我们研究Gupta等人[SODA 2010]提出的所谓超集输出场景下的差分隐私（differentially private, DP）设施选址问题。目前已知的ε-DP算法最优期望近似比为$O\left(\frac{\log n}{\sqrtε}\right)$，由Cohen-Addad等人[AISTATS 2022]提出，其中$n$表示度量空间的规模；而已知的最优下界为$Ω(1/\sqrtε)$[NeurIPS 2019]。在这篇短注中，我们给出任意ε-DP算法的期望近似比下界为$\tildeΩ\left(\min\left\{\log n, \sqrt{\frac{\log n}ε}\right\}\right)$，这是近似比必须随度量空间规模增长的首个证据。
英文摘要：
We consider the differentially private (DP) facility location problem in the so called super-set output setting proposed by Gupta et al. [SODA 2010]. The current best known expected approximation ratio for an $ε$-DP algorithm is $O\left(\frac{\log n}{\sqrtε}\right)$ due to Cohen-Addad et al. [AISTATS 2022] where $n$ denote the size of the metric space, meanwhile the best known lower bound is $Ω(1/\sqrtε)$ [NeurIPS 2019].
In this short note, we give a lower bound of $\tildeΩ\left(\min\left\{\log n, \sqrt{\frac{\log n}ε}\right\}\right)$ on the expected approximation ratio of any $ε$-DP algorithm, which is the first evidence that the approximation ratio has to grow with the size of the metric space.
A Simple Differentially Private Algorithm for Global Minimum Cut
在这篇文章中，我们提出了一个简单的差分私有算法的全球最小割问题，只使用一个调用的指数机制。这个问题首先由Gupta等人研究。[2010]，他们给出了一个具有接近最优效用保证的差分私有算法。我们在许多方面改进了他们的工作：我们的算法比Gupta et al. [2010]中给出的算法更简单，更自然，更有效，而且提供了更好的隐私和实用性保证。
Differentially Private Algorithms for Clustering with Stability Assumptions
Ben-Gurion University of the Negev（内盖夫本-古里安大学）
本文研究了在输入稳定性假设下的差分私有聚类问题。尽管关于差分隐私的研究越来越多，特别是关于差异隐私聚类的研究，但只有三项研究（Nissim et al. 2007，Wang et al. 2015，Huang et al. 2018）研究了私下聚类“好”k均值实例的问题，这三个都依赖于样本，聚合框架和所有三个测量实用程序在真正的集群中心和返回的中心之间的Wasserstein距离私有算法在这项工作中，我们改进了这一系列的多轴工作。我们提出了一个简单得多的算法聚类稳定的输入（不依赖于样本和聚合框架），并分析其效用的Wasserstein距离和k-means成本。此外，我们的算法有直接的类似物“好”的k-中位数的实例和本地模型的差分隐私。
Synthetic control is a causal inference tool used to estimate the treatment effects of an intervention by creating synthetic counterfactual data. This approach combines measurements from other similar observations (i.e., donor pool ) to predict a counterfactual time series of interest (i.e., target unit) by analyzing the relationship between the target and the donor pool before the intervention. As synthetic control tools are increasingly applied to sensitive or proprietary data, formal privacy protections are often required. In this work, we provide the first algorithms for differentially pri…
