Graphon-aided Joint Estimation of Multiple Graphs

For instance, one would expect certain levels of similarities between the We consider the problem of estimating the topology of multiple networks brain networks of different healthy individuals or between the same from nodal observations, where these networks are assumed social network observed at different points in time. Prominent methods to be drawn from the same (unknown) random graph model. We for multiple network inference include statistical approaches, adopt a graphon as our random graph model, which is a nonparametric primarily consisting of the joint estimation of Gaussian graphical model from which graphs of potentially different sizes can models [13-17]. These methods typically involve modifications on be drawn. The versatility of graphons allows us to tackle the joint the graphical lasso formulation with additional encouragement of inference problem even for the cases where the graphs to be recovered structural similarity. Estimation of time-varying graphs is widely contain different number of nodes and lack precise alignment popular, as the relationship between graphs is typically straightforward across the graphs. Our solution is based on combining a maximum to implement by considering that graph variation is smooth likelihood penalty with graphon estimation schemes and can be used across time [18, 19]. The above methods for estimating multiple networks to augment existing network inference methods. We validate our typically enforce similar structure, such as promoting similar proposed approach by comparing its performance against competing sparsity patterns [20].