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Boosted Conformal Prediction Intervals
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Proposes a post-training boosting procedure that improves conformity scores (Local, CQR, CQR-r generalizations) via gradient boosting on differentiable losses for conditional coverage deviation or interval length while preserving marginal coverage.
Problem
Conformal prediction intervals guarantee marginal coverage but may have poor conditional coverage and unnecessarily long intervals; the choice of conformity score constrains which properties can be achieved.
Approach
Searches over generalized conformity score families (Local family F and CQR family H containing Local, CQR, CQR-r) by gradient boosting (XGBoost) on differentiable surrogates of contrast-tree-based maximum conditional coverage deviation or average interval length, operating only on model predictions without retraining the model.
Key results
- Boosting Local for conditional coverage reduces max conditional coverage deviation on meps-19 from 15.36% to 5.66% (about 63% reduction) and on bike from 10.98% to 5.64%.
- Boosting Local for length reduces average length on blog from 2.056 to 0.972 (-52.74%) while keeping marginal coverage near 90%.
- Boosting CQR for length reduces average length on meps-21 by about 18.55% (2.585 to 2.105), but boosting CQR for conditional coverage gives little improvement (e.g., meps-19 unchanged at 5.507).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Boost the Local conformity score using the conditional-coverage loss | Local conformal prediction · meps-19 | maximum conditional coverage deviation (%): 15.357278 -> 5.656 | Helped |
| Boost the CQR conformity score using the conditional-coverage loss | CQR conformal prediction · meps-19 | maximum conditional coverage deviation (%): 5.506775 -> 5.507 | No clear effect |
| Boost the Local conformity score using the interval-length loss | Local conformal prediction · blog | average interval length: 2.056256 -> 0.972 | Helped |
| Boost the CQR conformity score using the interval-length loss | CQR conformal prediction · facebook-1 | average interval length: 1.198184 -> 1.072 | Helped |
| Boost the CQR conformity score using the interval-length loss | CQR conformal prediction · meps-21 | average interval length: 2.584983 -> 2.105 | Helped |
| Boost the CQR conformity score using the conditional-coverage loss | CQR conformal prediction · bike | maximum conditional coverage deviation (%): 4.933807 -> 4.925 | No clear effect |
Surprising findings
- Boosting the Local score makes it comparable to boosted CQR for conditional coverage, although CQR is already strong before boosting.
- Boosting for length on the Local score can increase conditional coverage deviation (e.g., blog 52.44% to 54.86%), showing that the non-targeted metric may worsen.
Limitations
- Greedy boosting has no global optimality guarantee; the starting score (Local vs CQR) affects performance.
- Gains for CQR baseline are small for conditional coverage; length-optimized intervals may undercover or overcover in some subgroups.
- Evaluation limited to 11 tabular datasets with random forest and small neural quantile regressors.
Experimental setup
Datasets: bike bio blog community concrete facebook-1 facebook-2 meps-19 meps-20 meps-21 star
Benchmarks: bike bio blog community concrete facebook-1 facebook-2 meps-19 meps-20 meps-21 star
Metrics: maximum conditional coverage deviation (contrast tree) average interval length marginal coverage
Baselines: Local CQR CQR-r CF-GNN ConTr
Builds on: locally adaptive conformal prediction conformalized quantile regression CQR-r contrast trees XGBoost
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- Conformal Prediction with Learned Features (ICML 2024 · similarity 0.87)
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