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Utility-Directed Conformal Prediction: A Decision-Aware Framework for Actionable Uncertainty Quantification
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Proposes utility-directed conformal prediction methods that build prediction sets minimizing a user-specified set cost while retaining marginal coverage, via penalized nonconformity scores, a separable penalized ratio, and a greedy optimizer-based score.
Problem
Standard conformal prediction guarantees coverage but ignores downstream decision utility, so prediction sets can be large or heterogeneous and not actionable for high-stakes decisions.
Approach
Incorporate a set-level cost into conformal nonconformity scores: a penalized score (rho + lambda * cost of marginal increments) tuned on validation data, a hyperparameter-free separable penalized ratio (p/ell thresholding), and a greedy-optimizer-derived ordering for non-separable costs; all conformalized with split conformal to keep marginal coverage.
Key results
- On separable loss, Separable Penalized Ratio reduces set cost on iNaturalist from 32.949 (base conformal) to 2.043 and on ImageNet from 150.162 to 5.277.
- On non-separable max-penalty loss, Penalized Conformal reduces iNaturalist cost from 0.591 to 0.076 and CIFAR-100 from 0.475 to 0.229, roughly 60-85% reductions.
- Conditional coverage by set size remains near the 0.9 target for most bins, and Penalized Conformal obtains smaller average sets than base conformal on all datasets (e.g., iNaturalist 1.20 vs 17.1).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the separable penalized ratio score instead of base conformal prediction | EfficientNet-B0 conformal prediction · CIFAR100, ImageNet, iNaturalist, Fitzpatrick, and Fitzpatrick Clean | separable loss: 29.146 (2.339) -> 4.442 (0.374); 150.162 (12.889) -> 5.277 (0.549); 32.949 (4.982) -> 2.043 (0.474); 86.373 (8.680) -> 6 | Helped |
| Add the cost penalty to the conformal score | EfficientNet-B0 conformal prediction · CIFAR100, ImageNet, iNaturalist, Fitzpatrick, and Fitzpatrick Clean | maximum penalty per set: 0.475 (0.003) -> 0.229 (0.003); 0.432 (0.003) -> 0.150 (0.002); 0.591 (0.002) -> 0.076 (0.001) | Helped |
| Use greedy loss-based label ordering instead of base conformal prediction | EfficientNet-B0 conformal prediction · Fitzpatrick and Fitzpatrick Clean | maximum penalty per set: 0.692 (0.005) -> 0.502 (0.007); 0.657 (0.004) -> 0.515 (0.007) | Helped |
| Use greedy loss-based label ordering instead of base conformal prediction | EfficientNet-B0 conformal prediction · Fitzpatrick and Fitzpatrick Clean | coverage loss: 6.134 (0.080) -> 2.940 (0.033); 4.634 (0.054) -> 3.144 (0.034) | Helped |
| Vary the penalty weight λ across the reported values (ablation) | Penalized Conformal · CIFAR100, ImageNet, iNaturalist, Fitzpatrick, and Fitzpatrick Clean | separable loss | Mixed |
| Vary the penalty weight λ across the reported values (ablation) | Penalized Conformal · CIFAR100, ImageNet, iNaturalist, Fitzpatrick, and Fitzpatrick Clean | maximum penalty per set | Mixed |
| Vary the penalty weight λ across the reported values (ablation) | Penalized Conformal · CIFAR100, ImageNet, iNaturalist, Fitzpatrick, and Fitzpatrick Clean | coverage loss | Mixed |
| Use a higher-accuracy base classifier (ablation) | Fitzpatrick classifier and conformal methods · Fitzpatrick Clean | downstream loss | Helped |
Surprising findings
- Greedy optimizer sets are substantially larger than base conformal sets (e.g., ImageNet 152 vs 74.8) yet achieve lower utility loss, indicating the utility is optimized at the expense of set size.
- On the Fitzpatrick dataset the penalized conformal method with tuned lambda did not outperform the principled greedy/ratio methods, which the authors attribute to too little data for reliable lambda tuning.
Limitations
- Marginal coverage only; conditional coverage is impossible without the true p(y|x), so per-instance guarantees are not provided.
- Penalized conformal requires tuning lambda on a validation split and resampling the calibration quantile, and performance depends on classifier quality (Fitzpatrick accuracy around 30%).
- Greedy methods yield much larger average set sizes, trading set compactness for utility.
Experimental setup
Datasets: CIFAR-100 iNaturalist ImageNet Fitzpatrick17k
Benchmarks: CIFAR-100 ImageNet iNaturalist Fitzpatrick Fitzpatrick Clean
Metrics: average set cost (separable sum of penalties) maximum penalty in set hierarchy coverage function loss conditional coverage by set size average set size
Baselines: Base Conformal (adaptive prediction sets) Penalized Conformal Bayesian neural network prediction sets Conformal risk control
Builds on: split conformal prediction adaptive prediction sets conformal risk control
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