${\sf DeepNC}$DeepNC: Deep Generative Network Completion

Most network data are collected from partially observable networks with both missing nodes and missing edges, for example, due to limited resources and privacy settings specified by users on social media. Thus, it stands to reason that inferring the missing parts of the networks by performing
network completion
should precede downstream applications. However, despite this need, the recovery of missing nodes and edges in such incomplete networks is an insufficiently explored problem due to the modeling difficulty, which is much more challenging than link prediction that only infers missing edges. In this paper, we present DeepNC, a novel method for inferring the missing parts of a network based on a
deep generative
model of graphs. Specifically, our method first learns a likelihood over edges via an
autoregressive generative
model, and then identifies the graph that maximizes the learned likelihood conditioned on the observable graph topology. Moreover, we propose a computationally efficient
${\sf DeepNC}$
algorithm that
consecutively
finds individual nodes that maximize the probability in each node generation step, as well as an enhanced version using the expectation-maximization algorithm. The runtime complexities of both algorithms are shown to be
almost linear
in the number of nodes in the network. We empirically demonstrate the superiority of DeepNC over state-of-the-art network completion approaches.