# Minimax Multi-Target Conformal Prediction with Applications to Imaging Inverse Problems

arXiv: https://arxiv.org/abs/2511.13533 · HTML: https://mlsanity.com/paper/2511.13533/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 64 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Image Quality Assessment: Unifying Structure and Texture Similarity](https://mlsanity.com/paper/2004.07728/) (2020)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Distribution Matching Losses Can Hallucinate Features in Medical Image Translation](https://mlsanity.com/paper/1805.08841/) (2018)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1904.01112/) (2019)
- [On hallucinations in tomographic image reconstruction](https://mlsanity.com/paper/2012.00646/) (2020)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems](https://mlsanity.com/paper/2001.01258/) (2020)
- [Conffusion: Confidence Intervals for Diffusion Models](https://mlsanity.com/paper/2211.09795/) (2022)
- [Conformal Prediction Bands for Multivariate Functional Data](https://mlsanity.com/paper/2106.01792/) (2021)
- [Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problems](https://mlsanity.com/paper/2305.10124/) (2023)
- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [Hallucination Index: An Image Quality Metric for Generative Reconstruction Models](https://mlsanity.com/paper/2407.12780/) (2024)
- [Semantic uncertainty intervals for disentangled latent spaces](https://mlsanity.com/paper/2207.10074/) (2022)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Optimal Transport-based Conformal Prediction](https://mlsanity.com/paper/2501.18991/) (2025)

## Built on by (most cited first, 1 of 1)

- [Quantifying Volumetric Risk: Class-Aware Asymmetric Weighted Conformal Prediction for 3D Medical Image Segmentation](https://mlsanity.com/paper/2610.09392/) (2026)

## Abstract (arXiv)

In ill-posed imaging inverse problems, uncertainty quantification remains a fundamental challenge, especially in safety-critical applications. Recently, conformal prediction has been used to quantify the uncertainty that the inverse problem contributes to downstream tasks like image classification, image quality assessment, fat mass quantification, etc. While existing works handle only a scalar estimation target, practical applications often involve multiple targets. In response, we propose an asymptotically minimax approach to multi-target conformal prediction that provides tight prediction intervals while ensuring joint marginal coverage. We then outline how our minimax approach can be applied to multi-metric blind image quality assessment, multi-task uncertainty quantification, and multi-round measurement acquisition. Finally, we numerically demonstrate the benefits of our minimax method, relative to existing multi-target conformal prediction methods, using both synthetic and magnetic resonance imaging (MRI) data. Code is available at https://github.com/jwen307/multi_target_minimax.