Local differential privacy (LDP) is a differential privacy (DP) paradigm in which individuals first apply a DP mechanism to their data (often by adding noise) before transmitting the result to a curator. In this article, we develop methodologies to infer causal effects from locally privatized data under the Rubin Causal Model framework. First, we present frequentist estimators under various privacy scenarios with their variance estimators and plug-in confidence intervals. We show that using a plug-in estimator results in inferior mean-squared error (MSE) compared to minimax lower bounds. In contrast, we show that using a customized privacy mechanism, we can match the lower bound, giving minimax optimal inference. We also develop a Bayesian nonparametric methodology along with a blocked Gibbs sampling algorithm, which can be applied to any of our proposed privacy mechanisms, and which performs especially well in terms of MSE for tight privacy budgets. Finally, we present simulation studies to evaluate the performance of our proposed frequentist and Bayesian methodologies for various privacy budgets, resulting in useful suggestions for performing causal inference for privatized data.

翻译：本地差分隐私（LDP）是一种差分隐私（DP）范式，其中个体在将数据发送到数据管理员之前，先对自身数据应用差分隐私机制（通常通过添加噪声）。本文在鲁宾因果模型框架下，发展了从本地隐私化数据中推断因果效应的方法。首先，我们提出了不同隐私场景下的频率派估计量，并给出了其方差估计量和插入式置信区间。研究表明，与极小化极大下界相比，使用插入式估计量会导致较差的均方误差（MSE）。相反，我们证明通过定制化的隐私机制可以匹配该下界，从而实现极小化极大最优推断。我们还开发了一种贝叶斯非参数方法以及相应的分块吉布斯采样算法，该方法可适用于我们提出的任何隐私机制，并在严格隐私预算下表现出优异的均方误差性能。最后，我们通过仿真研究评估了所提出的频率派和贝叶斯方法在不同隐私预算下的表现，为隐私数据的因果推断提供了实用建议。