Differential Analysis for Networks Obeying Conservation Laws
Differential Analysis for Networks Obeying Conservation Laws
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DOI：
10.1109/icassp49357.2023.10094876
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发表时间：
2023-01
期刊：
影响因子：
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通讯作者：
Anirudh Rayas;Rajasekhar Anguluri;Jiajun Cheng;Gautam Dasarathy
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文献类型：
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作者：
Anirudh Rayas;Rajasekhar Anguluri;Jiajun Cheng;Gautam Dasarathy
网络系统发生在不同的领域，如电子网络，大脑和意见网络，都知道遵守守恒定律。例如，电力网络服从基尔霍夫定律，而社交网络服从意见一致。守恒定律通常被建模为平衡方程，该平衡方程将网络节点处的适当注入流和势相关联。最近的工作考虑的问题，估计未知的结构，这样的网络系统的节点电位的观察（只有知识的统计注入流）。考虑到系统的动态特性，一个同样重要的任务是从数据中估计网络结构的变化-所谓的微分网络分析问题。也就是说，给定两组节点电位观测值，目标是估计底层网络之间的结构差异。我们制定了这个新的微分网络分析问题的系统遵守守恒律，并设计了一个凸估计学习的边缘变化直接从节点电位。我们推导出的条件下，估计是唯一的高维制度，并设计了一个有效的ADMM为基础的方法来进行估计。最后，我们证明了我们的方法的性能合成和基准电力网络数据。
Networked systems that occur in various domains, such as electric networks, the brain, and opinion networks, are known to obey conservation laws. For instance, electric networks obey Kirchoff’s laws, and social networks obey opinion consensus. Conservation laws are often modeled as balance equations that relate appropriate injected flows and potentials at the nodes of the networks. A recent line of work considers the problem of estimating the unknown structure of such networked systems from observations of node potentials (and only the knowledge of the statistics of injected flows). Given the dynamic nature of the systems under consideration, an equally important task is estimating the change in the structure of the network from data – the so called differential network analysis problem. That is, given two sets of node potential observations, the goal is to estimate the structural differences between the underlying networks. We formulate this novel differential network analysis problem for systems obeying conservation laws and devise a convex estimator to learn the edge changes directly from node potentials. We derive conditions under which the estimate is unique in the highdimensional regime and devise an efficient ADMM-based approach to perform the estimation. Finally, we demonstrate the performance of our approach on synthetic and benchmark power network data.