Theoretical Foundations of Differentially Private Statistics

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Given the ubiquity of large data sets, statistics and machine learning are used in numerous applications areas to perform inference and prediction. However, many data sets consist of sensitive personal information, and it is vital to make sure that the results of these procedures do not reveal this private information. As an example, suppose we are doing a hypothesis test on genetic data involving individuals who are HIV-positive. Recent results of Homer et al. have shown that, under certain conditions, it is possible to re-identify individuals who participated in such a study. Naturally, giving the socially-stigmatic nature of this condition, this would be a gross violation of individual privacy, thus discouraging individuals from participating in said research study. The goal of this research is to develop methods and tools for private statistics, and for a given task, answer the following central question: how much more data do we need to ensure that our solution to the task does not violate the privacy of the users? I will push forward simultaneously in both theoretical and practical directions. I plan to build on my recent theoretical work on fundamental problems in the area in a number of ways. First, my group and I will develop new algorithms and analysis in order to solve more complex and general tasks. Second, we will study privacy settings that directly match those applied in practice at large-scale deployments, and design time- and data-efficient algorithms for these settings. Finally, we will experiment with and tune theoretical algorithms to make code which is effective on real data. While there has been significant work conducted on privacy and statistics, this work differs primarily in two ways: a focus on understanding properties of the underlying population, rather than a specific data set, and investigating the cost of privacy with finite amounts of data, rather than the "asymptotic" setting where the amount of data tends to infinity. As statistical methods are only becoming more and more common, and privacy concerns are an increasingly common topic of public discourse, the importance of rigorous methods for private statistics is paramount. In particular, due to recent events demonstrating the power of massive amounts of user data (e.g., the Facebook-Cambridge Analytica data scandal), significant amounts of new policy are likely to be written to prevent such events from reoccurring. In turn, this will necessitate new highly qualified personnel trained in data privacy at virtually every company which deals with user data -- roles which my students will be prepared to fill.