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.

翻译：信息泄露可能危及隐私，因为公开的信息往往与私有信息存在关联。本文探讨推理隐私的概念，该概念通过限制贝叶斯对手在观测到发布信号后所能获得的推理能力来量化隐私泄露程度。我们的目标是设计一种推理隐私约束下的私有信息结构，使其在遵循推理隐私限制的同时，依据布莱克韦尔序原理最大化发布信号的信息量。为此，我们针对二元私有信息场景，设计了一种高效发布机制，实现了推理隐私约束下的布莱克韦尔最优私有信息结构。此外，我们提出了一种基于规划的方法，可在给定效用函数的情况下计算一般情形下的最优结构。我们的机制设计建立在对隐私约束下布莱克韦尔最优披露机制的几何特征刻画基础上，该理论成果可能具有独立的研究价值。