We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same first and second moments. We also derive a memory-friendly version of the proposed algorithm by applying a perturbation treatment commonly used in the literature of approximate message passing. In addition, a damping technique, which is demonstrated to be crucial for optimal performance, is introduced without computational strain, and the relationship to the message-passing version of alternating least squares, a method reported to be optimal in certain settings, is discussed. Experiments on synthetic datasets show that while the proposed algorithm quantitatively exhibits almost the same performance under settings where the earlier algorithm is optimal, it is advantageous when the observed datasets are corrupted by non-Gaussian noise. Experiments on real-world datasets also emphasize the performance differences between the two algorithms.

翻译：我们根据矩阵因素化,为噪音矩阵完成问题开发了一种信息传递算法。算法的根据是信仰传播的近似信息分布,而Gaussian的分布在第一和第二时刻相同。我们还通过应用近似信息传递文献中常用的扰动处理法,获得了一个有利于存储的拟议算法版本。此外,在采用一种对最佳性能至关重要的阻隔技术时,没有计算强度,并且讨论了与信息传递版本最小方块的关系,据报告,在某些环境中,这种方法是最佳的。合成数据集实验显示,虽然在早期算法最理想的情况下,拟议算法在数量上显示几乎相同的性能,但当观察到的数据集被非加西语噪音破坏时,这种性能是有利的。对现实世界数据集的实验也强调了两种算法之间的性差异。