Source Localization of Graph Diffusion via Variational Autoencoders for Graph Inverse Problems

TL;DR

This paper introduces SL-VAE, a probabilistic framework using variational autoencoders to accurately locate sources of graph diffusion processes, effectively handling uncertainty and complex diffusion patterns.

Contribution

It presents a novel probabilistic model that leverages deep generative models and prior knowledge to improve source localization in arbitrary diffusion scenarios.

Findings

SL-VAE outperforms existing methods with 20% higher AUC scores.

The framework effectively quantifies uncertainty in source localization.

Demonstrated robustness across 7 real-world datasets.

Abstract

Graph diffusion problems such as the propagation of rumors, computer viruses, or smart grid failures are ubiquitous and societal. Hence it is usually crucial to identify diffusion sources according to the current graph diffusion observations. Despite its tremendous necessity and significance in practice, source localization, as the inverse problem of graph diffusion, is extremely challenging as it is ill-posed: different sources may lead to the same graph diffusion patterns. Different from most traditional source localization methods, this paper focuses on a probabilistic manner to account for the uncertainty of different candidate sources. Such endeavors require overcoming challenges including 1) the uncertainty in graph diffusion source localization is hard to be quantified; 2) the complex patterns of the graph diffusion sources are difficult to be probabilistically characterized; 3) the generalization under any underlying diffusion patterns is hard to be imposed. To solve the above challenges, this paper presents a generic framework: Source Localization Variational AutoEncoder (SL-VAE) for locating the diffusion sources under arbitrary diffusion patterns. Particularly, we propose a probabilistic model that leverages the forward diffusion estimation model along with deep generative models to approximate the diffusion source distribution for quantifying the uncertainty. SL-VAE further utilizes prior knowledge of the source-observation pairs to characterize the complex patterns of diffusion sources by a learned generative prior. Lastly, a unified objective that integrates the forward diffusion estimation model is derived to enforce the model to generalize under arbitrary diffusion patterns. Extensive experiments are conducted on 7 real-world datasets to demonstrate the superiority of SL-VAE in reconstructing the diffusion sources by excelling other methods on average 20% in AUC score.