Interactive Fingerprinting Codes and the Hardness of Preventing False Discovery
Thomas Steinke, Jonathan Ullman

TL;DR
This paper establishes a tight computational hardness bound on answering adaptively chosen statistical queries with limited samples, linking the problem to interactive fingerprinting codes and advancing understanding of privacy and query-answering limitations.
Contribution
It introduces a new Fourier-analytic method for analyzing fingerprinting codes and proves a tight hardness bound for answering statistical queries efficiently, connecting privacy, complexity, and coding theory.
Findings
No efficient algorithm can answer more than O(n^2) adaptive queries with n samples under standard assumptions.
A new Fourier-analytic approach simplifies and improves fingerprinting code analysis.
The results imply that answering arbitrary adaptive queries efficiently is as hard as ensuring differential privacy.
Abstract
We show an essentially tight bound on the number of adaptively chosen statistical queries that a computationally efficient algorithm can answer accurately given samples from an unknown distribution. A statistical query asks for the expectation of a predicate over the underlying distribution, and an answer to a statistical query is accurate if it is "close" to the correct expectation over the distribution. This question was recently studied by Dwork et al., who showed how to answer queries efficiently, and also by Hardt and Ullman, who showed that answering queries is hard. We close the gap between the two bounds and show that, under a standard hardness assumption, there is no computationally efficient algorithm that, given samples from an unknown distribution, can give valid answers to adaptively chosen statistical queries. An…
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