McGlinchey, Aisling and Mason, Oliver (2020) Observations on the bias of nonnegative mechanisms for differential privacy. Foundations of Data Science, 2 (4). pp. 429-442. ISSN 2639-8001

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Abstract

We study two methods for differentially private analysis of bounded data and extend these to nonnegative queries. We first recall that for the Laplace mechanism, boundary inflated truncation (BIT) applied to nonnegative queries and truncation both lead to strictly positive bias. We then consider a generalization of BIT using translated ramp functions. We explicitly characterise the optimal function in this class for worst case bias. We show that applying any square-integrable post-processing function to a Laplace mechanism leads to a strictly positive maximal absolute bias. A corresponding result is also shown for a generalisation of truncation, which we refer to as restriction. We also briefly consider an alternative approach based on multiplicative mechanisms for positive data and show that, without additional restrictions, these mechanisms can lead to infinite bias.

Item Type:	Article
Additional Information:	This is the preprint version of the published article and is available at https://arxiv.org/abs/2101.02957. Cite as: Aisling McGlinchey, Oliver Mason. Observations on the bias of nonnegative mechanisms for differential privacy. Foundations of Data Science, 2020, 2 (4): 429-442. doi:10.3934/fods.2020020
Keywords:	Differential privacy; Laplace distribution; nonnegative data; bias; post-processing;
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	15524
Identification Number:	https://doi.org/10.3934/fods.2020020
Depositing User:	Oliver Mason
Date Deposited:	16 Feb 2022 16:41
Journal or Publication Title:	Foundations of Data Science
Publisher:	American Institute of Mathematical Sciences
Refereed:	Yes
URI:	Publisher Organisation
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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