Online Bayesian Inference of Diffusion Networks

TL;DR

This paper develops Bayesian methods for inferring both the structure and infection times of diffusion networks from time series data, using Monte Carlo techniques for batch and online inference.

Contribution

It introduces novel Bayesian inference algorithms that jointly estimate network structure and infection times from limited observational data.

Findings

Algorithms accurately recover network structure and infection times in simulations.

Proposed methods outperform existing approaches in real-world datasets.

Online inference enables real-time monitoring of contagion spread.

Abstract

Understanding the process by which a contagion disseminates throughout a network is of great importance in many real world applications. The required sophistication of the inference approach depends on the type of information we want to extract as well as the number of observations that are available to us. We analyze scenarios in which not only the underlying network structure (parental relationships and link strengths) needs to be detected, but also the infection times must be estimated. We assume that our only observation of the diffusion process is a set of time series, one for each node of the network, which exhibit changepoints when an infection occurs. After formulating a model to describe the contagion, and selecting appropriate prior distributions, we seek to find the set of model parameters that best explains our observations. Modeling the problem in a Bayesian framework, we exploit Monte Carlo Markov Chain, Sequential Monte Carlo, and time series analysis techniques to develop batch and online inference algorithms. We evaluate the performance of our proposed algorithms via numerical simulations of synthetic network contagions and analysis of real-world datasets.