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Online Localized Conformal Prediction
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Proposes Online Localized Conformal Prediction (OLCP), combining kernel-localized conformal quantiles with ACI-style online level updates, plus OLCP-Hedge, which selects bandwidths via constrained online convex optimization over experts.
Problem
Online conformal prediction for non-exchangeable time series is globally calibrated and thus inefficient under covariate-dependent heterogeneity; localized conformal methods assume exchangeability and are not designed for online streams.
Approach
Localize the online ACI calibration by weighting recent calibration scores by covariate similarity (kernel with bandwidth h), update the nominal level with coverage feedback, and aggregate bandwidth experts with a constrained OCO (virtual queue + AdaHedge) that minimizes set size subject to long-run coverage.
Key results
- In the heterogeneous simulation (B), OLCP-Hedge reaches coverage 0.900 with size 3.564 versus ACI 0.900 with 3.738 and DtACI 0.900 with 3.692.
- In the change-point simulation (C), OLCP-Hedge attains coverage 0.900 with size 6.348 versus ACI at 7.908 and DtACI at 7.840.
- On ELEC2, OLCP-Hedge gets coverage 0.899 with size 0.3351 versus ACI 0.900 with 0.3675; on ILINet OLCP-Hedge gets 0.900 with size 0.7478 versus ACI 0.9004 with 0.9004 size 0.9004 (ACI size 0.9004).
Surprising findings
- SPCI undercovers substantially (about 0.78 to 0.84 coverage) in all real datasets despite narrow intervals.
- Fixed-level LCP gives shorter intervals than ACI/DtACI but undercovers on several datasets.
Limitations
- OLCP-Hedge requires a uniformly feasible comparator (Assumption B), which may need conservative experts and be restrictive for unbounded regression.
- Full-information feedback and extra computational burden for expert aggregation.
- Depends on informative covariates and a suitable distance metric.
Experimental setup
Datasets: ELEC2 ILINet ETF volatility (SPY, QQQ, IWM, EEM, TLT with VIX)
Benchmarks: simulated AR scenarios A/B/C ELEC2 ILINet ETF volatility
Metrics: empirical marginal coverage average prediction set size running time
Baselines: CP LCP ACI DtACI SPCI
Builds on: adaptive conformal inference localized conformal prediction DtACI AdaHedge Sinha-Vaze constrained OCO
Closest papers by meaning
- Co-optimization for Adaptive Conformal Prediction (NeurIPS 2026 · similarity 0.89)
- Online Conformal Prediction via Online Optimization (ICML 2025 · similarity 0.89)
- Error-quantified Conformal Inference for Time Series (ICLR 2025 · similarity 0.89)
- Adaptive Conformal Inference by Betting (ICML 2024 · similarity 0.88)
- Multi-model Ensemble Conformal Prediction in Dynamic Environments (NeurIPS 2024 · similarity 0.88)
- Exploring the Noise Robustness of Online Conformal Prediction (NeurIPS 2025 · similarity 0.88)
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