When Unpaired Sets Support Shared-Corruption Calibration: Moment Geometry and Two-Sample Precision
Abstract
Collections of diverse observations often share one acquisition, processing, geometric, or channel corruption, while only an unpaired clean reference set is available. For a prescribed low-dimensional correction shared across observations, the observed and clean reference sets support inference only through the response of fixed moments. We formulate this problem as two-sample moment calibration and report a rank-aware information state combining local rank, scaled moment sensitivity, source-separated covariance, and a moment compatibility residual. Full rank gives local moment identifiability, whereas kernel directions remain unresolved to first order. A unified linearization separates observed-set and reference-set uncertainty. Under covariance weighting, the weakest scaled singular value determines worst-direction asymptotic amplification. For an orientation-preserving planar-similarity correction shared across observations, ensemble centroids and a nonzero third-order complex moment yield closed-form global population identification of translation, rotation, and isotropic scale under matched-population and no-clipping assumptions. Controlled validation tests the predicted N−1 and σmin−2 laws, Gaussian efficiency, and interval coverage. Bounded applications report color corrected-output quality, channel magnitude-response calibration, and a separate paired geometric de-beautification result. The framework therefore reports missing or weak information instead of treating every fitted correction as identified.
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BibTeX
@misc{cao2026when,
title = {{When Unpaired Sets Support Shared-Corruption Calibration: Moment Geometry and Two-Sample Precision}},
author = {Shuheng Cao and Zhenhao Zhang and Ruiqi Chen and Renjie Cao and Siyu Zhang and Zhaoxiang Feng and Lingwei Dang and Haoyang Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26209},
eprint = {2609.26209},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26209},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - When Unpaired Sets Support Shared-Corruption Calibration: Moment Geometry and Two-Sample Precision
AU - Shuheng Cao
AU - Zhenhao Zhang
AU - Ruiqi Chen
AU - Renjie Cao
AU - Siyu Zhang
AU - Zhaoxiang Feng
AU - Lingwei Dang
AU - Haoyang Wu
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.26209
UR - https://arxiv.org/abs/2609.26209
AB - Collections of diverse observations often share one acquisition, processing, geometric, or channel corruption, while only an unpaired clean reference set is available. For a prescribed low-dimensional correction shared across observations, the observed and clean reference sets support inference only through the response of fixed moments. We formulate this problem as two-sample moment calibration and report a rank-aware information state combining local rank, scaled moment sensitivity, source-separated covariance, and a moment compatibility residual. Full rank gives local moment identifiability, whereas kernel directions remain unresolved to first order. A unified linearization separates observed-set and reference-set uncertainty. Under covariance weighting, the weakest scaled singular value determines worst-direction asymptotic amplification. For an orientation-preserving planar-similarity correction shared across observations, ensemble centroids and a nonzero third-order complex moment yield closed-form global population identification of translation, rotation, and isotropic scale under matched-population and no-clipping assumptions. Controlled validation tests the predicted N^−1 and σ_min^−2 laws, Gaussian efficiency, and interval coverage. Bounded applications report color corrected-output quality, channel magnitude-response calibration, and a separate paired geometric de-beautification result. The framework therefore reports missing or weak information instead of treating every fitted correction as identified.
ER -