Gaussian Differential Privacy on Riemannian Manifolds
Authors: Yangdi Jiang, Xiaotian Chang, Yi Liu, Lei Ding, Linglong Kong, Bei Jiang
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Through simulations on one of the most prevalent manifolds in statistics, the unit sphere Sd, we demonstrate the superior utility of our Riemannian Gaussian mechanism in comparison to the previously proposed Riemannian Laplace mechanism for implementing GDP. |
| Researcher Affiliation | Academia | Yangdi Jiang, Xiaotian Chang, Yi Liu, Lei Ding, Linglong Kong, Bei Jiang* Department of Mathematical and Statistical Sciences University of Alberta |
| Pseudocode | Yes | Algorithm 1 Computing µ on S1 |
| Open Source Code | Yes | The R code is available in the Git Hub repository: https://github. com/Lei-Ding07/Gaussian-Differential-Privacy-on-Riemannian-Manifolds |
| Open Datasets | No | We initiate our analysis by generating sample data D = {x1, . . . , xn} from a ball of radius π/8 on S2 and subsequently computing the Fréchet mean x. The paper does not provide access information (link, citation, or repository) for this generated dataset. |
| Dataset Splits | No | The paper describes generating sample data and then applying privatization mechanisms, but does not provide specific details on training, validation, or test dataset splits. |
| Hardware Specification | Yes | Simulations are done in R on a Mac Mini computer with an Apple M1 processor with 8 GB of RAM running Mac OS 13. |
| Software Dependencies | No | Simulations are done in R on a Mac Mini computer with an Apple M1 processor with 8 GB of RAM running Mac OS 13. The paper mentions 'R' but does not specify its version or the versions of any critical libraries or packages used. |
| Experiment Setup | Yes | Throughout these simulations, we fix the sample size at n = 10 to maintain a constant sensitivity . With held constant, we let the rate σ = k/4 with 1 k 12. For each σ, we determine the privacy budget µ using two approaches: (i) using Algorithm 1 with nε set as 1000 for S1 and using µ = 1/σ for R; (ii) using Algorithm 2 with n = 1000, nε = 1000, m = 100, εmax = π/(2σ2) for S1 and εmax = max{10, 5/σ + 1/(2σ2)} for R. |