Private Data Release via Learning Thresholds

TL;DR

This paper introduces efficient algorithms for differentially private data release by reducing the problem to learning thresholded sums of predicates, enabling accurate release of complex query types with polynomial runtime.

Contribution

It presents a novel reduction from private data release to learning thresholded sums, leading to new algorithms for releasing conjunctions and parity queries efficiently.

Findings

Achieves polynomial-time algorithms for releasing k-way conjunctions.

Provides differentially private algorithms for releasing most parity queries.

Ensures bounded error with database sizes polynomial in data dimension.

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 a variety of algorithms for learning thresholds. These instantiations yield several 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: (*) Releasing all k-way conjunctions. For any given k, the resulting data release algorithm has bounded error as long as the database is of size at least d^{O(\sqrt{k\log(k\log d)})}. The running time is polynomial in the database size. (*) Releasing a (1-\gamma)-fraction of all parity queries. For any \gamma \geq \poly(1/d), the algorithm has bounded error as long as the database is of size at least \poly(d). The running time is polynomial in the database size. Several other instantiations yield further results for privacy-preserving data release. Of the two results highlighted above, 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 Jackson's Harmonic Sieve algorithm [Jackson 1997].