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Conformal Prediction with Learned Features
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Proposes Partition Learning Conformal Prediction (PLCP), which learns a partition of the covariate space from calibration data via alternating gradient descent so that prediction-set quantiles are conditionally valid, with theory bounding the mean squared conditional coverage error.
Problem
Conformal prediction with conditional coverage guarantees is impossible to achieve distribution-free with finite calibration data, and existing relaxations rely on predefined groups or covariate shift families that may not match the predictor's uncertainty structure.
Approach
Learn a soft partition of the covariate space (via a function class such as linear models or neural networks) jointly with one quantile per region by minimizing the empirical pinball loss over calibration data, so regions capture uncertainty-relevant structure instead of predefined groups.
Key results
- On the synthetic task, PLCP matched BatchGCP coverage on the 18 known groups and gave better coverage on the two unknown groups (19 and 20) without group information.
- On RxRx1, PLCP matched Conditional Calibration's coverage while producing smaller prediction sets than it.
- On MNIST under blur shift, PLCP achieved near-perfect coverage across all blur levels, while Split Conformal did not adapt.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Learned partition (PLCP) vs. CQR and LocalCP as conditional-validity methods | Conformal prediction with learned features · 2018 US Census and MNIST (appendix correlation metrics) | percent reduction in HSIC/Pearson correlation between interval length and covera: PLCP highest in all four cells (56.07/64.06 census; 73.36/86.08 MNIST) vs CQR and LocalCP | Helped |
| Learned partition (PLCP) vs. Split Conformal on synthetic group task and RxRx1 | PLCP · Synthetic regression and RxRx1 WILDS | coverage and set size | Mixed |
| Number of groups m tuned via doubling and bisection on validation set (bell-shaped MSCE vs m) | PLCP · Hyperparameter tuning | MSCE | Mixed |
Limitations
- Theoretical guarantees rely on Lipschitz-type regularity assumptions on the conditional score distribution, which are not distribution-free.
- Number of groups m must be tuned (via doubling and bisection on validation data), and the bell-shaped accuracy-vs-m relationship requires a held-out split.
Experimental setup
Datasets: 2018 US Census (Folktables) MNIST with Gaussian blur synthetic regression RxRx1 (WILDS)
Benchmarks: 2018 US Census (Folktables) MNIST with Gaussian blur synthetic regression RxRx1
Metrics: conditional coverage mean prediction interval length prediction set size HSIC Pearson correlation
Baselines: Split Conformal BatchGCP Conditional Calibration CQR LocalCP
Builds on: split conformal prediction conformalized quantile regression BatchGCP conditional calibration
Closest papers by meaning
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