Many existing mechanisms to achieve differential privacy (DP) on infinite-dimensional functional summaries often involve embedding these summaries into finite-dimensional subspaces and applying traditional DP techniques. Such mechanisms generally treat each dimension uniformly and struggle with complex, structured summaries. This work introduces a novel mechanism for DP functional summary release: the Independent Component Laplace Process (ICLP) mechanism. This mechanism treats the summaries of interest as truly infinite-dimensional objects, thereby addressing several limitations of existing mechanisms. We establish the feasibility of the proposed mechanism in multiple function spaces. Several statistical estimation problems are considered, and we demonstrate one can enhance the utility of sanitized summaries by oversmoothing their non-private counterpart. Numerical experiments on synthetic and real datasets demonstrate the efficacy of the proposed mechanism.

翻译：许多用于实现无穷维函数摘要差分隐私的现有机制，通常将这些摘要嵌入有限维子空间并应用传统差分隐私技术。这类机制往往对各维度一视同仁，难以处理复杂结构化摘要。本文提出一种新颖的差分隐私函数摘要发布机制：独立分量拉普拉斯过程机制。该机制将目标摘要视为真正的无穷维对象，从而解决了现有机制的若干局限性。我们在多个函数空间中论证了该机制的可行性，并考虑了若干统计估计问题。研究表明，通过过度平滑非隐私版本的摘要，可提升净化后摘要的实用性。在合成数据集与真实数据集上的数值实验验证了所提机制的有效性。