Pan-Private Uniformity Testing

by   Kareem Amin, et al.

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.


page 1

page 2

page 3

page 4


Exponential Separations in Local Differential Privacy Through Communication Complexity

We prove a general connection between the communication complexity of tw...

Connecting Robust Shuffle Privacy and Pan-Privacy

In the shuffle model of differential privacy, data-holding users send ra...

Differentially Private Learning of Hawkes Processes

Hawkes processes have recently gained increasing attention from the mach...

Local Differential Privacy for Physical Sensor Data and Sparse Recovery

In this work we explore the utility of locally differentially private th...

Test without Trust: Optimal Locally Private Distribution Testing

We study the problem of distribution testing when the samples can only b...

Private measurement of nonlinear correlations between data hosted across multiple parties

We introduce a differentially private method to measure nonlinear correl...

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

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