Differentially private ordinary least squares

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

17 Scopus citations


Linear regression is one of the most prevalent techniques in machine learning; however, it is also common to use linear regression for its explanatory capabilities rather than label prediction. Ordinary Least Squares (OLS) is often used in statistics to establish a correlation between an attribute (e.g. Gender) and a label (e.g. Income) in the presence of other (potentially correlated) features. OLS assumes a particular model that randomly generates the data, and derives t-values-representing the likelihood of each real value to be the true correlation. Using i-values, OLS can release a confidence interval, which is an interval on the reals that is likely to contain the true correlation; and when this interval does not intersect the origin, we can reject the null hypothesis as it is likely that the true correlation is non-zero. Our work aims at achieving similar guarantees on data under differentially private estimators. First, we show that for well-spread data, the Gaussian Johnson-Lindenstrauss Transform (JLT) gives a very good approximation of t-values; secondly, when JLT approximates Ridge regression (linear regression with/2-rcgularization) wc derive, under certain conditions, confidence intervals using the projected data; lastly, we derive, under different conditions, confidence intervals for the "Analyze Gauss" algorithm (Dwork et al., 2014).

Original languageEnglish
Title of host publication34th International Conference on Machine Learning, ICML 2017
PublisherInternational Machine Learning Society (IMLS)
Number of pages28
ISBN (Electronic)9781510855144
StatePublished - 2017
Externally publishedYes
Event34th International Conference on Machine Learning, ICML 2017 - Sydney, Australia
Duration: 6 Aug 201711 Aug 2017

Publication series

Name34th International Conference on Machine Learning, ICML 2017


Conference34th International Conference on Machine Learning, ICML 2017

Bibliographical note

Publisher Copyright:
Copyright © 2017 by the authors.


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