Randomized response, as a basic building-block for differentially private mechanism, has given rise to great interest and found various potential applications in science communities. In this work, we are concerned with three-elements randomized response (RR$_{3}$) along with relevant applications to the analysis of weighted bipartite graph upon differentially private guarantee. We develop a principled framework for estimating statistics produced by RR$_{3}$-based mechanisms, and then prove the corresponding estimations to be unbiased. At the same time, we study in detail several fundamental and significant members in RR$_{3}$ family, and derive the closed-form solutions to unbiased estimations. Next, we show potential applications of several RR$_{3}$-based mechanisms into the estimation of average degree and average weighted value on weighted bipartite graph when requiring local differential privacy guarantee. In the meantime, we determine the lower bounds for choice of relevant parameters by minimizing variance of statistics in order to design optimal RR$_{3}$-based local differential private mechanisms, with which we optimize previous protocols in the literature and put forward a version that achieves the tight bound. Last but most importantly, we observe that in the analysis of relational data such as weighted bipartite graph, a portion of privacy budget in local differential private mechanism is sometimes "consumed" by mechanism itself accidentally, resulting to a more stronger privacy guarantee than we would get by simply sequential compositions.

翻译：在这项工作中,我们关注三个要素随机响应(RR$+3美元),并关注在对加权双部分图表的分析中,在对有差异的私人担保进行加权双部分图表的分析中,我们开发了一个原则性框架,用于估算由RR$+3美元机制产生的统计数据,然后证明相应的估算是公正的。与此同时,我们详细研究了家庭内几个基本和重要成员,并找出了各种潜在的科学界应用。在这项工作中,我们关注三个要素随机响应(RR$+3美元),以及使用三个要素随机响应(RRRR$+3美元),同时,我们关注了在需要本地差异隐私保障时,对加权双部分图表的平均程度和平均加权价值进行的相关应用。与此同时,我们确定选择相关参数的下限,将统计数据差异降至最低,以便设计最优的RR$%3美元基地方差异私人机制,我们据此优化文献中的前项协议,并将封闭版本用于不偏倚的估计。接下来,我们展示了若干基于稳重的双层预算关系,我们有时通过双层机制观察了这种预算关系。