Empirical Bayes 1-bit matrix completion
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914549464039424 |
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| author | Matsuda, Takeru |
| author_facet | Matsuda, Takeru |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09509 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Empirical Bayes 1-bit matrix completion Matsuda, Takeru Machine Learning Methodology 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. |
| title | Empirical Bayes 1-bit matrix completion |
| topic | Machine Learning Methodology |
| url | https://arxiv.org/abs/2605.09509 |