Test without Trust: Optimal Locally Private Distribution Testing
Jayadev Acharya, Cl\'ement L. Canonne, Cody Freitag, Himanshu Tyagi

TL;DR
This paper investigates distribution testing under local differential privacy constraints, introducing a new mechanism called RAPTOR and analyzing the sample complexity for identity and independence testing.
Contribution
It introduces RAPTOR, a simple, one-bit communication mechanism for private testing, and provides sample complexity bounds for tests using existing and new mechanisms.
Findings
RAPTOR achieves sample optimality for private testing.
Existing mechanisms like RAPPOR require more samples than RAPTOR.
Proposed tests are computationally efficient.
Abstract
We study the problem of distribution testing when the samples can only be accessed using a locally differentially private mechanism and focus on two representative testing questions of identity (goodness-of-fit) and independence testing for discrete distributions. We are concerned with two settings: First, when we insist on using an already deployed, general-purpose locally differentially private mechanism such as the popular RAPPOR or the recently introduced Hadamard Response for collecting data, and must build our tests based on the data collected via this mechanism; and second, when no such restriction is imposed, and we can design a bespoke mechanism specifically for testing. For the latter purpose, we introduce the Randomized Aggregated Private Testing Optimal Response (RAPTOR) mechanism which is remarkably simple and requires only one bit of communication per sample. We propose…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsPrivacy-Preserving Technologies in Data · Mobile Crowdsensing and Crowdsourcing · Cryptography and Data Security
