# Estimating Diffusion Probability Changes for AsIC-SIS Model from Information Diffusion Results

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Akihiro Koide,
Kazumi Saito,
Kouzou Ohara,
Masahiro Kimura,
Hiroshi Motoda
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Proceedings of the Asian Conference on Machine Learning, PMLR 20:297-313, 2011.

#### Abstract

We address the problem of estimating changes in diffusion probability over a social network from the observed information diffusion results, which is possibly caused by an unknown external situation change. For this problem, we focused on the asynchronous independent cascade (AsIC) model in the SIS (Susceptible/Infected/Susceptible) setting in order to meet more realistic situations such as communication in a blogosphere. This model is referred to as the AsIC-SIS model. We assume that the diffusion parameter changes are approximated by a series of step functions, and their changes are reflected in the observed diffusion results. Thus, the problem is reduced to detecting how many step functions are needed, where in time each one starts and how long it lasts, and what the hight of each one is. The method employs the derivative of the likelihood function of the observed data that are assumed to be generated from the AsIC-SIS model, adopts a divide-and-conquer type greedy recursive partitioning, and utilizes an MDL model selection measure to determine the adequate number of step functions. The results obtained using real world network structures confirmed that the method works well as intended. The MDL criterion is useful to avoid overfitting, and the found pattern is not necessarily the same in terms of the number of step functions as the one assumed to be true, but the error is always reduced to a small value.

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