# Preserving Differential Privacy Between Features in Distributed Estimation

## TL;DR

This paper introduces PriDE, a scalable framework for distributed estimation that preserves differential privacy across features held by different data owners, enabling privacy-aware machine learning without a trusted curator.

## Contribution

The paper proposes PriDE, a novel method for distributed estimation that maintains differential privacy in vertically-partitioned data settings, with theoretical guarantees and empirical validation.

## Key findings

- PriDE preserves $(\epsilon,\delta)$-distributed differential privacy.
- PriDE achieves bounded estimation error compared to non-private estimates.
- Empirical results confirm PriDE's effectiveness on real and synthetic datasets.

## Abstract

Privacy is crucial in many applications of machine learning. Legal, ethical and societal issues restrict the sharing of sensitive data making it difficult to learn from datasets that are partitioned between many parties. One important instance of such a distributed setting arises when information about each record in the dataset is held by different data owners (the design matrix is "vertically-partitioned"). In this setting few approaches exist for private data sharing for the purposes of statistical estimation and the classical setup of differential privacy with a "trusted curator" preparing the data does not apply. We work with the notion of $(\epsilon,\delta)$-distributed differential privacy which extends single-party differential privacy to the distributed, vertically-partitioned case. We propose PriDE, a scalable framework for distributed estimation where each party communicates perturbed random projections of their locally held features ensuring $(\epsilon,\delta)$-distributed differential privacy is preserved. For $\ell_2$-penalized supervised learning problems PriDE has bounded estimation error compared with the optimal estimates obtained without privacy constraints in the non-distributed setting. We confirm this empirically on real world and synthetic datasets.