Empirical Bayes 1-bit matrix completion
It provides a principled and efficient approach for binary matrix completion with uncertainty quantification, benefiting recommendation systems and other applications.
The paper develops an empirical Bayes method for 1-bit matrix completion, achieving superior predictive accuracy, calibration reliability, and computational efficiency compared to existing methods.
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.