (1.079).
Limitations
- Evaluated only on Argoverse 1 and only with the authors' own data split, since official test labels are unavailable.
- Uncertainty is modeled per trajectory rather than per time step.
- Distribution shift is assumed to be temporal, and the method's theoretical guarantee under shift is not formally established in the text.
Experimental setup
Datasets: Argoverse 1 motion forecasting dataset
Benchmarks: Argoverse 1 motion forecasting
Metrics: minADE minFDE MR NLL coverage rate
Baselines: HiVT LaneGCN LBA LBF Trajectron++ SPCI
Builds on: split conformal prediction SPCI Gaussian process regression adaptive conformal prediction
Closest papers by meaning
- Conformal Prediction in The Loop: A Feedback-Based Uncertainty Model for Trajectory Optimization (NeurIPS 2025 · similarity 0.85)
- Conformalized Adaptive Forecasting of Heterogeneous Trajectories (ICML 2024 · similarity 0.85)
- Quantifying Uncertainty in Motion Prediction with Variational Bayesian Mixture (CVPR 2024 · similarity 0.84)
- CCTR: Calibrating Trajectory Prediction for Uncertainty-Aware Motion Planning in Autonomous Driving (AAAI 2024 · similarity 0.84)
- Proper Scoring Rules for Agentic Uncertainty Quantification (NeurIPS 2026 · similarity 0.84)
- C2F-TP: A Coarse-to-Fine Denoising Framework for Uncertainty-Aware Trajectory Prediction (AAAI 2025 · similarity 0.84)
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