Inferentially-Private Private Information

TL;DR

This paper introduces a new framework for privacy that limits what an adversary can infer from shared information, and proposes mechanisms to optimize information release while maintaining privacy constraints.

Contribution

It develops an efficient mechanism for binary private information and a programming approach for general cases under inferential privacy constraints.

Findings

Optimal private information structures are characterized geometrically.

Efficient algorithms are devised for binary private information.

A programming approach computes optimal structures for general cases.

Abstract

Information disclosure can compromise privacy when revealed information is correlated with private information. We consider the notion of inferential privacy, which measures privacy leakage by bounding the inferential power a Bayesian adversary can gain by observing a released signal. Our goal is to devise an inferentially-private private information structure that maximizes the informativeness of the released signal, following the Blackwell ordering principle, while adhering to inferential privacy constraints. To achieve this, we devise an efficient release mechanism that achieves the inferentially-private Blackwell optimal private information structure for the setting where the private information is binary. Additionally, we propose a programming approach to compute the optimal structure for general cases given the utility function. The design of our mechanisms builds on our geometric characterization of the Blackwell-optimal disclosure mechanisms under privacy constraints, which may be of independent interest.