Differentially Private Matrix Completion Revisited
This addresses privacy concerns in collaborative filtering systems for users, though it appears incremental as it builds on existing differential privacy and matrix completion methods.
The authors tackled the problem of user-level privacy-preserving collaborative filtering by developing the first provably joint differentially private algorithm with formal utility guarantees, showing it consistently outperforms state-of-the-art private algorithms in empirical evaluations.
We provide the first provably joint differentially private algorithm with formal utility guarantees for the problem of user-level privacy-preserving collaborative filtering. Our algorithm is based on the Frank-Wolfe method, and it consistently estimates the underlying preference matrix as long as the number of users $m$ is $ω(n^{5/4})$, where $n$ is the number of items, and each user provides her preference for at least $\sqrt{n}$ randomly selected items. Along the way, we provide an optimal differentially private algorithm for singular vector computation, based on the celebrated Oja's method, that provides significant savings in terms of space and time while operating on sparse matrices. We also empirically evaluate our algorithm on a suite of datasets, and show that it consistently outperforms the state-of-the-art private algorithms.