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The Skellam Mechanism for Differentially Private Federated Learning
- Publication Year :
- 2021
-
Abstract
- We introduce the multi-dimensional Skellam mechanism, a discrete differential privacy mechanism based on the difference of two independent Poisson random variables. To quantify its privacy guarantees, we analyze the privacy loss distribution via a numerical evaluation and provide a sharp bound on the R\'enyi divergence between two shifted Skellam distributions. While useful in both centralized and distributed privacy applications, we investigate how it can be applied in the context of federated learning with secure aggregation under communication constraints. Our theoretical findings and extensive experimental evaluations demonstrate that the Skellam mechanism provides the same privacy-accuracy trade-offs as the continuous Gaussian mechanism, even when the precision is low. More importantly, Skellam is closed under summation and sampling from it only requires sampling from a Poisson distribution -- an efficient routine that ships with all machine learning and data analysis software packages. These features, along with its discrete nature and competitive privacy-accuracy trade-offs, make it an attractive practical alternative to the newly introduced discrete Gaussian mechanism.<br />Comment: Paper published in NeurIPS 2021
- Subjects :
- FOS: Computer and information sciences
Computer Science - Machine Learning
Computer Science - Cryptography and Security
Statistics - Machine Learning
Probability (math.PR)
Computer Science - Data Structures and Algorithms
FOS: Mathematics
Data Structures and Algorithms (cs.DS)
Machine Learning (stat.ML)
Cryptography and Security (cs.CR)
Mathematics - Probability
Machine Learning (cs.LG)
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....894c69bd2eea1283da9743414049c38d