Matrix completion is a prevailing collaborative filtering method for recommendation systems that requires the data offered by users to provide personalized service. However, due to insidious attacks and unexpected inference, the release of user data often raises serious privacy concerns. Most of the existing solutions focus on improving the privacy guarantee for general matrix completion. As a special case, in recommendation systems where the observations are binary, one-bit matrix completion covers a broad range of real-life situations. In this paper, we propose a novel framework for one-bit matrix completion under the differential privacy constraint. In this framework, we develop several perturbation mechanisms and analyze the privacy-accuracy trade-off offered by each mechanism. The experiments conducted on both synthetic and real-world datasets demonstrate that our proposed approaches can maintain high-level privacy with little loss of completion accuracy.

翻译：矩阵的完成是建议系统的一种普遍合作过滤方法,它要求用户提供个人化服务的数据。然而,由于暗中攻击和意外推断,用户数据的发布往往引起严重的隐私问题。大多数现有解决方案侧重于改进一般矩阵完成的隐私保障。作为特殊情况,在观测为二元的推荐系统中,一元矩阵的完成涵盖广泛的现实生活情况。在本文件中,我们提议了一个在差异隐私限制下完成一元矩阵的新框架。在这个框架内,我们开发了几个扰动机制,并分析了每个机制提供的隐私-准确性交易。在合成和真实世界数据集上进行的实验表明,我们拟议的方法可以保持高层次的隐私,而完成准确性几乎没有损失。