Differentially Private Block Coordinate Descent for Linear Regression on Vertically Partitioned Data

Abstract

We present a differentially private extension of the block coordinate descent algorithm by means of objective perturbation. The algorithm iteratively performs linear regression in a federated setting on vertically partitioned data. In addition to a privacy guarantee, we derive a utility guarantee; a tolerance parameter indicates how much the differentially private regression may deviate from the analysis without differential privacy. The algorithm’s performance is compared with that of the standard block coordinate descent algorithm on both artificial test data and real-world data. We find that the algorithm is fast and able to generate practical predictions with single-digit privacy budgets, albeit with some accuracy loss.