Empirical Bayes 1-bit matrix completion

TL;DR

This paper introduces an empirical Bayes approach for 1-bit matrix completion that leverages low-rank structures, improving prediction accuracy, uncertainty quantification, and efficiency in binary matrix prediction tasks.

Contribution

It develops a novel empirical Bayes method inspired by the Efron--Morris estimator, tailored for binary matrices, enhancing existing matrix completion techniques.

Findings

Outperforms existing methods in predictive accuracy

Provides reliable uncertainty quantification

Achieves computational efficiency in simulations and real data

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.