发表机构
Institute for Artificial Intelligence, University of Central Florida; Department of CS, University of Central Florida; Department of ECE, The University of Texas at Austin（人工智能研究所，中央佛罗里达大学; 计算机科学系，中央佛罗里达大学; 电子工程系，德克萨斯大学奥斯汀分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究在贝叶斯逆问题中使用学习生成先验时因真值稀缺采用先验清洗的情况，指出其过度自信问题，通过对旧后验求平均产生旧正则化器，单个最佳档案更糟，部署时拟合档案的先验未覆盖盲子空间，建议分开数据支持置信度与继承信念。
AI 中文摘要
学习生成先验越来越多地用于不适定贝叶斯逆问题，其后验不确定性被视为从数据中获得。但训练需要真值，在地震和医学成像中稀缺，因此 recourse 是旧重建档案——先验清洗。当测量无信息时，后验恢复为先验，所以那里报告的不确定性是档案的而非数据的，部署中无任何东西能揭示它：仅在那些方向上不同的真值会导致相同的数据规律，基于模拟的校准等自一致性检查无论先验相信什么都会通过。该信念有确切来源：对测量上的旧后验求平均会产生旧正则化器，在数据可分辨处改进，在不可分辨处冻结。在继承信念比真值更紧的任何地方它都是过度自信的。单个最佳档案更糟，会使盲可信区间宽度坍缩为零。部署时，与真值训练的对照相比，拟合档案的扩散先验未覆盖算子的盲子空间，在非线性地下水算子上归一化流也是如此。我们建议报告测量能分辨哪些方向，将数据支持的置信度与通过管道继承的信念分开。
英文摘要
Where truths are scarce (e.g., seismic and medical imaging), learned priors in ill-posed inverse problems are trained on archives of legacy reconstructions---i.e., an older method's outputs---and their reported uncertainty is taken as data-driven. We show that this prior is, in the population limit, exactly the regularizer that produced its archive of posterior samples, advanced one expectation--maximization step toward the truth. While the step improves the regularizer on the directions the measurements resolve, it leaves the regularizer's assumption on the operator's blind subspace unchanged. An archive of single-best reconstructions collapses the blind interval to zero width. Neither error is detectable in practice, as truths differing only on the blind subspace share the data law, and simulation-based calibration is neutral by construction. We identify from the operator alone which directions the measurements do not inform, and, given a handful of ground-truth models, build intervals there that contain the truth as often as they claim to. We validate these findings on a two-dimensional example with closed-form predictions and in controlled experiments on seismic-imaging and groundwater-flow operators, against priors trained on the truth.
