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.

翻译：从各节点观测中得出的学习图表是一个突出的问题,被正式称为图形表层推断。然而,目前的方法是有限的,通常侧重于推断单一网络,它们假定所有节点都有观测结果。第一,许多当代设置涉及多个相关网络,第二,经常的情况是,只观察到一组节点,而其余的则仍然隐藏着。受这些事实的驱使,我们采用了一种联合图表表层推断方法,以模拟隐藏变量的影响。根据所观测到的信号是固定在所寻求的图表上的假设,并且图表是密切相关的,对多个网络的联合估计使我们能够利用这种关系来提高所学图的质量。此外,我们面对一个具有挑战性的问题,即模拟隐藏节点的影响,以尽量减少其有害影响。为了获得适用的方法,我们利用手边设置的特定结构,利用不同图表之间的相似性,这既影响观测到的,也影响隐藏的节点。为了测试拟议的方法,提供了合成和真实世界图表的数字模拟。