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f-DP has recently been proposed as a generalization of differential privacy allowing a lossless analysis of composition, post-processing, and privacy amplification via subsampling. In the setting of f-DP, we propose the concept of a canonical noise distribution (CND), the first mechanism designed for an arbitrary f-DP guarantee. The notion of CND captures whether an additive privacy mechanism perfectly matches the privacy guarantee of a given f. We prove that a CND always exists, and give a construction that produces a CND for any f. We show that private hypothesis tests are intimately related to CNDs, allowing for the release of private p-values at no additional privacy cost as well as the construction of uniformly most powerful (UMP) tests for binary data, within the general f-DP framework. We apply our techniques to the problem of difference of proportions testing, and construct a UMP unbiased (UMPU) "semi-private" test which upper bounds the performance of any f-DP test. Using this as a benchmark we propose a private test, based on the inversion of characteristic functions, which allows for optimal inference for the two population parameters and is nearly as powerful as the semi-private UMPU. When specialized to the case of (ϵ,0)-DP, we show empirically that our proposed test is more powerful than any (ϵ/sqrt(2))-DP test and has more accurate type I errors than the classic normal approximation test.
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The Test of Tests: A Framework for Differentially Private Hypothesis Testing
We present a generic framework for creating differentially private versions of any hypothesis test in a black-box way. We analyze the resulting tests analytically and experimentally. Most crucially, we show good practical performance for small data sets, showing that at ϵ = 1 we only need 5-6 times as much data as in the fully public setting. We compare our work to the one existing framework of this type, as well as to several individually-designed private hypothesis tests. Our framework is higher power than other generic solutions and at least competitive with (and often better than) individually-designed tests.
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- Award ID(s):
- 1817245
- PAR ID:
- 10483524
- Publisher / Repository:
- Proceedings of Machine Learning Research
- Date Published:
- Journal Name:
- Proceedings of the 40th International Conference on Machine Learning
- Volume:
- 202
- Page Range / eLocation ID:
- 16131-16151
- Format(s):
- Medium: X
- Location:
- Honolulu, Hawaii
- Sponsoring Org:
- National Science Foundation
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