Privacy-preserving ridge regression on distributed data

Ridge regression is a statistical method for modeling a linear relationship between a dependent variable and some explanatory values. It is a building-block that plays a major role in many learning algorithms such as recommendation systems. However, in many applications such as e-health, explanatory values contains private information owned by different patients that are not willing to share them, unless data privacy is guaranteed. In this paper, we propose a protocol for conducting privacy-preserving ridge regression (PPRR) over high-dimensional data. In our protocol, each user submits its data in an encrypted form to an evaluator and the evaluator computes a linear model of all users' data without learning their contents. The core encryption method is equipped with homomorphic properties to enable the evaluator to perform ridge regression over encrypted data. We implement our protocol and demonstrate that it is suitable for dealing with high-dimensional data distributed among millions of users. We also compare our protocol with the state-of-the-art solutions in terms of both computation and communication costs. The results show that our protocol outperforms most existing approaches based on secure multi-party computation, garbled circuit, fully homomorphic encryption, secret-sharing, and hybrid methods.