Logistic Regression Model for Differentially-Private Matrix Masked Data

TL;DR

This paper introduces a novel statistical analysis method for logistic regression on privacy-preserved data using matrix masking and noise addition, ensuring data privacy while maintaining analysis validity.

Contribution

It develops the first valid logistic regression analysis approach under local noise addition and matrix masking for privacy protection.

Findings

Proposed estimators are valid under asymptotic conditions.

The new method outperforms naive logistic regression on privacy-preserved data.

Simulations and real data confirm the effectiveness of the approach.

Abstract

A recently proposed scheme utilizing local noise addition and matrix masking enables data collection while protecting individual privacy from all parties, including the central data manager. Statistical analysis of such privacy-preserved data is particularly challenging for nonlinear models like logistic regression. By leveraging a relationship between logistic regression and linear regression estimators, we propose the first valid statistical analysis method for logistic regression under this setting. Theoretical analysis of the proposed estimators confirmed its validity under an asymptotic framework with increasing noise magnitude to account for strict privacy requirements. Simulations and real data analyses demonstrate the superiority of the proposed estimators over naive logistic regression methods on privacy-preserved data sets.