Joint Inference of Multiple Graphs with Hidden Variables from Stationary Graph Signals
Joint Inference of Multiple Graphs with Hidden Variables from Stationary Graph Signals
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DOI：
10.1109/icassp43922.2022.9747524
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
Samuel Rey;Andrei Buciulea;Madeline Navarro;Santiago Segarra;A. Marques
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作者：
Samuel Rey;Andrei Buciulea;Madeline Navarro;Santiago Segarra;A. Marques
从节点观测集合中学习图代表了一个被正式称为图拓扑推理的突出问题。然而，目前的方法是有限的，通常集中在推断单个网络，他们假设来自所有节点的观察是可用的。首先，许多现代设置涉及多个相关的网络，其次，通常情况下，只有一个节点子集被观察到，而其余节点仍然隐藏。基于这些事实，我们引入了一种联合图拓扑推理方法，对隐变量的影响进行建模。在假设观测信号在寻找的图上是平稳的，并且图之间密切相关的情况下，多网络的联合估计使我们能够利用这种关系来提高学习图的质量。此外，我们还面临一个具有挑战性的问题，即如何对隐藏节点的影响进行建模，以最大限度地减少它们的有害影响。为了获得一种可行的方法，我们利用了手头设置的特定结构，并利用了不同图之间的相似性，这同时影响了观察节点和隐藏节点。为了验证所提出的方法，给出了合成图和真实图的数值模拟。
Learning graphs from sets of nodal observations represents a prominent problem formally known as graph topology inference. However, current approaches are limited by typically focusing on inferring single networks, and they assume that observations from all nodes are available. First, many contemporary setups involve multiple related networks, and second, it is often the case that only a subset of nodes is observed while the rest remain hidden. Motivated by these facts, we introduce a joint graph topology inference method that models the influence of the hidden variables. Under the assumptions that the observed signals are stationary on the sought graphs and the graphs are closely related, the joint estimation of multiple networks allows us to exploit such relationships to improve the quality of the learned graphs. Moreover, we confront the challenging problem of modeling the influence of the hidden nodes to minimize their detrimental effect. To obtain an amenable approach, we take advantage of the particular structure of the setup at hand and leverage the similarity between the different graphs, which affects both the observed and the hidden nodes. To test the proposed method, numerical simulations over synthetic and real-world graphs are provided.