Private Empirical Risk Minimization With Analytic Gaussian Mechanism for Healthcare System

With the wide range application of machine learning in healthcare for helping humans drive crucial decisions, data privacy becomes an inevitable concern due to the utilization of sensitive data such as patients records and registers of a company. Thus, constructing a privacy preserving machine learning model while still maintaining high accuracy becomes a challenging problem. In this article, we propose two differentially private algorithms, i.e., Output Perturbation with aGM (OPERA) and Gradient Perturbation with aGM (GRPUA) for empirical risk minimization, a useful method to obtain a globally optimal classifier, by leveraging the analytic Gaussian mechanism (aGM) to achieve privacy preservation of sensitive medical data in a healthcare system. We theoretically analyze and prove utility upper bounds of proposed algorithms and compare them with prior algorithms in the literature. The analyses show that in the high privacy regime, our proposed algorithms can achieve a tighter utility bound for both settings: strongly convex and non-strongly convex loss functions. Besides, we evaluate the proposed private algorithms on five benchmark datasets. The simulation results demonstrate that our approaches can achieve higher accuracy and lower objective values compared with existing ones in all three datasets while providing differential privacy guarantees.