Pure Differential Privacy for Functional Summaries via a Laplace-like Process
This work addresses the challenge of applying differential privacy to complex, structured functional summaries, which is important for privacy-preserving data analysis in fields like statistics and machine learning, representing a novel method rather than an incremental improvement.
The paper tackled the problem of achieving differential privacy for infinite-dimensional functional summaries by introducing the Independent Component Laplace Process (ICLP) mechanism, which treats summaries as truly infinite-dimensional objects and demonstrates efficacy through numerical experiments on synthetic and real datasets.
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.