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The Dirichlet Mechanism for Differential Privacy on the Unit Simplex
- Source :
- ACC
- Publication Year :
- 2020
- Publisher :
- IEEE, 2020.
-
Abstract
- As members of a network share more information with each other and network providers, sensitive data leakage raises privacy concerns. To address this need for a class of problems, we introduce a novel mechanism that privatizes vectors belonging to the unit simplex. Such vectors can be seen 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 these developments. The introduced mechanism is a probabilistic mapping that maps a vector within the unit simplex to the same domain according to 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 the privacy guarantees of the mechanism for two cases, namely, identity queries and average queries. In the former case, we derive expressions for the differential privacy level of privatizing a single vector within the unit simplex. In the latter case, we study the mechanism for privatizing the average of a collection of vectors, each of which is in the unit simplex. We establish a trade-off between the strength of privacy and the variance of the mechanism output, and we introduce a parameter to balance the trade-off between them. Numerical results illustrate these developments.<br />Comment: Submitted to ACC 2020
- Subjects :
- Networking and Internet Architecture (cs.NI)
FOS: Computer and information sciences
021110 strategic, defence & security studies
Class (set theory)
Mathematical optimization
Computer Science - Cryptography and Security
Simplex
Computer science
0211 other engineering and technologies
02 engineering and technology
Variance (accounting)
Dirichlet distribution
Projection (linear algebra)
Domain (mathematical analysis)
Computer Science - Networking and Internet Architecture
symbols.namesake
symbols
Differential privacy
Markov decision process
Cryptography and Security (cs.CR)
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- 2020 American Control Conference (ACC)
- Accession number :
- edsair.doi.dedup.....9e9c81a1a7fa757fe83cfc31357483ec