Building a recommendation system involves analyzing user data, which can potentially leak sensitive information about users. Anonymizing user data is often not sufficient for preserving user privacy. Motivated by this, we propose a privacy-preserving recommendation system based on the differential privacy framework and matrix factorization, which is one of the most popular algorithms for recommendation systems. As differential privacy is a powerful and robust mathematical framework for designing privacy-preserving machine learning algorithms, it is possible to prevent adversaries from extracting sensitive user information even if the adversary possesses their publicly available (auxiliary) information. We implement differential privacy via the Gaussian mechanism in the form of output perturbation and release user profiles that satisfy privacy definitions. We employ R\ényi Differential Privacy for a tight characterization of the overall privacy loss. We perform extensive experiments on real data to demonstrate that our proposed algorithm can offer excellent utility for some parameter choices, while guaranteeing strict privacy.
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