Colloquium - Jordan Awan
Institution: Purdue University
Title: Canonical Noise Distributions and Private Hypothesis Tests
Date: November 16, 2021
Location: Zoom (Click here for meeting details)
Time: 10:20 AM - 11:10 AM Eastern Time
\(f\)-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 canonical noise distribution (CND) which captures whether an additive privacy mechanism is appropriately tailored for a given \(f\), and give a construction that produces a CND given an arbitrary tradeoff function \(f\). 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.
We apply our techniques to the problem of difference of proportions testing, and construct a UMP unbiased “semi-private” test which upper bounds the performance of any 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 \((Є,0)\)-DP, we show empirically that our proposed test is more powerful than any \((Є/\sqrt 2)\)-DP test and has more accurate type I errors than the classic normal approximation test.
MSU statistician attains uncommon Institute of Mathematical Statistics "Annals quadfecta" status
PhD student Nilanjan Chakraborty was recently presented with the William L. Harkness Award for outstanding teaching by a graduate student.
Mr. Andrew McDonald, an Honors College junior majoring in Computer Science in the College of Engineering; and Statistics, and Advanced Mathematics in the College of Natural Science, has been named a recipient of the nationally competitive Barry M. Goldwater Scholarship.