Extreme points of the local differential privacy polytope

被引：10

作者：

Holohan, Naoise ^{[1
,4
]}

Leith, Douglas J. ^{[1
]}

Mason, Oliver ^{[2
,3
]}

机构：

[1] Trinity Coll Dublin, Sch Comp Sci & Stat, Dublin, Ireland

[2] Maynooth Univ, Hamilton Inst, Dept Math & Stat, Maynooth, Kildare, Ireland

[3] Lero, Limerick, Ireland

[4] IBM Res, Dublin, Ireland

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2017年 / 534卷

基金：

爱尔兰科学基金会;

关键词：

Data privacy; Stochastic matrices; Matrix polytopes; Differential privacy; MATRICES;

D O I：

10.1016/j.laa.2017.08.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the convex polytope of n x n stochastic matrices that define locally &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. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：78 / 96

页数：19

共 50 条

[31] The Role of Interactivity in Local Differential Privacy
Joseph, Matthew
Mao, Jieming
Neel, Seth
Roth, Aaron
2019 IEEE 60TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS 2019), 2019, : 94 - 105
[32] A Comprehensive Survey on Local Differential Privacy
Xiong, Xingxing
Liu, Shubo
Li, Dan
Cai, Zhaohui
Niu, Xiaoguang
SECURITY AND COMMUNICATION NETWORKS, 2020, 2020
[33] RANDOMIZED REQUANTIZATION WITH LOCAL DIFFERENTIAL PRIVACY
Xiong, Sijie
Sarwate, Anand D.
Mandayam, Narayan B.
2016 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING PROCEEDINGS, 2016, : 2189 - 2193
[34] Local Differential Privacy for Federated Learning
Arachchige, Pathum Chamikara Mahawaga
Liu, Dongxi
Camtepe, Seyit
Nepal, Surya
Grobler, Marthie
Bertok, Peter
Khalil, Ibrahim
COMPUTER SECURITY - ESORICS 2022, PT I, 2022, 13554 : 195 - 216
[35] Mechanisms for Robust Local Differential Privacy
Lopuhaa-Zwakenberg, Milan
Goseling, Jasper
ENTROPY, 2024, 26 (03)
[36] Local Differential Privacy for Belief Functions
Li, Qiyu
Zhou, Chunlai
Qin, Biao
Xu, Zhiqiang
THIRTY-SIXTH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE / THIRTY-FOURTH CONFERENCE ON INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE / TWELVETH SYMPOSIUM ON EDUCATIONAL ADVANCES IN ARTIFICIAL INTELLIGENCE, 2022, : 10025 - 10033
[37] GENERATING RANDOM POINTS IN A POLYTOPE
RUBIN, PA
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 1984, 13 (03) : 375 - 396
[38] Privacy Enhanced Matrix Factorization for Recommendation with Local Differential Privacy
Shin, Hyejin
Kim, Sungwook
Shin, Junbum
Xiao, Xiaokui
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, 2018, 30 (09) : 1770 - 1782
[39] Privacy preserving classification on local differential privacy in data centers
Fan, Weibei
He, Jing
Guo, Mengjiao
Li, Peng
Han, Zhijie
Wang, Ruchuan
JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING, 2020, 135 (135) : 70 - 82
[40] Some observations about the extreme points of the Generalized Cardinality-Constrained Shortest Path Problem polytope
Monaco, Maria Flavia
Sammarra, Marcello
Moccia, Luigi
OPTIMIZATION LETTERS, 2008, 2 (04) : 577 - 585

← 1 2 3 4 5 →