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Synthetic-powered predictive inference
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Proposes Synthetic-powered predictive inference (SPI), which uses a score transporter (empirical quantile mapping of real to synthetic nonconformity scores) to calibrate conformal prediction sets with small real calibration sets plus large synthetic data, with finite-sample coverage bounds.
Problem
Conformal prediction yields uninformative or trivial prediction sets when the real labeled calibration set is very small, and synthetic data from a possibly different distribution cannot be naively pooled without breaking coverage.
Approach
A score transporter maps each real calibration/test score to a synthetic score within a probabilistic window derived from order statistics, then runs split conformal on the synthetic scores; coverage bounds hold without assumptions on the synthetic distribution, even when synthetic data depend on the real calibration set.
Key results
- On ImageNet with m=15 real calibration images, SPI achieves coverage within the theoretical bounds while OnlyReal produces trivial prediction sets containing all 30 labels at alpha=0.05-level settings.
- OnlySynth fails to reach target coverage for some classes (e.g., Siberian husky) due to distribution shift, whereas SPI maintains coverage with informative sets.
- On MEPS regression with m=15 and N=1000, SPI achieves coverage close to the nominal 0.9 level across age groups.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use SPI with synthetic images instead of OnlyReal | ImageNet-1k, Stable Diffusion · ImageNet, marginal and label-conditional | prediction set size | Helped |
| use SPI rather than OnlySynth | ImageNet-1k, Stable Diffusion · ImageNet, marginal and label-conditional | coverage | Helped |
| use SPI rather than OnlyReal | MEPS panel 21 regression · MEPS, age groups | coverage | Helped |
| use SPI-Subset instead of SPI-Whole (ablation) | SPI with k-nearest subset selection · ImageNet, label-conditional | prediction set size | Helped |
| select a k-nearest synthetic subset instead of using the whole synthetic set (ablation) | SPI with k-nearest subset selection · ImageNet, label-conditional | coverage | Helped |
| use SPI-Subset instead of SPI-Whole (ablation) | SPI with k-nearest subset selection · ImageNet, marginal | coverage variance | Hurt |
| use SPI-Subset instead of OnlyReal (ablation) | SPI with k-nearest subset selection · ImageNet, marginal and label-conditional | prediction set size | Helped |
Surprising findings
- Synthetic data can be correlated with the real calibration set and the worst-case coverage bounds still hold, with bounds depending only on m, N, alpha and beta.
Limitations
- Assumes real calibration data and test point are i.i.d./exchangeable; not extended to non-iid settings.
- Feature-conditional coverage not addressed.
- Subset-selection variant requires the synthetic subset size to be fixed in advance.
Experimental setup
Datasets: ImageNet MEPS
Benchmarks: ImageNet MEPS
Metrics: coverage rate prediction set size prediction interval width
Baselines: OnlyReal split conformal OnlySynth SPI-Whole
Builds on: split conformal prediction adaptive prediction sets conformalized quantile regression label-conditional conformal prediction
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