On integrating the number of synthetic data sets $m$ into the 'a priori' synthesis approach

TL;DR

This paper examines how to optimally choose the number of synthetic datasets for categorical data synthesis, balancing data utility and disclosure risk, and introduces new risk metrics with empirical validation.

Contribution

It introduces a framework for selecting the optimal number of synthetic datasets considering the risk-utility trade-off and proposes new risk assessment metrics for categorical data.

Findings

Increasing synthetic datasets improves utility but raises disclosure risk.

The paper proposes metrics τ₃(k,d) and τ₄(k,d) for risk assessment.

Empirical demonstrations validate the proposed methods.

Abstract

Until recently, multiple synthetic data sets were always released to analysts, to allow valid inferences to be obtained. However, under certain conditions - including when saturated count models are used to synthesize categorical data - single imputation ($m=1$) is sufficient. Nevertheless, increasing $m$ causes utility to improve, but at the expense of higher risk, an example of the risk-utility trade-off. The question, therefore, is: which value of $m$ is optimal with respect to the risk-utility trade-off? Moreover, the paper considers two ways of analysing categorical data sets: as they have a contingency table representation, multiple categorical data sets can be averaged before being analysed, as opposed to the usual way of averaging post-analysis. This paper also introduces a pair of metrics, $\tau_3(k,d)$ and $\tau_4(k,d)$, that are suited for assessing disclosure risk in multiple categorical synthetic data sets. Finally, the synthesis methods are demonstrated empirically.