Pan-Private Uniformity Testing

11/04/2019
by   Kareem Amin, et al.
0

A centrally differentially private algorithm maps raw data to differentially private outputs. In contrast, a locally differentially private algorithm may only access data through public interaction with data holders, and this interaction must be a differentially private function of the data. We study the intermediate model of pan-privacy. Unlike a locally private algorithm, a pan-private algorithm receives data in the clear. Unlike a centrally private algorithm, the algorithm receives data one element at a time and must maintain a differentially private internal state while processing this stream. First, we show that pan-privacy against multiple intrusions on the internal state is equivalent to sequentially interactive local privacy. Next, we contextualize pan-privacy against a single intrusion by analyzing the sample complexity of uniformity testing over domain [k]. Focusing on the dependence on k, centrally private uniformity testing has sample complexity Θ(√(k)), while noninteractive locally private uniformity testing has sample complexity Θ(k). We show that the sample complexity of pan-private uniformity testing is Θ(k^2/3). By a new Ω(k) lower bound for the sequentially interactive setting, we also separate pan-private from sequentially interactive locally private and multi-intrusion pan-private uniformity testing.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/01/2019

Exponential Separations in Local Differential Privacy Through Communication Complexity

We prove a general connection between the communication complexity of tw...
04/20/2020

Connecting Robust Shuffle Privacy and Pan-Privacy

In the shuffle model of differential privacy, data-holding users send ra...
07/27/2022

Differentially Private Learning of Hawkes Processes

Hawkes processes have recently gained increasing attention from the mach...
05/31/2017

Local Differential Privacy for Physical Sensor Data and Sparse Recovery

In this work we explore the utility of locally differentially private th...
08/07/2018

Test without Trust: Optimal Locally Private Distribution Testing

We study the problem of distribution testing when the samples can only b...
10/19/2021

Private measurement of nonlinear correlations between data hosted across multiple parties

We introduce a differentially private method to measure nonlinear correl...
04/16/2020

Private Learning of Halfspaces: Simplifying the Construction and Reducing the Sample Complexity

We present a differentially private learner for halfspaces over a finite...