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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.