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Conformalized Time Series with Semantic Features
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Proposes CT-SSF, which runs weighted conformal prediction in the latent feature space of a neural time-series forecaster, with attention-based weights learned to emphasize relevant calibration points, yielding tighter intervals with valid coverage.
Problem
Conformal prediction for time series violates exchangeability; existing reweighting methods use manually chosen weights in the output space, producing overly conservative intervals.
Approach
Compute non-conformity scores as surrogate-feature distances in the latent space of a neural network (split into feature function f and head g), with dynamically learned attention-based weights for weighted quantiles, then map bands back to output space via LiPRA perturbation analysis.
Key results
- On real-world data at alpha=0.1, CT-SSF reports widths of 0.21 (Elec), 0.19 (Stock), 0.012 (Weather), 0.52 (Wind), versus HopCPT at 0.23, 0.23, 0.017, 0.54, described as a 10%-20% reduction.
- In the synthetic simulation at alpha=0.05, CT-SSF width is 1.45 vs HopCPT 1.54 (about 4.6% reduction) with coverage 96.5%.
- Ablation shows CT-SSF widths more than 50% smaller than output-space variants CT-MO and CT-LO on synthetic data.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use latent semantic-space scores and adaptive weight adjustment instead of HopCPT | time-series conformal prediction · Simulations (α=0.05) | Width: 1.54±0.87 -> 1.45±0.23 | Helped |
| use latent semantic-space scores and adaptive weight adjustment instead of HopCPT | time-series conformal prediction · Simulations (α=0.1) | Width: 1.43±0.78 -> 1.23±0.15 | Helped |
| use latent semantic-space scores and adaptive weight adjustment instead of HopCPT | time-series conformal prediction · Electricity, Stock, Weather, and Wind (α=0.1) | Width: 0.23±0.05 -> 0.21±0.03; 0.23±0.04 -> 0.19±0.03; 0.017±0.004 -> 0.012±0.002; 0.54±0.04 -> 0.52±0.03 | Helped |
| add adaptive weight adjustment to semantic-space scores (CT-MS -> CT-SSF) (ablation) | CT-SSF · Synthetic data, miscoverage risks 0.05–0.3 | Width: null | Helped |
| add semantic-space scoring and adaptive weight adjustment rather than output-space variants CT-MO and CT-LO (ablation) | CT-SSF · Synthetic data, miscoverage risks 0.05–0.3 | Width: null | Helped |
| use the 4th rather than the 2nd RNN layer as the semantic feature space (ablation) | CT-SSF · Electricity (α=0.1) | Width: 0.23±0.09 -> 0.21±0.03 | Helped |
| use the 4th rather than the 2nd RNN layer as the semantic feature space (ablation) | CT-SSF · Stock (α=0.1) | Width: 0.39±0.12 -> 0.19±0.03 | Helped |
| use the 4th rather than the 2nd RNN layer as the semantic feature space (ablation) | CT-SSF · Weather (α=0.1) | Width: 0.018±0.004 -> 0.012±0.002 | Helped |
| use the 4th rather than the 2nd RNN layer as the semantic feature space (ablation) | CT-SSF · Wind (α=0.1) | Width: 1.00±.023 -> 0.54±0.12 | Helped |
Surprising findings
- NexCP with manually selected weights can yield wider intervals than standard split CP on the wind dataset.
- Optimal latent split for f and g was typically middle layers (3rd or 4th of 8) rather than deepest.
Limitations
- Relies on neural network base models, excluding simpler models such as ridge regression or random forests.
- Prediction interval length is sensitive to the choice of latent split between f and g, and a validation subset reduces calibration data.
- Theory assumes weights are fixed/independent of scores, while implementation learns data-driven weights.
Experimental setup
Datasets: Electricity (Harries 1999) Amazon stock Weather (2020, 10-min) MISO wind speed Synthetic simulation
Benchmarks: Synthetic simulation Electricity Amazon stock Weather Wind speed
Metrics: empirical coverage average prediction interval width
Baselines: Standard Split CP NexCP FeatureCP HopCPT CT-MS CT-LO CT-MO
Builds on: NexCP HopCPT Feature CP (surrogate feature band estimation) split conformal prediction LiPRA
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