Jackson, J; Mitra, R; Francis, B; Dove, I; (2022) On Integrating the Number of Synthetic Data Sets m into the a priori Synthesis Approach. In: Privacy in Statistical Databases. PSD 2022. (pp. pp. 205-219). Springer International Publishing: Cham, Switzerland.

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Abstract

The synthesis mechanism given in [4] uses saturated models, along with overdispersed count distributions, to generate synthetic categorical data. The mechanism is controlled by tuning parameters, which can be tuned according to a specific risk or utility metric. Thus expected properties of synthetic data sets can be determined analytically a priori, that is, before they are generated. While [4] considered the case of generating m=1 data set, this paper considers generating m>1 data sets. In effect, m becomes a tuning parameter and the role of m in relation to the risk-utility trade-off can be shown analytically. The paper introduces a pair of risk metrics, τ3(k,d) and τ4(k,d), that are suited to m>1 data sets; and also considers the more general issue of how best to analyse m>1 categorical data sets: average the data sets pre-analysis or average results post-analysis. Finally, the methods are demonstrated empirically with the synthesis of a constructed data set which is used to represent the English School Census.

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