提出多目标置信预测新方法，提升成像逆问题不确定性量化精度
Minimax Multi-Target Conformal Prediction with Applications to Imaging Inverse Problems
- 基于极小极大原理构建多目标置信预测框架
- 在合成与MRI数据上实现更紧的置信区间且保证联合覆盖性
- 适用于图像质量评估、多任务估计等实际成像场景
在病态成像逆问题中，不确定性量化仍是根本挑战，尤其在安全关键应用中。近年来，置信预测被用于量化逆问题对下游任务（如图像分类、图像质量评估、脂肪质量量化）带来的不确定性。现有方法仅处理标量估计目标，而实际应用常涉及多个目标。为此，本文提出一种渐近极小极大的多目标置信预测方法，可在保证联合边际覆盖率的同时提供更紧的预测区间。我们进一步说明该方法如何应用于多指标盲图像质量评估、多任务不确定性量化及多轮测量采集。最后，通过合成数据和磁共振成像（MRI）数据的数值实验，验证了所提方法相比现有方法的优势。代码已开源：https://github.com/jwen307/multi_target_minimax。
原文摘要 · Abstract (English)
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.
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