Research map / Label-efficient and robust learning / Domain adaptation and generalization
Optimal Aggregation of Prediction Intervals under Unsupervised Domain Shift
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Proposes convex aggregation of source-domain prediction intervals, transported to the target via bounded density ratio or measure-preserving map, to get minimal-width intervals with coverage under unsupervised domain shift.
Problem
Constructing prediction intervals on a target domain with minimal width and valid coverage when only source labels and target covariates are available (unsupervised domain shift).
Approach
Formulates shape estimation as a convex program (minimize target expected width of squared-residual bound subject to source coverage constraints, with hinge surrogate for indicator), then shrinks the shape by a source-estimated factor; for measure-preserving shifts, it transports the source interval via an estimated map T0. Model aggregation reduces to a linear program over candidate interval esti
Key results
- On airfoil over 200 experiments, the proposed method averaged 0.964 coverage with width 13.65 versus 0.954 coverage and width 20.53 for weighted conformal prediction.
- On the misspecification simulation, the proposed method kept average width near 2.07 across forest depths while WVAC's width grew from 3.08 to 5.00.
- Real estate experiment reports median width 36.9 for the proposed method versus 46.4 (WVAC) and 46.9 (WQC) with coverage 0.98.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use optimal aggregation instead of weighted conformal prediction | Airfoil shifted · Airfoil shifted | average width: 20.53 (SD = 4.13) -> 13.654 (SD = 2.22) | Helped |
| use optimal aggregation instead of weighted conformal prediction | Airfoil shifted · Airfoil shifted | coverage: 0.9535 (SD = 0.036) -> 0.964029 (SD = 0.04) | No clear effect |
| use optimal aggregation instead of WVAC | Real Estate shifted · Real Estate shifted | bandwidth (median): 46.392 -> 36.889 | Helped |
| use optimal aggregation instead of WQC | Real Estate shifted · Real Estate shifted | bandwidth (median): 46.858 -> 36.889 | Helped |
| use optimal aggregation instead of WVAC | Real Estate shifted · Real Estate shifted | coverage (median): 0.962 -> 0.98 | Helped |
| use optimal aggregation instead of WQC | Real Estate shifted · Real Estate shifted | coverage (median): 0.971 -> 0.98 | Helped |
| use optimal aggregation instead of WVAC | Real Estate shifted, coverage > 95% · Real Estate shifted, coverage > 95% | bandwidth (median): 50.703 -> 40.774 | Helped |
| use optimal aggregation instead of WQC | Real Estate shifted, coverage > 95% · Real Estate shifted, coverage > 95% | bandwidth (median): 51.031 -> 40.774 | Helped |
| use optimal aggregation instead of WVAC | Energy Efficiency shifted · Energy Efficiency shifted | coverage (median): 0.969 -> 0.995 | Helped |
| use optimal aggregation instead of WQC | Energy Efficiency shifted · Energy Efficiency shifted | coverage (median): 0.973 -> 0.995 | Helped |
| vary the random-forest variance estimator max depth from 3 to 15 (ablation) | Optimal aggregation · Model misspecification simulation | average width: 2.07(0.975) -> 2.08(0.97) | No clear effect |
| vary the random-forest variance estimator max depth from 3 to 15 (ablation) | WVAC · Model misspecification simulation | average width: 3.08(0.9712) -> 5.00(0.97) | Hurt |
Limitations
- Density ratio must be bounded (or consistently estimated) for covariate-shift guarantees; unbounded ratios need the transport-map setting.
- Transport map T0 must be known or estimated; theory assumes Lipschitz function classes and accurate T0 estimation.
- Data splitting reduces effective sample size for shape and shrinkage estimation.
Experimental setup
Datasets: airfoil self-noise (UCI) real estate valuation (UCI) energy efficiency (UCI) appliance energy prediction (UCI) ETT-small
Benchmarks: airfoil (UCI) real estate (UCI) energy efficiency (UCI) appliance energy ETT-small
Metrics: coverage average interval width
Baselines: weighted conformal prediction WVAC WQC
Builds on: weighted conformal prediction prediction interval aggregation (i.i.d.) optimal transport domain alignment
Closest papers by meaning
- Adaptive Risk Minimization: Learning to Adapt to Domain Shift (NeurIPS 2021 · similarity 0.87)
- Conformal Prediction under Lévy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations (NeurIPS 2025 · similarity 0.85)
- Multiply Robust Estimation for Local Distribution Shifts with Multiple Domains (ICML 2024 · similarity 0.85)
- Quantifying Uncertainty in the Presence of Distribution Shifts (NeurIPS 2025 · similarity 0.85)
- Not all distributional shifts are equal: Fine-grained robust conformal inference (ICML 2024 · similarity 0.84)
- Boosting Methods for Interval-censored Data with Regression and Classification (ICLR 2025 · similarity 0.84)
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