Wang Yulin, Luo Yu, Wu Hulin, Miao Hongyu
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China.
School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, China.
Stat Interface. 2019;12(3):365-375. doi: 10.4310/18-SII550.
Network systems are commonly encountered and investigated in various disciplines, and network dynamics that refer to collective node state changes over time are one area of particular interests of many researchers. Recently, dynamic structural equation model (DSEM) has been introduced into the field of network dynamics as a powerful statistical inference tool. In this study, in recognition that parameter identifiability is the prerequisite of reliable parameter inference, a general and efficient approach is proposed for the first time to address the structural parameter identifiability problem of linear DSEMs for cyclic networks. The key idea is to transform a DSEM to an equivalent frequency domain representation, then Masons gain is employed to deal with feedback loops in cyclic networks when generating identifiability equations. The identifiability result of every unknown parameter is obtained with the identifiability matrix method. The proposed approach is computationally efficient because no symbolic or expensive numerical computations are involved, and can be applicable to a broad range of linear DSEMs. Finally, selected benchmark examples of brain networks, social networks and molecular interaction networks are given to illustrate the potential application of the proposed method, and we compare the results from DSEMs, state-transition models and ordinary differential equation models.
网络系统在各个学科中普遍存在且受到研究，而网络动力学（指节点集体状态随时间的变化）是许多研究人员特别感兴趣的领域之一。最近，动态结构方程模型（DSEM）作为一种强大的统计推断工具被引入到网络动力学领域。在本研究中，认识到参数可识别性是可靠参数推断的前提，首次提出了一种通用且高效的方法来解决循环网络线性DSEM的结构参数可识别性问题。关键思想是将DSEM转换为等效的频域表示，然后在生成可识别性方程时使用梅森增益来处理循环网络中的反馈回路。通过可识别性矩阵方法获得每个未知参数的可识别性结果。所提出的方法计算效率高，因为不涉及符号或昂贵的数值计算，并且可应用于广泛的线性DSEM。最后，给出了脑网络、社交网络和分子相互作用网络的选定基准示例，以说明所提出方法的潜在应用，并比较了DSEM、状态转移模型和常微分方程模型的结果。
