Disclosure risk assessment with Bayesian non-parametric hierarchical modelling

TL;DR

This paper introduces a Bayesian non-parametric hierarchical model using Hierarchical Dirichlet Processes to accurately assess disclosure risks in microdata, eliminating the need for tuning parameters and effectively handling small samples and structural zeros.

Contribution

It proposes a novel non-parametric Bayesian model for disclosure risk assessment that removes the need for model tuning and improves accuracy with small samples.

Findings

Accurately estimates disclosure risk even with 1% sample size

Eliminates the need for model tuning parameters

Effective handling of structural zeros in data

Abstract

Micro and survey datasets often contain private information about individuals, like their health status, income or political preferences. Previous studies have shown that, even after data anonymization, a malicious intruder could still be able to identify individuals in the dataset by matching their variables to external information. Disclosure risk measures are statistical measures meant to quantify how big such a risk is for a specific dataset. One of the most common measures is the number of sample unique values that are also population-unique. \cite{Man12} have shown how mixed membership models can provide very accurate estimates of this measure. A limitation of that approach is that the number of extreme profiles has to be chosen by the modeller. In this article, we propose a non-parametric version of the model, based on the Hierarchical Dirichlet Process (HDP). The proposed approach does not require any tuning parameter or model selection step and provides accurate estimates of the disclosure risk measure, even with samples as small as 1$\%$ of the population size. Moreover, a data augmentation scheme to address the presence of structural zeros is presented. The proposed methodology is tested on a real dataset from the New York census.