Empirical Bayes 1-bit matrix completion

Takeru Matsuda

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arXiv · 2605.09509

Empirical Bayes 1-bit matrix completion

Takeru Matsuda

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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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Takeru Matsuda. 2026-05-10. Empirical Bayes 1-bit matrix completion. https://arxiv.org/abs/2605.09509

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