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Abstract:
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Differentially-private (DP) synthetic data techniques allow agencies like the U.S. Census to release public use microdata with relative privacy guarantees. However, DP synthetic data often need to conform with existing public information; in practice, this is frequently achieved by post-processing the private synthetic data through a deterministic function. This raises many questions about how to best achieve valid inference with such data. In this talk we 1) we show, theoretically and empirically, that using post-processing to incorporate public information in contingency tables can lead to sub-optimal inference, 2) we describe an alternative Bayesian sampling framework that directly incorporates both noise due to DP and public information constraints, leading to improved inference, 3) we demonstrate theoretical connections between this sampling framework and generalized (likelihood-free) Bayesian inference, and 4) we demonstrate the proposed methodology on a study of the relationship between mortality rate and race in small areas given privatized data from the CDC and U.S. Census. (joint work with J.Seeman, M. Reimherr)
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