Noise Calibration and Exact Recovery for Multiview Ordinal Rearrangement Data
Abstract
We studied simultaneous recovery of a latent group count, subject partition, and signature means from multiview ordinal ranks. A normalized reference rearrangement score is an affine Spearman correlation; the problem concerns the information retained by several such scores and their noise geometry. We develop an ordered-gap estimator with direction-specific concentration radii. Its finite-sample guarantee separates signature noise, missing groups, and candidate coverage, and allows the group count to grow under an attainable-margin condition. A coordinatewise partition followed by label-tuple refinement recovers groups even when every individual coordinate has population collisions. A binary-code construction explains why the one-dimensional inverse-group margin restriction need not govern a retained coordinate bank. We derive actual-law concentration from bounded ranking modules and a fixed-dimensional combinatorial central limit theorem under an observed permutation representation. A binary ordinal submodel gives logarithmic exact-recovery information scales. A subject-effect construction distinguishes persistent overlap from reducible measurement noise, and an additional ordinal anchor quantifies how new information lowers that error floor. Five focused simulation scenarios illustrate direction-specific calibration, growing-group recovery, coordinate collision resolution, variance reduction, and the effect of an additional ordinal anchor.
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BibTeX
@misc{chen2026noise,
title = {{Noise Calibration and Exact Recovery for Multiview Ordinal Rearrangement Data}},
author = {Fanghua Chen and Yizhou Cai and Ting Fung Ma and Yun Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38986},
eprint = {2610.38986},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38986},
}
RIS
TY - UNPB
TI - Noise Calibration and Exact Recovery for Multiview Ordinal Rearrangement Data
AU - Fanghua Chen
AU - Yizhou Cai
AU - Ting Fung Ma
AU - Yun Yang
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38986
UR - https://arxiv.org/abs/2610.38986
AB - We studied simultaneous recovery of a latent group count, subject partition, and signature means from multiview ordinal ranks. A normalized reference rearrangement score is an affine Spearman correlation; the problem concerns the information retained by several such scores and their noise geometry. We develop an ordered-gap estimator with direction-specific concentration radii. Its finite-sample guarantee separates signature noise, missing groups, and candidate coverage, and allows the group count to grow under an attainable-margin condition. A coordinatewise partition followed by label-tuple refinement recovers groups even when every individual coordinate has population collisions. A binary-code construction explains why the one-dimensional inverse-group margin restriction need not govern a retained coordinate bank. We derive actual-law concentration from bounded ranking modules and a fixed-dimensional combinatorial central limit theorem under an observed permutation representation. A binary ordinal submodel gives logarithmic exact-recovery information scales. A subject-effect construction distinguishes persistent overlap from reducible measurement noise, and an additional ordinal anchor quantifies how new information lowers that error floor. Five focused simulation scenarios illustrate direction-specific calibration, growing-group recovery, coordinate collision resolution, variance reduction, and the effect of an additional ordinal anchor.
ER -