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Private Posterior Inference Consistent with Public Information: A Case Study in Small Area Estimation from Synthetic Census Data

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Privacy in Statistical Databases (PSD 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12276))

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Abstract

Methods for generating differentially-private (DP) synthetic data have received recent attention as large government agencies such as the U.S. Census have decided to release DP synthetic data for public usage. In the synthetic data generation process, it is common to post-process the privatized results so that the final synthetic data agrees with what the data curator considers public information. Our contributions are three fold: 1) we show empirically that using post-processing to incorporate public information in contingency tables can lead to sub-optimal inference, 2) we propose an alternative Bayesian sampling framework that directly incorporates both noise due to DP and public information constraints, leading to improved inference, and 3) we demonstrate the proposed methodology on a study of the relationship between mortality rate and race in small areas given priviatized data from the CDC and U.S. Census.

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Acknowledgements

Thanks to Roberto Molinari at Penn State for helpful discussions, John Abowd and Philip Leclerc at the U.S. Census for discussions about their DP methodology, and Alexis Santos at Penn State for providing data. This work was supported in part by NSF Award No. SES-1853209 to The Pennsylvania State University.

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Authors and Affiliations

  1. Department of Statistics, Pennsylvania State University, University Park, USA

    Jeremy Seeman, Aleksandra Slavkovic & Matthew Reimherr

Authors
  1. Jeremy Seeman
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  2. Aleksandra Slavkovic
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  3. Matthew Reimherr
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Corresponding author

Correspondence to Jeremy Seeman .

Editor information

Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Catalonia, Spain

    Josep Domingo-Ferrer

  2. University of Oklahoma, Norman, OK, USA

    Krishnamurty Muralidhar

A Additional tables and figures

A Additional tables and figures

All code and data available on GitHub, here.

Table 3. Case study specifications
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Table 4. Raw joined data from CDC (first four non-identifier columns) and US Census (last four columns)
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Fig. 4.
figure 4

Posterior distributions of \(\hat{P}(H_1 \mid \textit{\textbf{Y}})\) using the three different methods outlined above. Vertical lines represent the true probabilities for each county.

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Seeman, J., Slavkovic, A., Reimherr, M. (2020). Private Posterior Inference Consistent with Public Information: A Case Study in Small Area Estimation from Synthetic Census Data. In: Domingo-Ferrer, J., Muralidhar, K. (eds) Privacy in Statistical Databases. PSD 2020. Lecture Notes in Computer Science(), vol 12276. Springer, Cham. https://doi.org/10.1007/978-3-030-57521-2_23

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  • DOI: https://doi.org/10.1007/978-3-030-57521-2_23

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-57521-2

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