Privacy-aware Minimum Error Probability Estimation: An Entropy Constrained Approach

TL;DR

This paper develops a convex optimization framework for designing privacy-aware estimators that minimize error while controlling private information leakage, including perfect privacy solutions ensuring independence between estimate and private data.

Contribution

It introduces a novel entropy-constrained approach for privacy-aware estimation, deriving conditions for optimal and perfect privacy estimators, and formulates the problem as convex and linear optimization problems.

Findings

Optimal privacy-aware estimator is obtained via convex optimization.

Perfect privacy estimator ensures independence between estimate and private info.

Conditions for the existence of perfect privacy estimators are established.

Abstract

This paper studies the design of an optimal privacyaware estimator of a public random variable based on noisy measurements which contain private information. The public random variable carries non-private information, however, its estimate will be correlated with the private information due to the estimation process. It is assumed that the estimate of the public random variable is revealed to an untrusted party. The objective is to design an estimator for the public random variable such that the leakage of the private information, via the estimation process, is kept below a certain level. The privacy metric is defined as the discrete conditional entropy of the private random variable, which carries the private information, given the output of the estimator. A binary loss function is considered for the estimation of the public random variable. It is shown that the optimal privacy-aware estimator is the solution of a (possibly infinite-dimensional) convex optimization problem. We next study the optimal perfect privacy estimator which ensures that the estimate of the public random variable is independent of the private information. A necessary and sufficient condition is derived which guarantees that an estimator satisfies the perfect privacy requirement. It is shown that the optimal perfect privacy estimator is the solution of a linear optimization problem. A sufficient condition for the existence of the optimal perfect privacy estimator is derived when the estimator has access to discretized measurements of sensors.