Learning Diffusions under Uncertainty

TL;DR

This paper proposes a novel method for inferring diffusion networks from uncertain probabilistic data, using constrained nonlinear regression and an alternating maximization algorithm, validated on synthetic and real-world networks.

Contribution

It introduces a new approach to diffusion network inference that handles uncertain data, extending beyond existing methods requiring exact infection times or statuses.

Findings

Effective inference from probabilistic infection data

The proposed method outperforms baseline approaches

The approach is computationally efficient and scalable

Abstract

To infer a diffusion network based on observations from historical diffusion processes, existing approaches assume that observation data contain exact occurrence time of each node infection, or at least the eventual infection statuses of nodes in each diffusion process. They determine potential influence relationships between nodes by identifying frequent sequences, or statistical correlations, among node infections. In some real-world settings, such as the spread of epidemics, tracing exact infection times is often infeasible due to a high cost; even obtaining precise infection statuses of nodes is a challenging task, since observable symptoms such as headache only partially reveal a node's true status. In this work, we investigate how to effectively infer a diffusion network from observation data with uncertainty. Provided with only probabilistic information about node infection statuses, we formulate the problem of diffusion network inference as a constrained nonlinear regression w.r.t. the probabilistic data. An alternating maximization method is designed to solve this regression problem iteratively, and the improvement of solution quality in each iteration can be theoretically guaranteed. Empirical studies are conducted on both synthetic and real-world networks, and the results verify the effectiveness and efficiency of our approach.