PreprintCC BY 4.0arXiv
Empirical Bayes 1-bit matrix completion
Abstract
The problem of predicting unobserved entries in a binary matrix, known as 1-bit matrix completion, has found diverse applications in fields such as recommendation systems. In this study, we develop an empirical Bayes method for 1-bit matrix completion motivated by the Efron--Morris estimator, a matrix generalization of the James--Stein estimator that shrinks singular values toward zero. The proposed method exploits the underlying low-rank structure of binary matrices, drawing parallels with multidimensional item response theory. Simulation studies and real-data applications demonstrate that the proposed method achieves competitive predictive accuracy and favorable predictive calibration.
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BibTeX
@misc{matsuda2026empirical,
title = {{Empirical Bayes 1-bit matrix completion}},
author = {Takeru Matsuda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.09509},
eprint = {2605.09509},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.09509},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Empirical Bayes 1-bit matrix completion
AU - Takeru Matsuda
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2605.09509
UR - https://arxiv.org/abs/2605.09509
AB - The problem of predicting unobserved entries in a binary matrix, known as 1-bit matrix completion, has found diverse applications in fields such as recommendation systems. In this study, we develop an empirical Bayes method for 1-bit matrix completion motivated by the Efron--Morris estimator, a matrix generalization of the James--Stein estimator that shrinks singular values toward zero. The proposed method exploits the underlying low-rank structure of binary matrices, drawing parallels with multidimensional item response theory. Simulation studies and real-data applications demonstrate that the proposed method achieves competitive predictive accuracy and favorable predictive calibration.
ER -