Priv'IT: Private and sample efficient identity testing
Name
cai17a.pdf
Description
Published version
Size
466.33 KB
Format
Adobe PDF
Checksum (MD5)
609265ae1c7232173ff0e243d1a2de3b
Author(s)
Cai, B
Daskalakis, C
Kamath, G
Date Issued
January 1, 2017
Journal
34th International Conference on Machine Learning, ICML 2017
Citation
Cai, B, Daskalakis, C and Kamath, G. 2017. "Priv'IT: Private and sample efficient identity testing." 34th International Conference on Machine Learning, ICML 2017, 2.
Version
Final published version
Abstract
© 2017 by the author(s). We develop differentially private hypothesis testing methods for the small sample regime. Given a sample V from a categorical distribution p over some domain ∑, an explicitly described distribution q over ∑, some privacy parameter e, accuracy parameter ϵ, and requirements βI and βII for the type I and type II errors of our test, the goal is to distinguish between p = q and dTV(p, q) ≥ α. We provide theoretical bounds for the sample size \V\ so that our method both satisfies (e, 0)-differential privacy, and guarantees βi and βu type I and type II errors. We show that differential privacy may come for free in some regimes of parameters, and we always beat the sample complexity resulting from running the χ2-test with noisy counts, or standard approaches such as repetition for endowing non-private χ2-style statistics with differential privacy guarantees. We experimentally compare the sample complexity of our method to that of recently proposed methods for private hypothesis testing (Gaboardi et al., 2016; Kifer & Rogers, 2017).
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://proceedings.mlr.press/v70/cai17a.html
