Introducing the Huber mechanism for differentially private low-rank matrix completion
This work addresses privacy concerns in matrix completion for applications handling sensitive data, but it is incremental as it builds on existing differential privacy mechanisms.
The authors tackled the problem of performing low-rank matrix completion with sensitive user data by proposing a novel noise addition mechanism inspired by Huber loss for differential privacy. They proved it achieves ε-differential privacy and showed it outperforms Laplacian and Gaussian mechanisms in some cases while being comparable otherwise.
Performing low-rank matrix completion with sensitive user data calls for privacy-preserving approaches. In this work, we propose a novel noise addition mechanism for preserving differential privacy where the noise distribution is inspired by Huber loss, a well-known loss function in robust statistics. The proposed Huber mechanism is evaluated against existing differential privacy mechanisms while solving the matrix completion problem using the Alternating Least Squares approach. We also propose using the Iteratively Re-Weighted Least Squares algorithm to complete low-rank matrices and study the performance of different noise mechanisms in both synthetic and real datasets. We prove that the proposed mechanism achieves ε-differential privacy similar to the Laplace mechanism. Furthermore, empirical results indicate that the Huber mechanism outperforms Laplacian and Gaussian in some cases and is comparable, otherwise.