Performing low-rank matrix completion with sensitive user data calls for privacy-preserving approaches. In this work, we propose a novel noise addition mechanism for preserving differential privacy where the noise distribution is inspired by Huber loss, a well-known loss function in robust statistics. The proposed Huber mechanism is evaluated against existing differential privacy mechanisms while solving the matrix completion problem using the Alternating Least Squares approach. We also propose using the Iteratively Re-Weighted Least Squares algorithm to complete low-rank matrices and study the performance of different noise mechanisms in both synthetic and real datasets. We prove that the proposed mechanism achieves {\epsilon}-differential privacy similar to the Laplace mechanism. Furthermore, empirical results indicate that the Huber mechanism outperforms Laplacian and Gaussian in some cases and is comparable, otherwise.

翻译：以敏感用户数据完成低级别矩阵要求采取保护隐私的方法。 在这项工作中,我们提议建立一个新的噪音添加机制,以在噪音分布受Huber丢失的启发下维护不同隐私,这是可靠统计数据中众所周知的一种损失功能。拟议的Huber机制根据现有的差异隐私机制进行评估,同时采用交替的最小广场方法解决矩阵完成问题。我们还提议使用“循环重整最小广场算法”,完成低级别矩阵,并研究合成和真实数据集中不同噪音机制的性能。我们证明拟议的机制实现了与Laplace机制相似的yepslon}差异隐私。此外,实证结果表明,Huber机制在某些情况下优于Laplacian和Gaussian,在其他情况下是可比的。