Cascade Size Distributions: Why They Matter and How to Compute Them Efficiently

TL;DR

This paper introduces an efficient message passing algorithm to accurately compute the probability distribution of cascade sizes in epidemic and information spread models, applicable to large and complex networks.

Contribution

It presents a novel, scalable, and exact-on-trees message passing method for cascade size distribution, improving over sampling-based approaches.

Findings

Exact on trees, approximate on dense networks

Scales efficiently to large networks

Performs well on real-world data

Abstract

Cascade models are central to understanding, predicting, and controlling epidemic spreading and information propagation. Related optimization, including influence maximization, model parameter inference, or the development of vaccination strategies, relies heavily on sampling from a model. This is either inefficient or inaccurate. As alternative, we present an efficient message passing algorithm that computes the probability distribution of the cascade size for the Independent Cascade Model on weighted directed networks and generalizations. Our approach is exact on trees but can be applied to any network topology. It approximates locally tree-like networks well, scales to large networks, and can lead to surprisingly good performance on more dense networks, as we also exemplify on real world data.