  In real-world and online social networks, individuals receive and transmit
information in real time. Cascading information transmissions (e.g. phone
calls, text messages, social media posts) may be understood as a realization of
a diffusion process operating on the network, and its branching path can be
represented by a directed tree. The process only traverses and thus reveals a
limited portion of the edges. The network reconstruction/inference problem is
to infer the unrevealed connections. Most existing approaches derive a
likelihood and attempt to find the network topology maximizing the likelihood,
a problem that is highly intractable. In this paper, we focus on the network
reconstruction problem for a broad class of real-world diffusion processes,
exemplified by a network diffusion scheme called respondent-driven sampling
(RDS). We prove that under realistic and general models of network diffusion,
the posterior distribution of an observed RDS realization is a Bayesian
log-submodular model.We then propose VINE (Variational Inference for Network
rEconstruction), a novel, accurate, and computationally efficient variational
inference algorithm, for the network reconstruction problem under this model.
Crucially, we do not assume any particular probabilistic model for the
underlying network. VINE recovers any connected graph with high accuracy as
shown by our experimental results on real-life networks.
