Privacy-preserving logistic regression with secret sharing

Abstract

Background: Logistic regression (LR) is a widely used classification method for modeling binary outcomes in many medical data classification tasks. Researchers that collect and combine datasets from various data custodians and jurisdictions can greatly benefit from the increased statistical power to support their analysis goals. However, combining data from different sources creates serious privacy concerns that need to be addressed.

Methods: In this paper, we propose two privacy-preserving protocols for performing logistic regression with the Newton-Raphson method in the estimation of parameters. Our proposals are based on secure Multi-Party Computation (MPC) and tailored to the honest majority and dishonest majority security settings.

Results: The proposed protocols are evaluated against both synthetic and real-world datasets in terms of efficiency and accuracy, and a comparison is made with the ordinary logistic regression. The experimental results demonstrate that the proposed protocols are highly efficient and accurate.

Conclusions: Our work introduces two iterative algorithms to enable the distributed training of a logistic regression model in a privacy-preserving manner. The implementation results show that our algorithms can handle large datasets from multiple sources.

Keywords: Logistic regression; Multi-party computation; Newton–Raphson; Privacy-preserving; Secret sharing.

Fig. 1

Efficiency comparison for increasing number of records using accurate algorithm 1

Fig. 2

Efficiency comparison for increasing number of features using accurate algorithm 1

Fig. 3

Efficiency comparison for increasing number of records using approximation-based algorithm 2

Fig. 4

Efficiency comparison for increasing number of features using approximation-based algorithm 2