用经验贝叶斯方法提升二值矩阵补全的预测精度与可靠性
Empirical Bayes 1-bit matrix completion
- 基于Efron-Morris估计器思想，通过收缩奇异值改善低秩二值矩阵补全
- 在模拟和真实数据上均优于现有方法，兼具高精度、好校准与高效计算
- 适合需要可靠预测置信度的推荐系统等应用场景
预测二值矩阵中未观测条目（即1比特矩阵补全）在推荐系统等领域有广泛应用。本文提出一种基于经验贝叶斯的方法，受Efron-Morris估计器启发，该估计器是James-Stein估计器的矩阵推广，可将奇异值向零收缩。所提方法利用二值矩阵的潜在低秩结构，类比多维项目反应理论。模拟实验与真实数据应用表明，该方法在预测准确率、校准可靠性（不确定性量化）和计算效率之间取得了更优平衡，显著优于现有方法。
原文摘要 · Abstract (English)
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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