标题： 贝叶斯网络中不确定参数的全局敏感性分析 显示英文标题

标题： Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks

摘要： 传统上，贝叶斯网络的敏感性分析研究以一次一个（OAT）的方式单独修改其条件概率表中的条目所产生的影响。 然而，这种方法无法全面说明每个输入的相关性，因为两个或更多参数的同时扰动通常会引发OAT分析无法捕捉的高阶效应。 我们建议进行全局方差基础的敏感性分析，其中$n$个参数同时被视为不确定，并对其重要性进行联合评估。 我们的方法通过将不确定性编码为$n$个网络的额外变量来实现。 为了在增加这些维度时防止维度灾难，我们使用低秩张量分解将新的势能分解为较小的因子。 最后，我们将Sobol方法应用于所得网络以获得$n$个全局敏感性指数。 使用由专家提取和学习得到的贝叶斯网络组成的基准数组，我们证明Sobol指数与OAT指数可能显著不同，从而揭示了不确定参数及其相互作用的真实影响。 显示英文摘要

摘要： Traditionally, the sensitivity analysis of a Bayesian network studies the impact of individually modifying the entries of its conditional probability tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a comprehensive account of each inputs' relevance, since simultaneous perturbations in two or more parameters often entail higher-order effects that cannot be captured by an OAT analysis. We propose to conduct global variance-based sensitivity analysis instead, whereby $n$ parameters are viewed as uncertain at once and their importance is assessed jointly. Our method works by encoding the uncertainties as $n$ additional variables of the network. To prevent the curse of dimensionality while adding these dimensions, we use low-rank tensor decomposition to break down the new potentials into smaller factors. Last, we apply the method of Sobol to the resulting network to obtain $n$ global sensitivity indices. Using a benchmark array of both expert-elicited and learned Bayesian networks, we demonstrate that the Sobol indices can significantly differ from the OAT indices, thus revealing the true influence of uncertain parameters and their interactions.