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Aligning Model Properties via Conformal Risk Control
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Proposes framing model alignment as property testing and post-processing a pre-trained regressor with conformal risk control, using proximity-oblivious tester losses to produce conformal bands that contain functions approximately satisfying properties like monotonicity and concavity.
Problem
Aligning pre-trained non-generative models (numerical/categorical outputs) with user-desired properties such as monotonicity or concavity, without retraining, and showing that alignment is needed even as model size and data grow under biased labels.
Approach
Map property-testing queries (proximity-oblivious testers) to loss functions for multi-dimensional conformal risk control over asymmetric prediction bands around a fixed model; prove that the resulting band contains an approximately property-satisfying function with probabilistic guarantees.
Key results
- On Power Plant at alpha=0.1, the conformal-adjusted model reaches risk 0.10 (target 0.1) versus unconstrained risk 0.75, with MSE 10.47 vs unconstrained 10.19 and constrained 16.21.
- Adjusted model's empirical risk closely tracks the target alpha across alpha = 0.1, 0.05, 0.01 (risk 0.10, 0.05, 0.01).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply conformal property alignment to unconstrained XGBoost | XGBoost regression · Combined Cycle Power Plant test | Risk: 0.75 -> 0.10; 0.75 -> 0.05; 0.75 -> 0.01 | Helped |
| Apply conformal property alignment to unconstrained XGBoost | XGBoost regression · Combined Cycle Power Plant test | MSE: 10.19 -> 10.47; 10.19 -> 11.42; 10.19 -> 14.46 | Hurt |
| Apply conformal property alignment to unconstrained XGBoost | XGBoost regression · Abalone test | Risk: 0.58 -> 0.09; 0.58 -> 0.04; 0.58 -> 0.01 | Helped |
| Apply conformal property alignment to unconstrained XGBoost | XGBoost regression · Abalone test | MSE: 5.41 -> 5.46; 5.41 -> 5.63; 5.41 -> 6.67 | Hurt |
Surprising findings
- The conformal-adjusted model outperforms the constrained (monotone-trained) XGBoost in MSE on Power Plant for all alpha, which the authors call fortuitous but unexpected.
- Theory suggests overparameterized random feature models cannot satisfy the property even as data grows when labels contain small biases.
Limitations
- Guarantees hold for the calibration-data distribution and depend on the detection probability of the tester; bound is loose when detection probability is near alpha.
- Experiments limited to monotonicity and concavity on small tabular UCI datasets with XGBoost.
- Non-adaptive testers only; concavity experiments mostly in appendix.
Experimental setup
Datasets: UCI Combined Cycle Power Plant UCI Abalone UCI Concrete
Benchmarks: UCI Combined Cycle Power Plant UCI Abalone UCI Concrete
Metrics: MSE property risk (monotonicity violation rate)
Baselines: unconstrained XGBoost constrained XGBoost (monotone trained on train+calibration)
Builds on: conformal risk control property testing XGBoost
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