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Relational Conformal Prediction for Correlated Time Series
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Proposes Relational Conformal Prediction (RelCP), a graph-based quantile-regression conformal method that learns sparse inter-series relations from calibration residuals to produce prediction intervals for correlated time series on top of any pre-trained forecaster.
Problem
Uncertainty quantification for correlated time series forecasting: existing conformal prediction methods for time series treat each series independently and ignore relational dependencies among series when building prediction intervals.
Approach
A hybrid global-local STGNN quantile regressor, trained on calibration residuals, with a learned sparse (K-NN, Gumbel-TopK) graph and node embeddings, estimates per-series error quantiles conditioned on neighboring residuals; an adaptive step fine-tunes only node embeddings over time.
Key results
- On the RNN base model for METR-LA, RelCP achieves Winkler 23.78 vs 40.80 for SCP and 25.63 for HopCPT, with PI-width 14.38.
- On AQI with RNN base model, RelCP attains Winkler 107.67 vs 148.61 for SCP, the best among compared methods.
- On GPVAR with RNN base, RelCP reaches PI-width 1.33 and Winkler 1.67 vs 2.14 for SCP, close to the theoretical optimum width of 1.315 at 90% coverage.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add relational graph-based quantile prediction | Relational Conformal Prediction versus strongest listed baseline · LA with RNN predictor | Winkler: 25.63{ $\pm$0.19} -> 23.78{ $\pm$0.20} | Helped |
| add relational graph-based quantile prediction | Relational Conformal Prediction versus strongest listed baseline · LA with Transformer predictor | Winkler: 25.37{ $\pm$0.33} -> 23.65{ $\pm$0.19} | Helped |
| add relational graph-based quantile prediction | Relational Conformal Prediction versus strongest listed baseline · LA with STGNN predictor | Winkler: 22.80{ $\pm$0.28} -> 24.70{ $\pm$0.16} | Hurt |
| add relational graph-based quantile prediction | Relational Conformal Prediction versus strongest listed baseline · CER with RNN predictor | Winkler: 3.84{ $\pm$0.01} -> 3.71{ $\pm$0.04} | Helped |
| add relational graph-based quantile prediction | Relational Conformal Prediction versus strongest listed baseline · CER with Transformer predictor | Winkler: 3.82{ $\pm$0.02} -> 3.67{ $\pm$0.02} | Helped |
| add relational graph-based quantile prediction | Relational Conformal Prediction versus strongest listed baseline · CER with STGNN predictor | Winkler: 3.49{ $\pm$0.02} -> 3.76{ $\pm$0.04} | Hurt |
| add relational graph-based quantile prediction | Relational Conformal Prediction versus strongest listed baseline · AIR with RNN predictor | Winkler: 113.11{ $\pm$0.77} -> 107.67{ $\pm$0.94} | Helped |
| add relational graph-based quantile prediction | Relational Conformal Prediction versus strongest listed baseline · AIR with Transformer predictor | Winkler: 112.71{ $\pm$0.44} -> 108.71{ $\pm$1.38} | Helped |
| add relational graph-based quantile prediction | Relational Conformal Prediction versus strongest listed baseline · AIR with STGNN predictor | Winkler: 109.65{ $\pm$0.30} -> 108.45{ $\pm$1.52} | Helped |
| add graph message passing and node embeddings (ablation) | Relational Conformal Prediction · GPVAR-RNN | Winkler: 2.04{ $\pm$0.00} -> 1.67{ $\pm$0.00} | Helped |
| learn the graph rather than use a supplied true graph (ablation) | Relational Conformal Prediction · GPVAR-RNN | Winkler: 1.66{ $\pm$0.00} -> 1.67{ $\pm$0.00} | No clear effect |
| add adaptive updates to node embeddings (ablation) | Relational Conformal Prediction · CER with RNN predictor | Winkler: 3.71 { $\pm$ 0.03} -> 3.49 { $\pm$ 0.02} | Helped |
Surprising findings
- Standard SCP is competitive when the base predictor is an STGNN that already models spatial dependencies, since residuals become largely uncorrelated (GPVAR-STGNN).
- NexCP and SeqCP show notably larger coverage gaps (e.g., SeqCP -6.93 to -13.60 on METR-LA).
Limitations
- Produces separate per-series intervals and does not model the joint distribution of the time series.
- Coverage guarantees under non-stationarity are not established; the adaptive component is heuristic.
- Coverage gap is noticeably negative on CER (about -3 to -5%), and the method prioritizes Winkler score over coverage.
Experimental setup
Datasets: METR-LA AQI (Chinese air quality) CER smart metering GPVAR synthetic
Benchmarks: METR-LA AQI CER GPVAR
Metrics: Delta Coverage PI-Width Winkler score
Baselines: SCP SeqCP NexCP SPCI HopCPT CoRNN
Builds on: split conformal prediction NExCP SPCI HopCPT Gumbel-TopK implicit quantile networks
Closest papers by meaning
- Error-quantified Conformal Inference for Time Series (ICLR 2025 · similarity 0.87)
- Conformalized Time Series with Semantic Features (NeurIPS 2024 · similarity 0.87)
- Conformal Prediction for Time-series Forecasting with Change Points (NeurIPS 2025 · similarity 0.87)
- Conformal prediction for multi-dimensional time series by ellipsoidal sets (ICML 2024 · similarity 0.86)
- Kernel-based Optimally Weighted Conformal Time-Series Prediction (ICLR 2025 · similarity 0.86)
- Filtered Conformal Ellipsoids for Graph-Native Time Series (NeurIPS 2026 · similarity 0.86)
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