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Statistically Valid Inferences from Differentially Private Data Releases, with Application to the Facebook URLs Dataset

Published online by Cambridge University Press:  20 April 2022

Georgina Evans Open the ORCID record for Georgina Evans [Opens in a new window]  and
Gary King Open the ORCID record for Gary King [Opens in a new window]
Georgina Evans
Affiliation:
Department of Government, Harvard University, Cambridge, MA 02138, USA. E-mail: GeorginaEvans@g.harvard.edu, URL: https://Georgina-Evans.com
Gary King*
Affiliation:
Institute for Quantitative Social Science, Harvard University, Cambridge, MA 02138, USA. E-mail: King@Harvard.edu, URL: https://GaryKing.org
*
Corresponding author Gary King
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Abstract

We offer methods to analyze the “differentially private” Facebook URLs Dataset which, at over 40 trillion cell values, is one of the largest social science research datasets ever constructed. The version of differential privacy used in the URLs dataset has specially calibrated random noise added, which provides mathematical guarantees for the privacy of individual research subjects while still making it possible to learn about aggregate patterns of interest to social scientists. Unfortunately, random noise creates measurement error which induces statistical bias—including attenuation, exaggeration, switched signs, or incorrect uncertainty estimates. We adapt methods developed to correct for naturally occurring measurement error, with special attention to computational efficiency for large datasets. The result is statistically valid linear regression estimates and descriptive statistics that can be interpreted as ordinary analyses of nonconfidential data but with appropriately larger standard errors.

Keywords

privacymeasurement errorlinear regressiondescriptive statistics
Type
Article
Information
Political Analysis , Volume 31 , Issue 1 , January 2023 , pp. 1 - 21
Copyright
© The Author(s) 2022. Published by Cambridge University Press on behalf of the Society for Political Methodology

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Footnotes

Edited by Jeff Gill

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