As a prevailing collaborative filtering method for recommendation systems, one-bit matrix completion requires data collected by users to provide personalized service. Due to insidious attacks and unexpected inference, the release of users' data often raises serious privacy concerns. To address this issue, differential privacy(DP) has been widely used in standard matrix completion models. To date, however, little has been known about how to apply DP to achieve privacy protection in one-bit matrix completion. In this paper, we propose a unified framework for ensuring a strong privacy guarantee of one-bit matrix completion with DP. In our framework, we develop four different private perturbation mechanisms corresponding to different stages of one-bit matrix completion. For each mechanism, we design a privacy-preserving algorithm and provide a theoretical recovery error bound under the proper conditions. Numerical experiments on synthetic and real-world datasets demonstrate the effectiveness of our proposal. Compared to the one-bit matrix completion without privacy protection, our proposed mechanisms can maintain high-level privacy protection with marginal loss of completion accuracy.
翻译:作为建议系统的一种普遍合作过滤方法,完成一比基矩阵需要用户收集的数据,以提供个性化服务。由于暗中攻击和意外推断,发布用户数据往往引起严重的隐私问题。为解决这一问题,标准矩阵完成模型广泛使用了差异隐私(DP),但迄今为止,在如何应用DP实现一比基矩阵完成隐私保护方面,还鲜为人知。在本文件中,我们提出了一个统一框架,以确保与DP一道完成一比基矩阵的强大隐私保障。在我们的框架中,我们开发了四种与一比基矩阵完成的不同阶段相对应的不同私人扰动机制。我们为每个机制设计了一种隐私保护算法,并提供了在适当条件下约束的理论回收错误。合成和现实世界数据集的量化实验表明我们提案的有效性。与没有隐私保护的一比基矩阵完成相比,我们提议的机制可以保持高层次的隐私保护,同时略微丧失完成准确性。