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Neural Conformal Control for Time Series Forecasting
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Proposes NCC, a neural-network conformal controller for time series that learns adaptive quantiles with control-inspired losses, monotonicity constraints, and multi-view encoders, keeping long-term coverage guarantees.
Problem
Conformal prediction for non-stationary time series suffers from miscalibration, quantile crossing (distributional inconsistency) across confidence levels, underuse of auxiliary multi-view data, and poor few-shot performance.
Approach
Replace the fixed update rule of conformal control (ACI/C-PID) with an end-to-end neural quantile predictor trained with quantile, coverage (log-loss on sigmoid-approximated errors), efficiency, and monotonicity losses; a cumulative ReLU output design plus test-time adaptation enforces consistent intervals, and a windowed-average integral correction conformalizes outputs for long-term coverage.
Key results
- NCC achieves the lowest calibration score (CS) on most dataset/horizon settings in the seq2seq experiments, and the best CS on at least four datasets under each base forecaster.
- In the COVID-19 few-shot setup, NCC's cumulative CS drops below 0.1 quickly while other methods remain high by week 10.
- Incorporating multi-view data reduces CS by up to 18% overall and about 10% on covid-19.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add coverage loss (with efficiency loss) (ablation) | NCC · five datasets, one-step predictions | CS: 0.154 -> 0.104 (flu); 0.0883 -> 0.0551 (covid-19); 0.0466 -> 0.0221 (weather); 0.115 -> 0.0289 (smd); 0.0472 -> 0.0161 ( | Helped |
| add quantile loss (ablation) | NCC · five datasets, one-step predictions | WIS: 0.162 -> 0.134 (flu); 0.218 -> 0.113 (covid-19); 0.235 -> 0.108 (weather); 0.101 -> 0.0791 (smd); 0.134 -> 0.0876 (elect | Helped |
| add quantile loss (ablation) | NCC · five datasets, one-step predictions | CS: 0.0967 -> 0.104 (flu); 0.0600 -> 0.0551 (covid-19); 0.0235 -> 0.0221 (weather); 0.0444 -> 0.0289 (smd); 0.0175 -> 0.0161 | Mixed |
| add multi-view data (ablation) | NCC · COVID-19 | CS: $0.0551 \pm 0.0037$ -> $0.0501 \pm 0.0049$ | Helped |
| add multi-view data (ablation) | NCC · flu and weather | CS: flu: $0.104 \pm 0.004$ -> $0.143 \pm 0.080$; weather: $0.0221\pm 0.007$ -> $0.0237\pm 0.0086$ | Mixed |
| add multi-view data (ablation) | NCC · SMD | CS: $0.0289\pm 0.005$ -> $0.0244\pm 0.0114$ | Helped |
| add multi-view data (ablation) | NCC · electric | CS: $0.0161\pm 0.0020$ -> $0.0144\pm 0.0025$ | Helped |
| add monotonicity loss and test-time adaptation (ablation) | NCC · five datasets | DCS | Helped |
| use NCC instead of ACI | ThetaModel · Weather | CS: 0.0291 -> 0.0413 | Hurt |
| use NCC instead of ACI | ThetaModel · COVID-19, Flu, and Electric | CS: 0.0841 -> 0.0595 (Covid); 0.0813 -> 0.0678 (Flu); 0.0347 -> 0.0173 (Elec) | Helped |
Surprising findings
- C-PID has 0% valid (distributionally consistent) intervals on flu before sorting, and some conformal control baselines produce quantile crossing in many cases.
- Among baselines, more adaptive methods (lower CS) tended to have less consistent intervals (lower DCS), except NCC.
Limitations
- Produces wider prediction intervals than some baselines on a few datasets, attributed to loss balancing where efficiency loss is overlooked.
- Performance is sensitive to hyperparameters, requiring Bayesian optimization.
- Theoretical guarantee holds only for long-term average coverage, not per-step coverage.
Experimental setup
Datasets: flu (CDC wILI with Google search data) covid-19 hospitalization (CDC with Google search data) weather (Germany 2020) electric smd (server machine dataset)
Benchmarks: flu covid-19 weather electric smd
Metrics: Calibration Score (CS) CRPS Weighted Interval Score (WIS) Distribution Consistency Score (DCS)
Baselines: ACI C-PID NEXCP CF-RNN Conformalized quantile regression
Builds on: adaptive conformal inference conformal PID control conformalized quantile regression Informer
Closest papers by meaning
- Conformal Prediction for Time-series Forecasting with Change Points (NeurIPS 2025 · similarity 0.87)
- Error-quantified Conformal Inference for Time Series (ICLR 2025 · similarity 0.87)
- Non-Exchangeable Conformal Risk Control (ICLR 2024 · similarity 0.86)
- Conformalized Adaptive Forecasting of Heterogeneous Trajectories (ICML 2024 · similarity 0.85)
- Kernel-based Optimally Weighted Conformal Time-Series Prediction (ICLR 2025 · similarity 0.85)
- Conformalized Time Series with Semantic Features (NeurIPS 2024 · similarity 0.85)
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