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Conformalized Adaptive Forecasting of Heterogeneous Trajectories
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Proposes CAFHT, a conformal method that wraps ACI prediction bands with a split-conformal max-score calibration to give simultaneous marginal coverage over entire heterogeneous trajectories, with data-driven learning-rate tuning.
Problem
Constructing simultaneous prediction bands covering the entire path of a new trajectory with finite-sample guarantees, while remaining informative under heterogeneous (heteroscedastic) trajectories of varying unpredictability, as needed for motion planning.
Approach
Combine ACI's online adaptive interval widths (which adapt to each trajectory's difficulty) with a split-conformal calibration over trajectory-level max-normalized or additive conformity scores, yielding simultaneous coverage guarantees; the learning rate is tuned by data splitting or a DKW/Markov correction.
Key results
- On synthetic AR trajectories with dynamic noise, CAFHT achieves 90% simultaneous marginal coverage with narrower average width and higher conditional coverage than NCTP, while CFRNN bands are so wide as to be uninformative.
- On ORCA pedestrian trajectories with 10% hard pedestrians, CAFHT yields relatively narrow bands with higher conditional coverage than NCTP at 90% marginal coverage.
- CFRNN becomes increasingly conservative as the prediction horizon T grows, while NCTP has the lowest conditional coverage among methods at large horizons.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CAFHT instead of NCTP | conformal forecasting bands · Synthetic heterogeneous trajectories (dynamic noise) | average width | Helped |
| Use CAFHT instead of NCTP | conformal forecasting bands · Synthetic heterogeneous trajectories (dynamic noise) | hard-trajectory simultaneous coverage | Helped |
| Use CAFHT instead of CFRNN | conformal forecasting bands · Synthetic heterogeneous trajectories (dynamic noise) | average width | Helped |
| Use CAFHT instead of CFRNN | conformal forecasting bands · Synthetic heterogeneous trajectories (dynamic noise) | hard-trajectory simultaneous coverage | Mixed |
| Use CAFHT instead of NCTP | conformal forecasting bands · Synthetic heterogeneous trajectories across prediction horizons | average width | Helped |
| Use CAFHT instead of NCTP | conformal forecasting bands · Synthetic heterogeneous trajectories across prediction horizons | hard-trajectory simultaneous coverage | Helped |
| Use CAFHT instead of NCTP | conformal forecasting bands · ORCA pedestrian trajectories | average width | Helped |
| Use CAFHT instead of NCTP | conformal forecasting bands · ORCA pedestrian trajectories | hard-trajectory simultaneous coverage | Helped |
| Add ACI warm-start scores (ablation) | ACI-based CAFHT · Finite-horizon trajectory forecasting | average width | Helped |
Surprising findings
- CFRNN attains the highest conditional coverage but only by producing bands so wide they are practically uninformative.
Limitations
- Guarantee is marginal, not conditional; conditional coverage is only approximate and empirical.
- Tuning the ACI learning rate by data splitting reduces calibration data or requires conservative corrections.
- Experiments are limited to simulated synthetic and ORCA pedestrian data, not real-world motion planning data.
Experimental setup
Datasets: synthetic AR trajectories ORCA pedestrian trajectories
Benchmarks: synthetic AR trajectories ORCA pedestrian trajectories
Metrics: simultaneous marginal coverage average band width simultaneous conditional coverage on hard trajectories
Baselines: CFRNN NCTP CopulaCPTS
Builds on: Adaptive Conformal Inference Conformal Forecasting RNN Conformalized quantile regression Conformal PID
Closest papers by meaning
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- Multi-model Ensemble Conformal Prediction in Dynamic Environments (NeurIPS 2024 · similarity 0.85)
- Neural Conformal Control for Time Series Forecasting (AAAI 2025 · similarity 0.85)
- Conformal Prediction for Time-series Forecasting with Change Points (NeurIPS 2025 · similarity 0.85)
- Online Localized Conformal Prediction (NeurIPS 2026 · similarity 0.85)
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