# Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regression

arXiv: https://arxiv.org/abs/2503.02205 · HTML: https://mlsanity.com/paper/2503.02205/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 50 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 30 of 35)

- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Flexible distribution-free conditional predictive bands using density estimators](https://mlsanity.com/paper/1910.05575/) (2019)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Conformal Prediction for Deep Classifier via Label Ranking](https://mlsanity.com/paper/2310.06430/) (2023)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Selection and Aggregation of Conformal Prediction Sets](https://mlsanity.com/paper/2104.13871/) (2021)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Probabilistic Conformal Prediction Using Conditional Random Samples](https://mlsanity.com/paper/2206.06584/) (2022)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Conformal Prediction Bands for Multivariate Functional Data](https://mlsanity.com/paper/2106.01792/) (2021)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Split Localized Conformal Prediction](https://mlsanity.com/paper/2206.13092/) (2022)
- [Probabilistic Conformal Prediction with Approximate Conditional Validity](https://mlsanity.com/paper/2407.01794/) (2024)
- [Trustworthy Classification through Rank-Based Conformal Prediction Sets](https://mlsanity.com/paper/2407.04407/) (2024)
- [Optimal Transport-based Conformal Prediction](https://mlsanity.com/paper/2501.18991/) (2025)
- [Anomalous Edge Detection in Edge Exchangeable Social Network Models](https://mlsanity.com/paper/2109.12727/) (2021)
- [Conformal Prediction for Network-Assisted Regression](https://mlsanity.com/paper/2302.10095/) (2023)
- [Normalizing Flows for Conformal Regression](https://mlsanity.com/paper/2406.03346/) (2024)
- [Conformal Load Prediction with Transductive Graph Autoencoders](https://mlsanity.com/paper/2406.08281/) (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)
- [Game-Theoretic Defenses for Robust Conformal Prediction Against Adversarial Attacks in Medical Imaging](https://mlsanity.com/paper/2411.04376/) (2024)
- [Conformal link prediction for false discovery rate control](https://mlsanity.com/paper/2306.14693/) (2023)
- [Entropy Reweighted Conformal Classification](https://mlsanity.com/paper/2407.17377/) (2024)
- [Conformalized Interval Arithmetic with Symmetric Calibration](https://mlsanity.com/paper/2408.10939/) (2024)

## Built on by (most cited first, 6 of 6)

- [Conditional Conformal Risk Adaptation](https://mlsanity.com/paper/2504.07611/) (2025)
- [Enhancing Adversarial Robustness with Conformal Prediction: A Framework for Guaranteed Model Reliability](https://mlsanity.com/paper/2506.07804/) (2025)
- [Enhanced Route Planning with Calibrated Uncertainty Set](https://mlsanity.com/paper/2503.10088/) (2025)
- [Residual Reweighted Conformal Prediction for Graph Neural Networks](https://mlsanity.com/paper/2506.07854/) (2025)
- [Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks](https://mlsanity.com/paper/2508.11025/) (2025)
- [Multi-Variable Conformal Prediction: Optimizing Prediction Sets without Data Splitting](https://mlsanity.com/paper/2605.12341/) (2026)

## Abstract (arXiv)

We introduce Volume-Sorted Prediction Set (VSPS), a novel method for uncertainty quantification in multi-target regression that uses conditional normalizing flows with conformal calibration. This approach constructs flexible, non-convex predictive regions with guaranteed coverage probabilities, overcoming limitations of traditional methods. By learning a transformation where the conditional distribution of responses follows a known form, VSPS identifies dense regions in the original space using the Jacobian determinant. This enables the creation of prediction regions that adapt to the true underlying distribution, focusing on areas of high probability density. Experimental results demonstrate that VSPS produces smaller, more informative prediction regions while maintaining robust coverage guarantees, enhancing uncertainty modeling in complex, high-dimensional settings.