Submodular Variational Inference for Network Reconstruction

TL;DR

This paper introduces VINE, a variational inference algorithm that accurately reconstructs network structures from diffusion data without assuming specific probabilistic models, applicable to real-world social networks.

Contribution

The paper proves the Bayesian log-submodular nature of the diffusion process and develops VINE, a novel, efficient algorithm for network reconstruction from diffusion observations.

Findings

VINE accurately reconstructs connected networks from diffusion data.

The model applies to real-world social network diffusion processes.

VINE outperforms existing methods in accuracy and efficiency.

Abstract

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.