aiqbench analysis
This research exposes a critical flaw in using learned generative priors for Bayesian inverse problems where ground truth is scarce, revealing that uncertainty estimates often inherit overconfidence from legacy archives rather than reflecting actual data information. The study demonstrates standard validation checks like simulation-based calibration fail to detect this "prior laundering," urging practitioners to explicitly separate confidence supported by measurements from beliefs inherited through the training pipeline.
Prior laundering: learned priors with inherited, undetectable overconfidence
arXiv:2607.21721v1 Announce Type: cross Abstract: Learned generative priors are increasingly used for ill-posed Bayesian inverse problems, their posterior uncertainty treated as earned from data. But training one requires truths, scarce in seismic and medical imaging, so the recourse is an archive of legacy reconstructions---prior laundering. Where the measurements are uninformative the posterior reverts to the prior, so the uncertainty reported there is the archive's, not the data's, and nothing in deployment reveals it: truths differing only on those directions induce identical data laws, and self-consistency checks such as simulation-based calibration pass whatever the prior believes. That belief has an exact source: averaging the legacy posterior over the measurements yields the old regularizer advanced a single expectation--maximization step---improved where the data resolve, frozen where they cannot. It is overconfident wherever the inherited belief is tighter than the truth. A single-best archive is worse, collapsing the blind credible interval to zero width. Deployed, a diffusion prior fit to the archive under-covers the operator's blind subspace, unlike a truth-trained control, and a normalizing flow does the same on a nonlinear groundwater operator. We recommend reporting which directions the measurements resolve, separating confidence the data support from belief inherited through the pipeline.
Abstract:Learned generative priors are increasingly used for ill-posed Bayesian inverse problems, their posterior uncertainty treated as earned from data. But training one requires truths, scarce in seismic and medical imaging, so the recourse is an archive of legacy reconstructions---prior laundering. Where the measurements are uninformative the posterior reverts to the prior, so the uncertainty reported there is the archive's, not the data's, and nothing in deployment reveals it: truths differing only on those directions induce identical data laws, and self-consistency checks such as simulation-based calibration pass whatever the prior believes. That belief has an exact source: averaging the legacy posterior over the measurements yields the old regularizer advanced a single expectation--maximization step---improved where the data resolve, frozen where they cannot. It is overconfident wherever the inherited belief is tighter than the truth. A single-best archive is worse, collapsing the blind credible interval to zero width. Deployed, a diffusion prior fit to the archive under-covers the operator's blind subspace, unlike a truth-trained control, and a normalizing flow does the same on a nonlinear groundwater operator. We recommend reporting which directions the measurements resolve, separating confidence the data support from belief inherited through the pipeline.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2607.21721 [stat.ML]
(or arXiv:2607.21721v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2607.21721 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 290 words
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