Differentially Private Uniformly Most Powerful Tests for Binomial Data
Authors: Jordan Awan, Aleksandra Slavković
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our simulation results demonstrate that our tests have exact type I error, and are more powerful than current techniques. In Section 8, we verify through simulations that our UMP tests have exact type I error, and are more powerful than current techniques. In this section, we study both the empirical power and the empirical type I error of our DP-UMP test against the normal approximation proposed by VS09. In Figure 1, we plot the empirical power of our UMP test, the Normal Approximation from VS09, and the non-private UMP. In Figure 2 we plot the empirical type I error of the DP-UMP and the Normal Approximation tests. |
| Researcher Affiliation | Academia | Jordan Awan Department of Statistics Penn State University University Park, PA 16802 awan@psu.edu Aleksandra Slavkovi c Department of Statistics Penn State University University Park, PA 16802 sesa@psu.edu |
| Pseudocode | Yes | Algorithm 1 UMP one-sided p-value for binomial data under (ϵ, δ)-DP... Algorithm 2 Sample from Tulap distribution: N Tulap(m, b, q) |
| Open Source Code | No | The paper does not provide a statement or link indicating that the source code for the described methodology is publicly available. |
| Open Datasets | No | The paper describes simulations generating data from Binomial distributions (e.g., 'Binom(n, .95)', 'Binom(30, θ0)') and discusses sign/median tests using iid pairs, but it does not specify or provide access to any pre-existing, publicly available or open dataset. |
| Dataset Splits | No | The paper describes simulation setups but does not provide specific training, validation, or test dataset splits in terms of percentages, sample counts, or references to predefined splits, as it primarily uses simulated data rather than a fixed dataset split. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., CPU, GPU models, memory) used for running the simulations or experiments. |
| Software Dependencies | No | The paper does not list any specific software dependencies with version numbers (e.g., Python, PyTorch, TensorFlow, specific libraries or solvers). |
| Experiment Setup | Yes | For each n, we generate 10,000 samples from Binom(n, .95). We privatize each X by adding N Tulap(0, e ϵ, 0) for the DP-UMP and L Lap(1/ϵ) for the Normal Approximation. We compute the UMP p-value via Algorithm 1 and the approximate p-value for X+L, using the cdf of N X, n/4 + 2/ϵ2 . The empirical power is given by (10000) 1#{p-value< .05}. ... We fix ϵ = 1 and δ = 0, and vary θ0. For each θ0, we generate 100,000 samples from Binom(30, θ0). For each sample, we compute the DP-UMP and Normal Approximation tests at type I error α = .05. |