Optimal disclosure risk assessment

02/14/2019
by   Federico Camerlenghi, et al.
0

Protection against disclosure is a legal and ethical obligation for agencies releasing microdata files for public use. Consider a microdata sample of size n from a finite population of size n̅=n+λ n, with λ>0, such that each record contains two disjoint types of information: identifying categorical information and sensitive information. Any decision about releasing data is supported by the estimation of measures of disclosure risk, which are functionals of the number of sample records with a unique combination of values of identifying variables. The most common measure is arguably the number τ_1 of sample unique records that are population uniques. In this paper, we first study nonparametric estimation of τ_1 under the Poisson abundance model for sample records. We introduce a class of linear estimators of τ_1 that are simple, computationally efficient and scalable to massive datasets, and we give uniform theoretical guarantees for them. In particular, we show that they provably estimate τ_1 all of the way up to the sampling fraction (λ+1)^-1∝ ( n)^-1, with vanishing normalized mean-square error (NMSE) for large n. We then establish a lower bound for the minimax NMSE for the estimation of τ_1, which allows us to show that: i) (λ+1)^-1∝ ( n)^-1 is the smallest possible sampling fraction; ii) estimators' NMSE is near optimal, in the sense of matching the minimax lower bound, for large n. This is the main result of our paper, and it provides a precise answer to an open question about the feasibility of nonparametric estimation of τ_1 under the Poisson abundance model and for a sampling fraction (λ+1)^-1<1/2.

READ FULL TEXT
research
04/03/2018

Simple estimators for network sampling

Some conceptually simple estimators for network sampling are introduced....
research
10/27/2022

The Optimal Sample Size in Crosswise Model for Sensitive Questions

The problem is in the estimation of the fraction of population with a st...
research
02/18/2017

Sample complexity of population recovery

The problem of population recovery refers to estimating a distribution b...
research
02/07/2023

Near-Minimax-Optimal Risk-Sensitive Reinforcement Learning with CVaR

In this paper, we study risk-sensitive Reinforcement Learning (RL), focu...
research
12/15/2020

Minimax Risk and Uniform Convergence Rates for Nonparametric Dyadic Regression

Let i=1,…,N index a simple random sample of units drawn from some large ...
research
04/07/2021

Near-optimal estimation of the unseen under regularly varying tail populations

Given n samples from a population of individuals belonging to different ...
research
05/05/2021

Public Communication can Facilitate Low-Risk Coordination under Surveillance

Consider a sub-population of rebels that wish to initiate a revolution. ...

Please sign up or login with your details

Forgot password? Click here to reset