Shape And Structure Preserving Differential Privacy

Authors: Carlos Soto, Karthik Bharath, Matthew Reimherr, Aleksandra Slavković

NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental In this Section, we consider two simulated examples and a real data example on 2D shapes. For the former, we consider the positively curved unit d-sphere and the set of symmetric positive definite matrices (SPDM), which when equipped with an affine invariant metric is negatively curved.
Researcher Affiliation Academia Carlos Soto Department of Statistics Pennsylvania State University University Park, PA cjs7363@psu.edu Karthik Bharath School of Mathematical Sciences University of Nottingham Nottingham, UK Karthik.Bharath@nottingham.ac.uk Matthew Reimherr Department of Statistics Pennsylvania State University University Park, PA mreimherr@psu.edu Aleksandra Slavkovic Department of Statistics Pennsylvania State University University Park, PA sesa@psu.edu
Pseudocode No The paper describes mathematical formulations and theoretical concepts but does not contain structured pseudocode or algorithm blocks.
Open Source Code Yes All code is provided as a zipped folder.
Open Datasets Yes As an application we consider the pre-processed corpus callosum data of Cornea et al. [2017] from the Alzheimer s Disease Neuroimaging Initiative (ADNI). (...) We generate random samples D from S2 1 and compute the Fréchet mean x, both as described in the Supplemental material.
Dataset Splits No The paper mentions generating random samples and using a dataset but does not provide specific dataset splits (e.g., percentages or counts) for training, validation, or testing in the main text. It refers to 'replicates' for utility comparison, not data partitioning.
Hardware Specification No The main paper does not explicitly describe the specific hardware (e.g., GPU/CPU models, memory amounts) used for running its experiments. It states in the checklist that this information is included in the Supplemental materials.
Software Dependencies No The paper does not provide specific ancillary software details, such as library names with version numbers (e.g., Python 3.8, PyTorch 1.9), in the main text.
Experiment Setup Yes In each scenario we sample from KNG via Metropolis-Hastings, a Monte Carlo Markov Chain method. (...) We set ϵ = 1 and sanitize x with three separate methods; first with the proposed method KNG on manifolds to produce x KNG, second with the Laplace on manifolds as in Reimherr et al. [2021] to produce x L, and lastly embedding x into R3 and privatizing with the Euclidean Laplace to produce x E. (...) For each sample size, 10000 replicates were used for S2 1, whereas 500 were used for P(k).