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

A. Koide, K. Saito, K. Ohara, M. Kimura & H. Motoda; JMLR W&CP
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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