Revisiting Differentially Private Hypothesis Tests for Categorical Data
Yue Wang Jaewoo Lee Daniel Kifer Department of Computer Science and Engineering, Penn State University, USA
Abstract
In this paper, we consider methods for performing hypothesis tests on data protected by a statistical disclosure control technology known as differential privacy. Previous approaches to differentially private hypothesis testing either perturbed the test statistic with random noise having large variance (and resulted in a significant loss of power) or added smaller amounts of noise directly to the data but failed to adjust the test in response to the added noise (resulting in biased, unreliable $p$ -values). In this paper, we develop a variety of practical hypothesis tests that address these problems. Using a different asymptotic regime that is more suited to hypothesis testing with privacy, we show a modified equivalence between chi-squared tests and likelihood ratio tests. We then develop differentially private likelihood ratio and chi-squared tests for a variety of applications on tabular data (i.e., independence, sample proportions, and goodness-of-fit tests). Experimental evaluations on small and large datasets using a wide variety of privacy settings demonstrate the practicality and reliability of our methods.
中文速览
对表格数据做假设检验时，如果数据同时要受差分隐私（differential privacy）保护，现有方法要么往检验统计量上加大量噪声导致检验效力极低，要么直接在加噪数据上跑现成软件却忘了校正，结果 p 值严重偏差、结论不可靠。本文的思路是先用拉普拉斯机制（Laplace mechanism）对原始列联表的单元格计数加噪，再重新推导加噪后似然比检验（likelihood ratio test）和卡方检验（chi-squared test）在新渐近框架下的极限分布，用这个经过校正的分布来计算 p 值，从而同时满足隐私保护和统计可靠性两个目标。作者为独立性检验、样本比例检验和拟合优度检验分别给出了具体的私有化检验程序，并在真实大小数据集上做了大量实验，验证新方法的 p 值在各种隐私参数设置下都显著比此前方法更准确、更稳健。这项工作填补了差分隐私与假设检验之间长期存在的方法论空白，为在不泄露个人信息的前提下对敏感数据做可靠统计推断提供了切实可用的工具。
原文 arXiv:1511.03376;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1511.03376v4