Max-Information, Differential Privacy, and Post-Selection Hypothesis Testing
Ryan Rogers Department of Applied Mathematics and Computational Science, University of Pennsylvania. Email: Supported in part by a grant from the Sloan foundation and NSF grant CNS-1253345 Aaron Roth Department of Computer and Information Sciences, University of Pennsylvania. Email: Supported in part by a grant from the Sloan foundation, a Google Faculty Research Award, and NSF grants CNS-1513694 and CNS-1253345. Adam Smith Computer Science and Engineering Department, The Pennsylvania State University. Email: Supported in part by a grant from the Sloan foundation, a Google Faculty Research Award, and NSF grant IIS-1447700. Om Thakkar
Abstract
In this paper, we initiate a principled study of how the generalization properties of approximate differential privacy can be used to perform adaptive hypothesis testing, while giving statistically valid $p$ -value corrections. We do this by observing that the guarantees of algorithms with bounded approximate max-information are sufficient to correct the $p$ -values of adaptively chosen hypotheses, and then by proving that algorithms that satisfy $(\epsilon,\delta)$ -differential privacy have bounded approximate max-information when their inputs are drawn from a product distribution.
原文 arXiv:1604.03924;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1604.03924v2