Where truths are scarce (e.g., seismic and medical imaging), a prior for an ill-posed inverse problem is trained on an archive of legacy reconstructions---an older method's outputs---and its uncertainty is treated as data-driven. In the population limit, an archive of posterior samples is the regularizer that produced it, advanced one expectation-maximization step toward the truth. On directions the operator resolves, it improves the assumption; on its blind subspace, the step is the identity, so the assumption survives unchanged however often it is rebuilt. An archive of single-best reconstructions, one per survey, keeps no spread there: the blind interval collapses whatever the penalty was, so error becomes overconfidence. The assumption enters as the archive and leaves as a reported spread, and nothing in deployment tests it. Two truths differing only there share the data law, and no procedure using survey and archive alone can both report a finite blind interval and guarantee coverage over indistinguishable truths. The question requires information the survey does not carry. We provide a resolvability statement that names affected directions from the operator, state how many reference truths are needed to test a prior on them, and use those references to build an interval that contains the truth as claimed, even if the prior is wrong. On synthetic experiments with seismic and groundwater operators, the archive-trained prior's intervals contain the truth less often on the blind subspace than on resolved directions, while the truth-trained control shows no gap of that sign or size. On seismic, a random subspace of the same size gives the same result, so the separation follows the operator. On groundwater, rebuilding the archive using the survey and a handful of boreholes brings the prior's reports toward the truth on directions those boreholes reach, while leaving the rest unchanged.
Label noise presents a fundamental challenge in modern machine learning, especially when large-scale datasets are generated via automated processes. An increasingly common and important data paradigm, particularly in domains like medical imaging, involves learning from a large dataset with coarse, noisy labels supplemented by a small, expert-verified, clean dataset. This setting constitutes a typical information transfer and fusion problem. However, the significant distribution shift between the noisy and clean data violates the core overall parametric similarity assumptions of existing statistical transfer learning methods, while their reliance on parametric models is ill-suited for complex data like images. To address these limitations, this paper develops a generic model-agnostic nonparametric framework for classification with label noise, which applies to a broad class of classifiers. Our approach leverages the small clean dataset to ``purify'' the large noisy one and carefully manages the remaining ambiguous samples. This framework is underpinned by a rigorous statistical theory. Its empirical performance is demonstrated through simulations and a real-world application to medical image analysis for pneumonia diagnosis.