# On training locally adaptive CP

arXiv: https://arxiv.org/abs/2306.04648 · HTML: https://mlsanity.com/paper/2306.04648/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 24 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [Flexible distribution-free conditional predictive bands using density estimators](https://mlsanity.com/paper/1910.05575/) (2019)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Regression Conformal Prediction with Nearest Neighbours](https://mlsanity.com/paper/1401.3880/) (2014)
- [Split Localized Conformal Prediction](https://mlsanity.com/paper/2206.13092/) (2022)

## Built on by (most cited first, 8 of 8)

- [Normalizing Flows for Conformal Regression](https://mlsanity.com/paper/2406.03346/) (2024)
- [Weighted Aggregation of Conformity Scores for Classification](https://mlsanity.com/paper/2407.10230/) (2024)
- [Conformal Thresholded Intervals for Efficient Regression](https://mlsanity.com/paper/2407.14495/) (2024)
- [Entropy Reweighted Conformal Classification](https://mlsanity.com/paper/2407.17377/) (2024)
- [Enhanced Route Planning with Calibrated Uncertainty Set](https://mlsanity.com/paper/2503.10088/) (2025)
- [SEMF: Supervised Expectation-Maximization Framework for Predicting Intervals](https://mlsanity.com/paper/2405.18176/) (2024)
- [Co-optimization for Adaptive Conformal Prediction](https://mlsanity.com/paper/2603.01719/) (2026)
- [Conformal Calibration for Multi-Modal Regression with Missing Modalities](https://mlsanity.com/paper/2608.07795/) (2026)

## Abstract (arXiv)

We address the problem of making Conformal Prediction (CP) intervals locally adaptive. Most existing methods focus on approximating the object-conditional validity of the intervals by partitioning or re-weighting the calibration set. Our strategy is new and conceptually different. Instead of re-weighting the calibration data, we redefine the conformity measure through a trainable change of variables, A → φX(A), that depends explicitly on the object attributes, X. Under certain conditions and if φX is monotonic in A for any X, the transformations produce prediction intervals that are guaranteed to be marginally valid and have X-dependent sizes. We describe how to parameterize and train φX to maximize the interval efficiency. Contrary to other CP-aware training methods, the objective function is smooth and can be minimized through standard gradient methods without approximations.