Differential Privacy for Functions and Functional Data

TL;DR

This paper introduces a method for achieving differential privacy in the release of functions by adding Gaussian process noise, extending privacy guarantees to functional data in RKHS settings.

Contribution

It develops a novel approach for differentially private function release using Gaussian processes, expanding privacy techniques beyond finite-dimensional outputs.

Findings

Gaussian process noise ensures differential privacy for functions

Method applies to kernel density estimation and SVMs

Sensitivity measured in RKHS norm guides noise level

Abstract

Differential privacy is a framework for privately releasing summaries of a database. Previous work has focused mainly on methods for which the output is a finite dimensional vector, or an element of some discrete set. We develop methods for releasing functions while preserving differential privacy. Specifically, we show that adding an appropriate Gaussian process to the function of interest yields differential privacy. When the functions lie in the same RKHS as the Gaussian process, then the correct noise level is established by measuring the "sensitivity" of the function in the RKHS norm. As examples we consider kernel density estimation, kernel support vector machines, and functions in reproducing kernel Hilbert spaces.