MVG-Mechansim

A module to assist with the implementation of the Matrix-Variate Gaussian (MVG) mechanism for differential privacy under matrix-valued query. Please see the following papers for the detail on the MVG mechanism.

Conference version:

Thee Chanyaswad, Alex Dytso, H. Vincent Poor, and Prateek Mittal. "MVG Mechanism: Differential Privacy under Matrix-Valued Query." 2018 ACM SIGSAC Conference on Computer and Communications Security (CCS'18), 2018. (https://dl.acm.org/citation.cfm?doid=3243734.3243750)

Full version:

Thee Chanyaswad, Alex Dytso, H. Vincent Poor, and Prateek Mittal. "A Differential Privacy Mechanism Design Under Matrix-Valued Query." arXiv:1802.10077 [cs.LG], 2018 (https://arxiv.org/abs/1802.10077)

Functionality

The module currently implements three main functionalities:

1. compute_precision_budget implements the calculation of the precision budget. It takes the following input parameters:
   • the dimension of the matrix-valued query function: m x n,
   • gamma as defined in the paper,
   • the sensitivity s2 as defined in the paper,
   • and the privacy parameters, epsilon and delta.
2. generate_mvg_noise_via_affine_tx implements the MVG sampler based on the affine transformation method.
3. generate_mvg_noise_via_multivariate_gaussian implements the MVG sampler based on the equivalence to the multivariate Gaussian.

Both implementations of the MVG sampler take the row-wise and column-wise covariance matrices as the inputs, and return an instance of the desired random matrix noise as the output.

Prerequisites

The module is implemented in Python 2 and uses numpy.

Author

• Thee Chanyaswad