Privacy-preserving matrix factorization for recommendation systems using Gaussian mechanism and functional mechanism

Building a recommendation system involves analyzing user data, which can potentially leak sensitive information about users. As shown in numerous recent works, anonymizing user data is not sufficient for preserving user privacy. Differential Privacy is a mathematically rigorous privacy guarantee that has been adopted by numerous corporations and government entities for preserving user privacy in such scenarios. Developing differentially private machine learning algorithms typically involve adding randomness into the algorithm pipeline, which evidently degrades the performance of the algorithm—giving raise to privacy-utility trade-off. Existing differentially private matrix factorization algorithms offer poor privacy-utility trade-off for use in practical systems. Motivated by this, we propose two differentially private matrix factorization algorithms for application in recommendation systems, which provide better privacy-utility trade-off compared to the existing approaches. Our first algorithm adopts the framework of noisy gradient descent using the Gaussian Mechanism, whereas our second algorithm extends the Functional Mechanism framework to incorporate it into matrix factorization. In both cases, we perform theoretical analysis of the privacy of the algorithms. Additionally, we employ Rényi differential privacy to analyze the algorithms for a tight characterization of the overall privacy loss. We perform extensive experiments on real data by varying relevant privacy, algorithm, and dataset parameters. We compare the performance of our proposed algorithms with existing non-private and differentially private algorithms, and demonstrate that our algorithms can provide utility close to that of the non-private algorithm while guaranteeing strict privacy, outperforming the existing approaches.