Private Synthetic Data for Multitask Learning and Marginal Queries
Authors: Giuseppe Vietri, Cedric Archambeau, Sergul Aydore, William Brown, Michael Kearns, Aaron Roth, Ankit Siva, Shuai Tang, Steven Z. Wu

We provide a differentially private algorithm for producing  synthetic data simultaneously useful for multiple tasks: marginal queries and multitask machine learning (ML). A key innovation in our algorithm is the ability to directly handle numerical features, in contrast to a number of related prior approaches which require numerical features to be first converted into {high cardinality} categorical features via {a binning strategy}. Higher binning granularity is required for better accuracy, but this negatively impacts scalability. Eliminating the need for binning allows us to produce synthetic data preserving large numbers of statistical queries such as marginals on numerical features, and class conditional linear threshold queries. Preserving the latter means that the fraction of points of each class label above a particular half-space is roughly the same in both the real and synthetic data. This is the property that is needed to train a linear classifier in a multitask setting. Our algorithm also allows us to produce high quality synthetic data for mixed marginal queries, that combine both categorical  and numerical features. Our method consistently runs 2-5x faster than the best comparable techniques, and provides significant accuracy improvements in both marginal queries and linear prediction tasks for mixed-type datasets.