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.

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