In this work, we study the event occurrences of user activities on online social network platforms. To characterize the social activity interactions among network users, we propose a network group Hawkes (NGH) process model. Particularly, the observe
d network structure information is employed to model the users dynamic posting behaviors. Furthermore, the users are clustered into latent groups according to their dynamic behavior patterns. To estimate the model, a constraint maximum likelihood approach is proposed. Theoretically, we establish the consistency and asymptotic normality of the estimators. In addition, we show that the group memberships can be identified consistently. To conduct estimation, a branching representation structure is firstly introduced, and a stochastic EM (StEM) algorithm is developed to tackle the computational problem. Lastly, we apply the proposed method to a social network data collected from Sina Weibo, and identify the infuential network users as an interesting application.
We propose a latent topic model with a Markovian transition for process data, which consist of time-stamped events recorded in a log file. Such data are becoming more widely available in computer-based educational assessment with complex problem solv
ing items. The proposed model can be viewed as an extension of the hierarchical Bayesian topic model with a hidden Markov structure to accommodate the underlying evolution of an examinees latent state. Using topic transition probabilities along with response times enables us to capture examinees learning trajectories, making clustering/classification more efficient. A forward-backward variational expectation-maximization (FB-VEM) algorithm is developed to tackle the challenging computational problem. Useful theoretical properties are established under certain asymptotic regimes. The proposed method is applied to a complex problem solving item in 2012 Programme for International Student Assessment (PISA 2012).
