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    Extreme points of the local differential privacy polytope


    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:

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