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Conformal Prediction via Regression-as-Classification
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Converts regression into classification by binning the output range and applies classification conformal prediction with an ordinal distance-based loss plus entropy regularization to produce shorter conformal intervals for regression.
Problem
Conformal prediction for regression is hard when the output distribution is heteroscedastic, multimodal, or skewed; distribution-estimation approaches are sensitive to estimation error and yield unstable intervals.
Approach
Discretize the regression target into K bins treated as classes, train a softmax network with an ordinal loss (expected distance-based penalty |y - ŷ|^p) minus an entropy term, then apply classification-style conformal prediction using linearly interpolated probabilities to obtain interval sets that can be disjoint and adapt to label shape.
Key results
- Intervals produced by the proposed method are the shortest on 10 of 16 datasets at 90% coverage.
- Coverage is approximately 0.90 across methods and datasets, consistent with the conformal guarantee.
- Ablation shows removing entropy or using MLE loss yields sharper, overconfident densities and generally longer intervals on most datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use R2CCP instead of the other conformal prediction baselines | Regression conformal prediction · UCI and MEPS datasets | interval length | Helped |
| Add entropy regularization to the distance-based loss (ablation) | R2CCP · Most datasets | interval length | Helped |
| Remove entropy regularization (ablation) | R2CCP · Bimodal | interval length | No clear effect |
| Replace the distance-based error term with MLE (ablation) | R2CCP · Across datasets | interval length | Mixed |
| Add entropy regularization to the MLE loss (ablation) | R2CCP · Across datasets | interval length | No clear effect |
| Increase the number of output bins (ablation) | R2CCP on Concrete · Concrete | interval length | Helped |
Surprising findings
- On Bimodal, Log-Normal, Parkinsons, and Solar, the method is not best; other loss variants or KDE produce shorter intervals.
- Prediction error is not strongly correlated with interval length.
Limitations
- Requires larger networks and careful per-dataset training hyperparameters (learning rate, batch size) to avoid divergence.
- Learned probabilities do not directly mirror the ground-truth distribution because entropy regularization introduces bias.
- Not superior to some baselines on several datasets (Bimodal, Log-Normal, Parkinsons, Solar).
Experimental setup
Datasets: UCI regression datasets (Bio, Blog, Concrete, Community, Energy, Forest, Stock, Cancer, Solar, Parkinsons, Pendulum, Dia MEPS-19 MEPS-20 MEPS-21 synthetic heteroscedastic data synthetic bimodal data synthetic log-normal data
Benchmarks: UCI regression datasets MEPS-19 MEPS-20 MEPS-21 synthetic bimodal synthetic log-normal
Metrics: interval length coverage
Baselines: KDE Lasso Conformal Bayes CHR CQR DCP
Builds on: conformal quantile regression conformal histogram regression classification conformal prediction regression-as-classification
Closest papers by meaning
- A Unified Comparative Study with Generalized Conformity Scores for Multi-Output Conformal Regression (ICML 2025 · similarity 0.89)
- Co-optimization for Adaptive Conformal Prediction (NeurIPS 2026 · similarity 0.89)
- Backward Conformal Prediction (NeurIPS 2025 · similarity 0.88)
- Optimal transport-based conformal prediction (ICML 2025 · similarity 0.88)
- Scalable and adaptive prediction bands with kernel sum-of-squares (NeurIPS 2025 · similarity 0.87)
- Conformal Prediction with Learned Features (ICML 2024 · similarity 0.87)
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