The goal of this paper is to develop a practical and general-purpose approach to construct confidence intervals for differentially private parametric estimation. We find that the parametric bootstrap is a simple and effective solution. It cleanly reasons about variability of both the data sample and the randomized privacy mechanism and applies "out of the box" to a wide class of private estimation routines. It can also help correct bias caused by clipping data to limit sensitivity. We prove that the parametric bootstrap gives consistent confidence intervals in two broadly relevant settings, including a novel adaptation to linear regression that avoids accessing the covariate data multiple times. We demonstrate its effectiveness for a variety of estimators, and find that it provides confidence intervals with good coverage even at modest sample sizes and performs better than alternative approaches.
翻译:本文的目的是制定实用的通用方法,为不同的私人参数估计建立信任间隔。我们发现,参数靴子是一个简单有效的解决方案。数据抽样和随机隐私机制的变异性都有清楚的理由,并且将“从盒子外”应用到广泛的私人估计例行程序。它也有助于纠正剪切数据造成的偏差,以限制敏感度。我们证明,参数靴子在两个广泛相关的环境中提供了一致的信任间隔,包括对线性回归进行新的调整,避免多次访问共变数据。我们向各种估计者展示了它的有效性,发现它提供了良好的信任间隔,即使抽样规模较小,而且比替代方法效果更好。