标题： 图结构连续李雅普诺夫模型的可辨识性 显示英文标题

标题： Structural Identifiability of Graphical Continuous Lyapunov Models

摘要： 我们证明了无循环图的连续Lyapunov模型（GCLMs）模型等价性的两个特征。 第一个结果表明，两个图是模型等价的当且仅当它们具有相同的骨架和等价的诱导4节点子图。 我们还通过结构化边反转给出了一个转换性特征。 这两个定理分别是Verma和Pearl以及Chickering对贝叶斯网络的著名结果的Lyapunov类比。 我们的结果对GCLMs因果推断理论有广泛的影响。 首先，我们发现无循环GCLMs的模型等价类细化了相应贝叶斯网络的类。 此外，我们获得了测试给定有向无环图的模型等价性和结构可识别性的多项式时间算法。 显示英文摘要

摘要： We prove two characterizations of model equivalence of acyclic graphical continuous Lyapunov models (GCLMs) with uncorrelated noise. The first result shows that two graphs are model equivalent if and only if they have the same skeleton and equivalent induced 4-node subgraphs. We also give a transformational characterization via structured edge reversals. The two theorems are Lyapunov analogues of celebrated results for Bayesian networks by Verma and Pearl, and Chickering, respectively. Our results have broad consequences for the theory of causal inference of GCLMs. First, we find that model equivalence classes of acyclic GCLMs refine the corresponding classes of Bayesian networks. Furthermore, we obtain polynomial-time algorithms to test model equivalence and structural identifiability of given directed acyclic graphs.