# Pure Differential Privacy for Functional Summaries with a Laplace-like Process

arXiv: https://arxiv.org/abs/2309.00125 · HTML: https://mlsanity.com/paper/2309.00125/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 31 Aug 2023.

## Builds on (most cited first, 9 of 9)

- [Differentially Private Simple Linear Regression](https://mlsanity.com/paper/2007.05157/) (2020)
- [Frequentist coverage and sup-norm convergence rate in Gaussian process regression](https://mlsanity.com/paper/1708.04753/) (2017)
- [Heterogeneous Gaussian Mechanism: Preserving Differential Privacy in Deep Learning with Provable Robustness](https://mlsanity.com/paper/1906.01444/) (2019)
- [The Bernstein Mechanism: Function Release under Differential Privacy](https://mlsanity.com/paper/1507.04499/) (2015)
- [Benefits and Pitfalls of the Exponential Mechanism with Applications to Hilbert Spaces and Functional PCA](https://mlsanity.com/paper/1901.10864/) (2019)
- [Structure and Sensitivity in Differential Privacy: Comparing K-Norm Mechanisms](https://mlsanity.com/paper/1801.09236/) (2018)
- [KNG: The K-Norm Gradient Mechanism](https://mlsanity.com/paper/1905.09436/) (2019)
- [Faster Private Release of Marginals on Small Databases](https://mlsanity.com/paper/1304.3754/) (2013)
- [Elliptical Perturbations for Differential Privacy](https://mlsanity.com/paper/1905.09420/) (2019)

## Abstract (arXiv)

Many existing mechanisms for achieving differential privacy (DP) on infinite-dimensional functional summaries typically involve embedding these functional summaries into finite-dimensional subspaces and applying traditional multivariate DP techniques. These mechanisms generally treat each dimension uniformly and struggle with complex, structured summaries. This work introduces a novel mechanism to achieve pure DP for functional summaries in a separable infinite-dimensional Hilbert space, named the Independent Component Laplace Process (ICLP) mechanism. This mechanism treats the summaries of interest as truly infinite-dimensional functional objects, thereby addressing several limitations of the existing mechanisms. Several statistical estimation problems are considered, and we demonstrate how one can enhance the utility of private summaries by oversmoothing the non-private counterparts. Numerical experiments on synthetic and real datasets demonstrate the effectiveness of the proposed mechanism.