Private Alternating Least Squares: Practical Private Matrix Completion with Tighter Rates

TL;DR

This paper introduces a differentially private variant of the Alternating-Least-Squares method for matrix completion, achieving near-optimal sample complexity and improved privacy-utility trade-offs, validated on benchmark datasets.

Contribution

It presents the first global convergence analysis of a DP-ensured ALS algorithm and demonstrates superior accuracy over existing methods in practical settings.

Findings

Achieves nearly optimal sample complexity for DP matrix completion.

Provides the first convergence analysis of noisy ALS under DP.

Outperforms existing algorithms on benchmark datasets.

Abstract

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.