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.

传统上，贝叶斯网络的敏感性分析研究了以逐个修改其条件概率表的方式对其影响，我们提出进行全局基于方差的敏感性分析，使用低秩张量分解来降低维度，并通过 Sobol 法得出全局敏感性指标，从而展示不确定参数及其交互作用的真实影响。

贝叶斯网络中不确定参数的全局敏感性分析

Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks

This paper explores the application of active learning strategies to
adaptively learn Sobol indices for global sensitivity analysis. We demonstrate
that active learning for Sobol indices poses unique challenges due to the
definition of the Sobol index as a ratio of variances estimated from Gaussian
process surrogates. Consequently, learning strategies must either focus on
convergence in the numerator or the denominator of this ratio. However, rapid
convergence in either one does not guarantee convergence in the Sobol index. We
propose a novel strategy for active learning that focuses on resolving the main
effects of the Gaussian process (associated with the numerator of the Sobol
index) and compare this with existing strategies based on convergence in the
total variance (the denominator of the Sobol index). The new strategy,
implemented through a new learning function termed the MUSIC (minimize
uncertainty in Sobol index convergence), generally converges in Sobol index
error more rapidly than the existing strategies based on the Expected
Improvement for Global Fit (EIGF) and the Variance Improvement for Global Fit
(VIGF). Both strategies are compared with simple sequential random sampling and
the MUSIC learning function generally converges most rapidly for
low-dimensional problems. However, for high-dimensional problems, the
performance is comparable to random sampling. The new learning strategy is
demonstrated for a practical case of adaptive experimental design for
large-scale Boundary Layer Wind Tunnel experiments.

该论文探讨了将主动学习策略应用于自适应学习 Sobol 指数的全局敏感性分析，提出了一种基于主要效应解决高斯过程的学习策略，并比较了基于总方差的现有策略。实验证明，该策略在小维问题上收敛速度最快，但在大维问题上，性能与随机抽样相当。论文还以大规模边界层风洞实验的自适应实验设计为实例进行了演示。