Utility Analysis of Horizontally Merged Multi-Party Synthetic Data with Differential Privacy

A large amount of data is often needed to train machine learning algorithms with confidence. One way to achieve the necessary data volume is to share and combine data from multiple parties. On the other hand, how to protect sensitive personal information during data sharing is always a challenge. We focus on data sharing when parties have overlapping attributes but non-overlapping individuals. One approach to achieve privacy protection is through sharing differentially private synthetic data. Each party generates synthetic data at its own preferred privacy budget, which are then released and horizontally merged across the parties. The total privacy cost for this approach is capped at the maximum individual budget employed by a party. We derive the mean squared error bounds for the parameter estimation in common regression analysis based on the merged sanitized data across parties. We identify through theoretical analysis the conditions under which the utility of sharing and merging sanitized data outweighs the perturbation introduced for satisfying differential privacy and surpasses that based on individual party data. The experiments suggest that sanitized HOMM data obtained at a practically reasonable small privacy cost can lead to smaller prediction and estimation errors than individual parties, demonstrating benefits of data sharing while protecting privacy.