Private Alternating Least Squares: Practical Private Matrix Completion with Tighter Rates
This addresses the problem of practical private matrix completion for applications like recommendation systems, offering a more efficient and accurate solution compared to existing techniques.
The paper tackles differentially private matrix completion under user-level privacy by designing a private Alternating-Least-Squares (ALS) method, achieving nearly optimal sample complexity and the best known privacy/utility trade-off, with error bounds scaling significantly better than prior methods and demonstrating higher accuracy on benchmarks.
We study the problem of differentially private (DP) matrix completion under user-level privacy. We design a joint differentially private variant of the popular Alternating-Least-Squares (ALS) method that achieves: i) (nearly) optimal sample complexity for matrix completion (in terms of number of items, users), and ii) the best known privacy/utility trade-off both theoretically, as well as on benchmark data sets. In particular, we provide the first global convergence analysis of ALS with noise introduced to ensure DP, and show that, in comparison to the best known alternative (the Private Frank-Wolfe algorithm by Jain et al. (2018)), our error bounds scale significantly better with respect to the number of items and users, which is critical in practical problems. Extensive validation on standard benchmarks demonstrate that the algorithm, in combination with carefully designed sampling procedures, is significantly more accurate than existing techniques, thus promising to be the first practical DP embedding model.