In this work, we propose a new mechanism for releasing differentially private functional summaries called the Independent Component Laplace Process, or ICLP, mechanism. By treating the functional summaries of interest as truly infinite-dimensional objects and perturbing them with the ICLP noise, this new mechanism relaxes assumptions on data trajectories and preserves higher utility compared to classical finite-dimensional subspace embedding approaches in the literature. We establish the feasibility of the proposed mechanism in multiple function spaces. Several statistical estimation problems are considered, and we demonstrate by slightly over-smoothing the summary, the privacy cost will not dominate the statistical error and is asymptotically negligible. Numerical experiments on synthetic and real datasets demonstrate the efficacy of the proposed mechanism.

我们提出了一种新的机制，称为独立成份拉普拉斯过程（ICLP），用于释放具有差分隐私的功能性摘要。通过将感兴趣的功能性摘要视为真正的无限维对象，并使用ICLP噪声对其进行扰动，该机制放松了对数据轨迹的假设，并相对于文献中的经典有限维子空间嵌入方法保留了更高的效用。我们在多个函数空间中验证了所提出机制的可行性。我们考虑了几个统计估计问题，并通过略微过度平滑的摘要证明，隐私成本不会主导统计误差，并在渐进意义下可忽略。对合成和真实数据集进行的数字实验证明了所提出机制的有效性。

通过独立的成分拉普拉斯过程实现差分隐私功能摘要