A Primer on Private Statistics

Statistics and machine learning are now ubiquitous in data analysis. Given a dataset, one immediately wonders what it allows us to infer about the underlying population. However, modern datasets don't exist in a vacuum: they often contain sensitive information about the individuals they represent. Without proper care, statistical procedures will result in gross violations of privacy. Motivated by the shortcomings of ad hoc methods for data anonymization, Dwork, McSherry, Nissim, and Smith introduced the celebrated notion of differential privacy [DMNS06]. From its inception, some of the driving motivations for differential privacy were applications in statistics and the social sciences, notably disclosure limitation for the US Census. And yet, the lion's share of differential privacy research has taken place within the computer science community. As a result, the specific applications being studied are often not formulated using statistical terminology, or even as statistical problems.