论文标题
用于重建三角形线性动态网络的算法，并验证正确性
An algorithm for reconstruction of triangle-free linear dynamic networks with verification of correctness
论文作者
论文摘要
从观察数据重建动态系统网络是一个活跃的研究领域。许多方法保证在相对强烈的假设中，即网络动力学受严格的因果转移函数的控制。但是，在许多实际情况下，严格的因果模型不足以描述系统，并且有必要考虑具有包括直接进料术语的动力学模型。在直接进食的情况下，保证一致的重建是一项更具挑战性的任务。确实，在网络上没有其他假设下，我们证明，即使在无限数据的限制下，任何重建方法都容易被推断出在真实网络（误报）中不存在的边缘（误报）或未检测到网络中存在的边缘（false负面）。但是，对于本文介绍的一类无三角网络，可以提供一些一致性保证。我们提出了一种方法，该方法要么准确地恢复了无三角网络的拓扑，该网络证明其正确性，要么输出比实际网络拓扑更稀疏的图，并指定该图没有错误的阳性，但是有错误的负面因素。
Reconstructing a network of dynamic systems from observational data is an active area of research. Many approaches guarantee a consistent reconstruction under the relatively strong assumption that the network dynamics is governed by strictly causal transfer functions. However, in many practical scenarios, strictly causal models are not adequate to describe the system and it is necessary to consider models with dynamics that include direct feedthrough terms. In presence of direct feedthroughs, guaranteeing a consistent reconstruction is a more challenging task. Indeed, under no additional assumptions on the network, we prove that, even in the limit of infinite data, any reconstruction method is susceptible to inferring edges that do not exist in the true network (false positives) or not detecting edges that are present in the network (false negative). However, for a class of triangle-free networks introduced in this article, some consistency guarantees can be provided. We present a method that either exactly recovers the topology of a triangle-free network certifying its correctness or outputs a graph that is sparser than the topology of the actual network, specifying that such a graph has no false positives, but there are false negatives.
