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AdaptNC: Adaptive Nonconformity Scores for Conformal Prediction under Distribution Shift
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Proposes AdaptNC, which jointly adapts a convex-template nonconformity score (via KDE high-density regions with DtACI-based history reweighting) and the conformal threshold online, with a replay buffer to mitigate coverage shock, and reports smaller prediction volumes than DtACI and Split/Shape CP on three robotics case studies.
Problem
Online conformal prediction under distribution shift keeps the nonconformity score fixed, so prediction regions can only be resized, not reshaped, leading to conservative, volume-inefficient regions when error geometry changes in robotic settings.
Approach
Jointly adapt the nonconformity score parameters (a convex-hull shape template fit to weighted high-density residuals, with weights from DtACI expert mixtures) and the conformal threshold online, and replay recent observations after each score update to recalibrate DtACI's expert state ("coverage shock" mitigation).
Key results
- Multirotor tracking: AdaptNC reaches 92.5% global coverage with volume 0.04 m^2 versus DtACI 87.4% with 0.44 m^2 (about 11x smaller).
- Indoor localization: AdaptNC achieves 90.6% coverage with 27.76 m^2 volume versus DtACI 92.2% with 43.09 m^2.
- Social navigation: AdaptNC attains 91.6% coverage, while DtACI reaches 80.0% and Split CP 3.0%; Split CP and Shape CP have much smaller volume but severe undercoverage.
Surprising findings
- Split CP and Shape-CP achieve small volumes only by severely undercovering (about 3% coverage in social navigation).
- Vacuous coverage rate is about 25% for AdaptNC versus about 20% for DtACI.
Limitations
- Vacuous (infinite) prediction sets occur about 25% of the time, slightly more than DtACI.
- Theoretical guarantees are asymptotic and rely on a boundary anti-concentration assumption; finite-sample replay guarantees are open.
- Score update costs about 100 ms, dominated by KDE evaluation, and is restricted to low-dimensional outputs (d<=3) for efficiency analysis.
Experimental setup
Datasets: simulated indoor localization wireless signal data simulated social navigation trajectories (8 agents) simulated multirotor tracking trajectories
Benchmarks: Indoor Localization Social Navigation Multirotor Tracking
Metrics: global coverage prediction region volume mean local coverage
Baselines: DtACI Split Conformal Prediction AdaptNC without replay Shape-CP
Builds on: DtACI Adaptive Conformal Inference Shape-CP Monte Carlo kernel density estimation
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