One-Bit Matrix Completion with Differential Privacy

TL;DR

This paper introduces a unified framework for applying differential privacy to one-bit matrix completion, developing four mechanisms that balance privacy and accuracy, validated through theoretical bounds and experiments.

Contribution

It is the first to systematically incorporate differential privacy into one-bit matrix completion with four tailored mechanisms and theoretical error analysis.

Findings

Mechanisms achieve strong privacy with minimal accuracy loss.

Theoretical recovery error bounds are established.

Experimental results confirm effectiveness on real datasets.

Abstract

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.