Confidence intervals for the population mean of normally distributed data are some of the most standard statistical outputs one might want from a database. In this work we give practical differentially private algorithms for this task. We provide five algorithms and then compare them to each other and to prior work. We give concrete, experimental analysis of their accuracy and find that our algorithms provide much more accurate confidence intervals than prior work. For example, in one setting (with ε = 0.1 and n = 2782) our algorithm yields an interval that is only 1/15th the size of the standard set by prior work.
Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take as our starting point traditional nonparametric tests, which require no distributional assumption (e.g., normality) about the data distribution. We present private analogues of the Kruskal-Wallis, Mann-Whitney, and Wilcoxon signed-rank tests, as well as the parametric one-sample t-test. These tests use novel test statistics developed specifically for the pr…
We propose the approach of model-based differentially private synthesis (modips) in the Bayesian framework for releasing individual-level surrogate/synthetic datasets with privacy guarantees given the original data. The modips technique integrates the concept of differential privacy into model-based data synthesis. We introduce several variants for the general modips approach and different procedures to obtaining privacy-preserving posterior samples, a key step in modips. The uncertainty from the sanitization and synthetic process in modips can be accounted for by releasing multiple synthetic …
In this work, we design differentially private hypothesis tests for the following problems in the general linear model: testing a linear relationship and testing for the presence of mixtures. The majority of our hypothesis tests are based on differentially private versions of the $F$-statistic for the general linear model framework, which are uniformly most powerful unbiased in the non-private setting. We also present other tests for these problems, one of which is based on the differentially private nonparametric tests of Couch, Kazan, Shi, Bray, and Groce (CCS 2019), which is especially suit…
We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially private algorithms to estimate confidence intervals. Crucially, our algorithms guarantee a finite sample coverage, as opposed to an asymptotic coverage. Unlike most previous differentially private algorithms, we do not require the domain of the samples to be bounded. We also prove lower bounds on the expected size of any differentially private confidence set showi…
Randomized response is one of the oldest and most well-known methods for analyzing confidential data. However, its utility for differentially private hypothesis testing is limited because it cannot achieve high privacy levels and low type I error rates simultaneously. In this article, we show how to overcome this issue with the subsample and aggregate technique. The result is a general-purpose method that can be used for both frequentist and Bayesian testing. {{We illustrate the performance of our proposal in three scenarios: goodness-of-fit testing for linear regression models, nonparametric …
Protection of individual privacy is a common concern when releasing and sharing data and information. Differential privacy (DP) formalizes privacy in probabilistic terms without making assumptions about the background knowledge of data intruders, and thus provides a robust concept for privacy protection. Practical applications of DP involve development of differentially private mechanisms to generate sanitized results at a pre-specified privacy budget. For the sanitization of statistics with publicly known bounds such as proportions and correlation coefficients, the bounding constraints will n…
Several algorithms exist for creating differentially private counts from contingency tables, such as two-way or three-way marginal counts. The resulting noisy counts generally do not correspond to a coherent contingency table, so that some post-processing step is needed if one wants the released counts to correspond to a coherent contingency table. We present a latent class modeling approach for post-processing differentially private marginal counts that can be used (i) to create differentially private synthetic data from the set of marginal counts, and (ii) to enable posterior inferences abou…
We propose methods to release and analyze synthetic graphs in order to protect privacy of individual relationships captured by the social network. Proposed techniques aim at fitting and estimating a wide class of exponential random graph models (ERGMs) in a differentially private manner, and thus offer rigorous privacy guarantees. More specifically, we use the randomized response mechanism to release networks under $ε$-edge differential privacy. To maintain utility for statistical inference, treating the original graph as missing, we propose a way to use likelihood based inference and Markov c…
We propose a method for the release of differentially private synthetic datasets. In many contexts, data contain sensitive values which cannot be released in their original form in order to protect individuals' privacy. Synthetic data is a protection method that releases alternative values in place of the original ones, and differential privacy (DP) is a formal guarantee for quantifying the privacy loss. We propose a method that maximizes the distributional similarity of the synthetic data relative to the original data using a measure known as the pMSE, while guaranteeing epsilon-differential …
Survival function estimation is used in many disciplines, but it is most common in medical analytics in the form of the Kaplan-Meier estimator. Sensitive data (patient records) is used in the estimation without any explicit control on the information leakage, which is a significant privacy concern. We propose a first differentially private estimator of the survival function and show that it can be easily extended to provide differentially private confidence intervals and test statistics without spending any extra privacy budget. We further provide extensions for differentially private estimati…
