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. The proposed joint network and graphon estimation is further enhanced with the introduction of a robust method for noisy graph sampling information. We validate our proposed approach by comparing its performance against competing methods in synthetic and real-world datasets.
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.
The estimation of probabilities of network edges from the observed adjacency matrix has important applications to predicting missing links and network denoising. It has usually been addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighborhood smoothing to estimate the expectation of the adjacency matrix directly, without making the structural assumptions that graphon estimation requires. The neighborhood smoothing method requires little tuning, has a competitive mean-squared error rate, and outperforms many benchmark methods on link prediction in simulated and real networks.