局部差分隐私协议的简介：使用块设计
An introduction to local differential privacy protocols using block designs
AI总结：
本文介绍了LDP协议与块设计的关系，证明纯LDP协议等同于（r,λ）-设计，并探讨了BIBD基于TPM的最优估计器方法。
摘要：
局部差分隐私（LDP）协议的设计近年来引起了相当大的研究兴趣。LDP协议利用转移概率矩阵（TPM）对实验结果进行随机编码。几位作者观察到，平衡不完全块设计（BIBDs）提供了LDP协议中TPM的良好例子。事实上，已证明基于BIBD的LDP协议提供了最优估计器。在本文主要的概述性论文中，我们给出了LDP协议及其与块设计联系的详细介绍。我们证明了一类称为纯LDP协议的子类等同于（r,λ）-设计（其中包括平衡不完全块设计作为特殊情况）。LDP方案的无偏估计器是转移概率矩阵的左逆。我们显示，基于BIBD的TPM的最优估计器正是由此TPM对应的Moore-Penrose逆得到的。我们还回顾了一些现有工作中纯协议背景下最优LDP协议的相关研究。
英文摘要：
The design of protocols for local differential privacy (or LDP) has been a topic of considerable research interest in recent years. LDP protocols utilise the randomised encoding of outcomes of an experiment using a transition probability matrix (TPM). Several authors have observed that balanced incomplete block designs (BIBDs) provide nice examples of TPMs for LDP protocols. Indeed, it has been shown that such BIBD-based LDP protocols provide optimal estimators. In this primarily expository paper, we give a detailed introduction to LDP protocols and their connections with block designs. We prove that a subclass of LDP protocols known as pure LDP protocols are equivalent to $(r,λ)$-designs (which contain balanced incomplete block designs as a special case). An unbiased estimator for an LDP scheme is a left inverse of the transition probability matrix. We show that the optimal estimators for BIBD-based TPMs are precisely those obtained from the Moore-Penrose inverse of the corresponding TPM. We also review some existing work on optimal LDP protocols in the context of pure protocols.
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