Differentially Private Inference for Binomial Data

on YouTube ↗38m

" summary

Derives the first differentially private uniformly most powerful tests for Bernoulli/binomial data under (ε,Δ)-DP and introduces the two-lap distribution (a truncated uniform-plus-geometric/staircase noise). Tests equal the CDF of that noise applied to X, so releasing Z = X + TwoLap yields private p‑values and confidence intervals; simulations (n=30) show higher power than prior normal-approx methods and exact Type I error. Also gives a UMP unbiased construction for two‑sided testing and an asymptotic simplification with K ≈ nθ0.

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" chapters (9)

1. 0:00Start
2. 0:20Literature on Hypothesis Testing under DP
3. 2:01Overview
4. 2:36Differential Privacy
5. 3:31Hypothesis Testing Background
6. 6:21Preliminary Setup
7. 12:42Proposed Tulap Distribution
8. 17:09Two Sided Tests
9. 22:20Two Side Simulations

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