Differentially Private Multi-Party Data Release for Linear Regression

TL;DR

This paper introduces a novel differentially private method for multi-party linear regression data release, addressing privacy concerns while ensuring convergence to optimal solutions as data size grows.

Contribution

It proposes a new DP approach for multi-party linear regression that overcomes eigenvalue issues and guarantees asymptotic convergence to the non-private solution.

Findings

The Gaussian mechanism faces eigenvalue problems in this setting.

The proposed method converges to the optimal solution asymptotically.

Experimental results validate theoretical guarantees on real-world data.

Abstract

Differentially Private (DP) data release is a promising technique to disseminate data without compromising the privacy of data subjects. However the majority of prior work has focused on scenarios where a single party owns all the data. In this paper we focus on the multi-party setting, where different stakeholders own disjoint sets of attributes belonging to the same group of data subjects. Within the context of linear regression that allow all parties to train models on the complete data without the ability to infer private attributes or identities of individuals, we start with directly applying Gaussian mechanism and show it has the small eigenvalue problem. We further propose our novel method and prove it asymptotically converges to the optimal (non-private) solutions with increasing dataset size. We substantiate the theoretical results through experiments on both artificial and real-world datasets.