Multivariate Hawkes process analysis of posts on a web service about uncomfortable gender experiences

We propose a method for the modelling of the propagation of text data in web site space among some groups by using a multivariate Hawkes process with a sparse structure. For estimation, we introduced a hybrid method using a quasi-maximum likelihood estimator (QMLE) and a $L^1$-penalized QMLE. As a real example, we investigated posts on a Japanese web service about uncomfortable gender experiences, which we classified into 12 groups by age and sex, and we calculated the magnitude of the correlation between each group. In addition, we visualized the propagation structure of posts in each group by summarizing the results in a directed Hawkes graph and a heat map of time integrals of kernel functions.

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