用数学严谨的波浪散射方法，为图像不确定性提供可解释基准。
Bayesian Scattering: A Principled Baseline for Uncertainty on Image Data
- 结合非学习的波浪散射特征与概率模型，避免过拟合
- 在机构、国家间分布偏移下仍保持合理置信度估计
- 适合需要可解释不确定性的医疗与分子优化场景
图像数据的不确定性量化目前依赖复杂深度学习方法，但缺乏可解释且数学严谨的基准。本文提出贝叶斯散射方法，作为类似贝叶斯线性回归在表格数据中的基础角色。该方法将波浪散射变换——一种基于几何原理的深度非学习特征提取器——与简单概率头结合。由于散射特征由几何原则导出而非训练所得，能有效避免对训练分布的过拟合，从而在显著分布偏移下仍提供合理不确定性估计。我们在多个任务中验证其有效性，包括医疗影像中的机构间偏移、跨国家财富映射，以及分子性质的贝叶斯优化。结果表明，贝叶斯散射是复杂不确定性量化方法的一个稳健基线。
原文摘要 · Abstract (English)
Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step baseline akin to the role of Bayesian linear regression for tabular data. Our method couples the wavelet scattering transform-a deep, non-learned feature extractor-with a simple probabilistic head. Because scattering features are derived from geometric principles rather than learned, they avoid overfitting the training distribution. This helps provide sensible uncertainty estimates even under significant distribution shifts. We validate this on diverse tasks, including medical imaging under institution shift, wealth mapping under country-to-country shift, and Bayesian optimization of molecular properties. Our results suggest that Bayesian scattering is a solid baseline for complex uncertainty quantification methods.
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