# Normalizing Flows for Conformal Regression

arXiv: https://arxiv.org/abs/2406.03346 · HTML: https://mlsanity.com/paper/2406.03346/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## Builds on (most cited first, 19 of 19)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [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)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [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)
- [Criteria of efficiency for conformal prediction](https://mlsanity.com/paper/1603.04416/) (2016)
- [Locally Valid and Discriminative Prediction Intervals for Deep Learning Models](https://mlsanity.com/paper/2106.00225/) (2021)
- [Conformal calibrators](https://mlsanity.com/paper/1902.06579/) (2019)
- [Training conformal predictors](https://mlsanity.com/paper/2005.07037/) (2020)
- [Understanding Neural Architecture Search Techniques](https://mlsanity.com/paper/1904.00438/) (2019)
- [Adaptive Conformal Regression with Jackknife+ Rescaled Scores](https://mlsanity.com/paper/2305.19901/) (2023)
- [On training locally adaptive CP](https://mlsanity.com/paper/2306.04648/) (2023)

## Built on by (most cited first, 11 of 11)

- [Wasserstein-regularized Conformal Prediction under General Distribution Shift](https://mlsanity.com/paper/2501.13430/) (2025)
- [Weighted Aggregation of Conformity Scores for Classification](https://mlsanity.com/paper/2407.10230/) (2024)
- [Conformal Generative Modeling with Improved Sample Efficiency through Sequential Greedy Filtering](https://mlsanity.com/paper/2410.01660/) (2024)
- [Entropy Reweighted Conformal Classification](https://mlsanity.com/paper/2407.17377/) (2024)
- [Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regression](https://mlsanity.com/paper/2503.02205/) (2025)
- [Federated Conditional Conformal Prediction via Generative Models](https://mlsanity.com/paper/2510.13297/) (2025)
- [Interpretable Multivariate Conformal Prediction with Fast Transductive Standardization](https://mlsanity.com/paper/2512.15383/) (2025)
- [Adaptive Cumulative Mass Calibration with Conformal Prediction](https://mlsanity.com/paper/2505.15437/) (2025)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [Robust Conditional Conformal Prediction via Branched Normalizing Flow](https://mlsanity.com/paper/2605.01868/) (2026)
- [How Synthetic Labels Improve Conformal Prediction: A Perspective on Conditional Coverage](https://mlsanity.com/paper/2609.33482/) (2026)

## Abstract (arXiv)

Conformal Prediction (CP) algorithms estimate the uncertainty of a prediction model by calibrating its outputs on labeled data. The same calibration scheme usually applies to any model and data without modifications. The obtained prediction intervals are valid by construction but could be inefficient, i.e. unnecessarily big, if the prediction errors are not uniformly distributed over the input space. We present a general scheme to localize the intervals by training the calibration process. The standard prediction error is replaced by an optimized distance metric that depends explicitly on the object attributes. Learning the optimal metric is equivalent to training a Normalizing Flow that acts on the joint distribution of the errors and the inputs. Unlike the Error Reweighting CP algorithm of Papadopoulos et al. (2008), the framework allows estimating the gap between nominal and empirical conditional validity. The approach is compatible with existing locally-adaptive CP strategies based on re-weighting the calibration samples and applies to any point-prediction model without retraining.