Private data release via learning thresholds

TL;DR: In this paper, Nissim et al. considered the problem of differentially private data release for a set of statistical queries on the data, and obtained algorithms whose running time is polynomial, or at least subexponential, in the data dimensionality.

Abstract: This work considers computationally efficient privacy-preserving data release. We study the task of analyzing a database containing sensitive information about individual participants. Given a set of statistical queries on the data, we want to release approximate answers to the queries while also guaranteeing differential privacy---protecting each participant's sensitive data.Our focus is on computationally efficient data release algorithms; we seek algorithms whose running time is polynomial, or at least sub-exponential, in the data dimensionality. Our primary contribution is a computationally efficient reduction from differentially private data release for a class of counting queries, to learning thresholded sums of predicates from a related class.We instantiate this general reduction with algorithms for learning thresholds, obtaining new results for differentially private data release. As two examples, taking {0, 1}d to be the data domain (of dimension d), we obtain differentially private algorithms for:1. Releasing all k-way conjunction counting queries (or k-way contingency tables). For any given k, the resulting data release algorithm has bounded error as long as the database is of size at least dO [EQUATION] (ignoring the dependence on other parameters). The running time is polynomial in the database size. The best sub-exponential time algorithms known prior to our work required a database of size O (dk/2) [Dwork McSherry Nissim and Smith 2006].2. Releasing any family of counting queries that is specified by a constant depth AC0 predicate. This algorithm releases accurate answers to a (1 − γ)-fraction of the queries in the family. For any γ ≥ quasipoly(1/d), the algorithm has bounded error as long as the database is of size at least quasipoly(d) (again ignoring the dependence on other parameters). The running time is quasipoly(d).The first learning algorithm uses techniques for representing thresholded sums of predicates as low-degree polynomial threshold functions. The second learning algorithm is based on a result of Jackson Klivans and Servedio [JKS 2002], and utilizes Fourier analysis of the database viewed as a function mapping queries to answers.