Propose, Test, Release: Differentially private estimation with high probability

02/19/2020
by   Victor-Emmanuel Brunel, et al.
0

We derive concentration inequalities for differentially private median and mean estimators building on the "Propose, Test, Release" (PTR) mechanism introduced by Dwork and Lei (2009). We introduce a new general version of the PTR mechanism that allows us to derive high probability error bounds for differentially private estimators. Our algorithms provide the first statistical guarantees for differentially private estimation of the median and mean without any boundedness assumptions on the data, and without assuming that the target population parameter lies in some known bounded interval. Our procedures do not rely on any truncation of the data and provide the first sub-Gaussian high probability bounds for differentially private median and mean estimation, for possibly heavy tailed random variables.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/27/2019

Differentially private sub-Gaussian location estimators

We tackle the problem of estimating a location parameter with differenti...
research
10/12/2022

Concentration of the exponential mechanism and differentially private multivariate medians

We prove concentration inequalities for the output of the exponential me...
research
03/19/2021

Differentially private inference via noisy optimization

We propose a general optimization-based framework for computing differen...
research
04/22/2022

Sharper Utility Bounds for Differentially Private Models

In this paper, by introducing Generalized Bernstein condition, we propos...
research
01/07/2021

Differentially private depth functions and their associated medians

In this paper, we investigate the differentially private estimation of d...
research
06/11/2020

CoinPress: Practical Private Mean and Covariance Estimation

We present simple differentially private estimators for the mean and cov...
research
11/27/2015

Algorithms for Differentially Private Multi-Armed Bandits

We present differentially private algorithms for the stochastic Multi-Ar...

Please sign up or login with your details

Forgot password? Click here to reset