Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing
Marco Gaboardi This work has been partially supported by the “PrivInfer - Programming Languages for Differential Privacy: Conditioning and Inference” EPSRC project EP/M022358/1 and by the University of Dundee, UK. University at Buffalo, SUNY Hyun woo Lim University of California, Los Angeles Ryan Rogers University of Pennsylvania Salil P. Vadhan Also supported by a Simons Investigator grant. Work done in part while visiting the Department of Applied Mathematics and the Shing-Tung Yau Center at National Chiao-Tung University in Taiwan. Harvard University
Abstract
Hypothesis testing is a useful statistical tool in determining whether a given model should be rejected based on a sample from the population. Sample data may contain sensitive information about individuals, such as medical information. Thus it is important to design statistical tests that guarantee the privacy of subjects in the data. In this work, we study hypothesis testing subject to differential privacy, specifically chi-squared tests for goodness of fit for multinomial data and independence between two categorical variables.
中文速览
保护个人隐私与做统计检验之间存在天然矛盾——直接把加了噪声的数据套进经典卡方检验，显著性水平会严重失控。针对这一问题，论文聚焦于分类数据上的两类经典检验：多项分布的拟合优度检验（goodness of fit test）和两个分类变量的独立性检验（independence test），在差分隐私（differential privacy）框架下分别提出了基于蒙特卡洛模拟和基于渐近分布的四种新检验方法，核心思路是在判断显著性时把为保护隐私而注入的 Laplace 或 Gaussian 噪声的分布一并纳入考量，而非忽略它。实验结果表明，新方法能稳定地将第一类错误（误拒真实假设）控制在目标水平 α 以内，而只需适度增加样本量就能恢复与经典非隐私检验相当的统计功效（statistical power）。这项工作为社会科学、医学等涉及敏感数据的研究场景提供了一套既严格保护隐私、又能得出可靠统计结论的实用工具。
原文 arXiv:1602.03090;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1602.03090v2