Empirical Bayes 1-bit matrix completion

• URL: http://arxiv.org/abs/2605.09509v1
• Date: Sun, 10 May 2026 12:42:19 GMT
• Title: Empirical Bayes 1-bit matrix completion
• Abstract summary: A 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.<n>We develop an empirical Bayes method for 1-bit matrix completion motivated by the Efron--Morris estimator.
• Score: 7.064683197536012
• License: http://creativecommons.org/licenses/by/4.0/
• 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 a superior balance of predictive accuracy, calibration reliability (uncertainty quantification), and computational efficiency compared to existing methods.

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