We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is a nonparametric model from which graphs of potentially different sizes can be drawn. The versatility of graphons allows us to tackle the joint inference problem even for the cases where the graphs to be recovered contain different number of nodes and lack precise alignment across the graphs. Our solution is based on combining a maximum likelihood penalty with graphon estimation schemes and can be used to augment existing network inference methods. We validate our proposed approach by comparing its performance against competing methods in synthetic and real-world datasets.

翻译：我们考虑从节点观测中估算多个网络的地形学问题,在这些网络中,假设这些网络是从同一个(未知的)随机图形模型中提取的。我们采用一个图形作为我们的随机图形模型,这是一个非参数模型,可以从中绘制可能不同大小的图表。图形的多功能性使我们能够解决共同推论问题,即使要回收的图表含有不同数目的节点,而且图中缺乏精确的对齐。我们的解决办法是把最大可能性的罚款与图表估算方案结合起来,并可用于扩大现有的网络推论方法。我们通过比较其与合成和现实世界数据集中相互竞争的方法相比,验证了我们所提议的方法。