Title
Differential Privacy On The Unit Simplex Via The Dirichlet Mechanism
Abstract
As members of network systems share more information among agents and with network providers, sensitive data leakage raises privacy concerns. Motivated by such concerns, we introduce a novel mechanism that privatizes vectors belonging to the unit simplex. Such vectors can be found in many applications, such as privatizing a decision-making policy in a Markov decision process. We use differential privacy as the underlying mathematical framework for this work. The introduced mechanism is a probabilistic mapping that maps a vector within the unit simplex to the same domain using a Dirichlet distribution. We find the mechanism well-suited for inputs within the unit simplex because it always returns a privatized output that is also in the unit simplex. Therefore, no further projection back onto the unit simplex is required. We verify and quantify the privacy guarantees of the mechanism for three cases: identity queries, average queries, and general linear queries. We establish a trade-off between the level of privacy and the accuracy of the mechanism output, and we introduce a parameter to balance the trade-off between them. Numerical results illustrate the proposed mechanism.
Year
DOI
Venue
2021
10.1109/TIFS.2021.3052356
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY
Keywords
DocType
Volume
Privacy, Differential privacy, Probabilistic logic, Decision making, Markov processes, Additive noise, Privatization, (i) Data privacy, (ii) Learning (artificial intelligence), (iii) Uncertain systems
Journal
16
ISSN
Citations 
PageRank 
1556-6013
0
0.34
References 
Authors
0
5
Name
Order
Citations
PageRank
Parham Gohari100.34
Bo Wu22111.57
Calvin Hawkins300.34
Hale, M.T.4176.84
Ufuk Topcu51032115.78