Differentially Private Significance Tests for Regression Coefficients

• Published in: Journal of computational and graphical statistics Vol. 28; no. 2; pp. 440 - 453
• Main Authors: Barrientos, Andrés F., Reiter, Jerome P., Machanavajjhala, Ashwin, Chen, Yan
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 03.04.2019; American Statistical Association, the Institute of Mathematical Statistics, and the Interface Foundation of North America; Taylor & Francis Ltd
• Subjects: Algorithms; Confidentiality; Disclosure; Laplace; Privacy; Query; Regression analysis; Regression coefficients; Statistical analysis; Statistical models; Statistical significance; Synthetic; Verification
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1080/10618600.2018.1538881

Many data producers seek to provide users access to confidential data without unduly compromising data subjects' privacy and confidentiality. One general strategy is to require users to do analyses without seeing the confidential data; for example, analysts only get access to synthetic data or query systems that provide disclosure-protected outputs of statistical models. With synthetic data or redacted outputs, the analyst never really knows how much to trust the resulting findings. In particular, if the user did the same analysis on the confidential data, would regression coefficients of interest be statistically significant or not? We present algorithms for assessing this question that satisfy differential privacy. We describe conditions under which the algorithms should give accurate answers about statistical significance. We illustrate the properties of the proposed methods using artificial and genuine data. Supplementary materials for this article are available online.