Estimation of Edge Infection Probabilities in the Inverse Infection Problem

Abstract

Several methods have been proposed recently to estimate the edge infection probabilities in infection or diffusion models. In this paper we will use the framework of the Generalized Cascade Model to define the Inverse Infection Problem-the problem of calculating these probabilities. We are going to show that the problem can be reduced to an optimization task and we will give a particle swarm based method as a solution. We will show, that direct estimation of the separate edge infection values is possible, although only on small graphs with a few thousand edges. To reduce the dimensionality of the task, the edge infection values can be considered as functions of known attributes on the vertices or edges of the graph, this way only the unknown coefficients of these functions have to be estimated. We are going to evaluate our method on artificially created infection scenarios. Our main points of interest are the accuracy and stability of the estimation.

A Generalized Framework for the Estimation of Edge Infection Probabilities

“…The Inverse Infection Problem (IIP), as appeared in [22,23], can be considered the predecessor of the GIIM. The GIIM uses the same FPSO optimization method as the IIP, and the RMSE error function is one method used to guide the search in both models.…”

“…Recently, several authors have proposed models to estimate these values. Many of the models assume that the time stamps of the infection for each node are given [13][14][15][16][17][18][19][20], although some approaches do not require this property [21][22][23]. Current estimation methods are based on a variety of infection models [15], but most often, the SIR model or one of its variants is used [16][17][18]21].…”

Finding early adopters of innovation in social networks

“…However, the literature also ignored the problem of determining where the probabilities of influence between users come from (Goyal et al 2010). Recently, Qiang et al (2019) proposed two learning models that are aimed at understanding person-to-person influence in information diffusion from historical cascades, while Bóta et al (2015) and Bóta et al (2016) considered the Inverse Infection Problem as a way to estimate the hidden edge infection probabilities.…”