# Empirical Bayes 1-bit matrix completion

arXiv: https://arxiv.org/abs/2605.09509 · HTML: https://mlsanity.com/paper/2605.09509/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 35 references that are in the map.
- First posted on arXiv 10 May 2026.

## Builds on (most cited first, 7 of 7)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion](https://mlsanity.com/paper/1309.6013/) (2013)
- [1-bit Matrix Completion: PAC-Bayesian Analysis of a Variational Approximation](https://mlsanity.com/paper/1604.04191/) (2016)
- [1-Bit Matrix Completion under Exact Low-Rank Constraint](https://mlsanity.com/paper/1502.06689/) (2015)
- [A Majorization-Minimization Gauss-Newton Method for 1-Bit Matrix Completion](https://mlsanity.com/paper/2304.13940/) (2023)
- [Empirical Bayes Matrix Completion](https://mlsanity.com/paper/1706.01252/) (2017)
- [Empirical Bayes data integreation for multi-response regression](https://mlsanity.com/paper/2602.13538/) (2026)

## Abstract (arXiv)

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.