Recovery of the causal structure of dynamic networks from noisy measurements has long been a problem of intense interest across many areas of science and engineering. Many algorithms have been proposed, but there is little work that compares the performance of the algorithms to converse bounds. As a step to address this problem, this paper gives lower bounds on the error probability for causal network support recovery in a linear Gaussian setting. The bounds are based on the use of the Bhattacharyya coefficient for binary hypothesis testing problems with mixture probability distributions. Comparison of the bounds and the performance achieved by two representative recovery algorithms are given for sparse random networks based on the Erd\H{o}s-R\'enyi model.
翻译:从噪音测量中恢复动态网络的因果结构长期以来一直是许多科学和工程领域引起极大兴趣的一个问题。许多算法已经提出,但很少将算法的性能与反向界限进行比较。作为解决这一问题的一个步骤,本文对因果网络在线性高斯环境下支持恢复的误差概率给出了较低的限制。界限以Bhattacharyya系数用于混合概率分布的二进制假设测试问题为基础。对基于Erd\H{o}s-R\'enyi模型的稀散随机网络的界限和两个具有代表性的恢复算法的性能进行了比较。