Holohan, Naoise and Leith, Douglas J. and Mason, Oliver (2017) Extreme points of the local differential privacy polytope. Linear Algebra and its Applications, 534. pp. 78-96. ISSN 0024-3795

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Abstract

We study the convex polytope of n x n stochastic matrices that define locally ϵ-differentially private mechanisms. We first present invariance properties of the polytope and results reducing the number of constraints needed to define it. Our main results concern the extreme points of the polytope. In particular, we completely characterise these for matrices with 1, 2 or n non-zero columns.

Item Type:	Article
Keywords:	Data privacy; Stochastic matrices; Matrix polytopes; Differential privacy;
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	11658
Identification Number:	https://doi.org/10.1016/j.laa.2017.08.011
Depositing User:	Oliver Mason
Date Deposited:	06 Nov 2019 15:49
Journal or Publication Title:	Linear Algebra and its Applications
Publisher:	Elsevier
Refereed:	Yes
URI:	https://www.sciencedirect.com
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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