基于等变自助法的自监督置信区间预测用于图像不确定性量化
Self-Supervised Conformal Prediction with Equivariant Bootstrapping for Image Uncertainty Quantification
AI总结：
本文提出了一种基于等变自助法的自监督置信区间预测方法，用于图像不确定性量化，通过利用数据对称性生成启发式覆盖范围，并通过置信预测校准步骤进行细化，避免了对地面真实数据的依赖，特别在弱引力透镜质量映射中展示了其有效性。
摘要：
逆问题在现代科学研究中无处不在，涉及从受噪声干扰的观测中恢复底层信号，通常通过测量算子转换。这些问题往往病态，特别是在成像领域，导致多个可能的解决方案和重建图像中的显著不确定性。在物理和生物科学领域，准确的不确定性量化（UQ）对于可信的科学分析和可靠的诊断至关重要。当前的成像UQ方法往往不足；它们可能不准确，或者需要不可用或难以获取的地面真实数据进行校准，这可能由于校准数据与观测数据之间的分布偏移而引入隐藏的偏见。我们介绍了一种UQ方法，利用等变自助法生成启发式覆盖范围，通过利用数据对称性。然后通过置信预测校准步骤细化这些覆盖范围，同时关键地采用自监督方法以避免对地面真实校准数据的需求。我们通过弱引力透镜质量映射展示了该方法，其中我们旨在从遥远星系的弱引力透镜形变测量中重建收敛场。质量映射特别受益于自监督方法，因为生成校准数据成本高昂且依赖于特定的宇宙学模型，这可能在下游宇宙学推断任务中引入偏见。
英文摘要：
Inverse problems are ubiquitous in modern scientific studies and involve recovering an underlying signal from noisy observations often transformed by a measurement operator. These problems are frequently ill-posed, particularly in imaging, leading to multiple plausible solutions and considerable uncertainty in reconstructed images. In fields like the physical and biological sciences, accurate uncertainty quantification (UQ) is critical for trustworthy scientific analyses and confident diagnoses. Current UQ methods for imaging often fall short; they can be inaccurate, or require unavailable or difficult-to-acquire ground truth data for calibration, which can introduce hidden biases due to distribution shifts between calibration and observed data. We introduce a UQ approach that leverages equivariant bootstrapping to generate heuristic coverages by exploiting data symmetries. We then refine these coverages through a conformal prediction calibration step, while crucially employing a self-supervised approach to avoid the need for ground truth calibration data. We demonstrate this method with weak lensing mass-mapping, where we aim to reconstruct the convergence field from shear measurements of distant galaxies weakly-lensed by gravitational fields. Mass-mapping in particular benefits from the self-supervised approach, as simulating calibration data is expensive and relies on specific cosmological models that could introduce biases in downstream cosmological inference tasks.
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