Learning Human Activity Patterns Using Clustered Point Processes With Active and Inactive States

Jingfei Zhang, Biao Cai, Xuening Zhu, Hansheng Wang, Ganggang Xu, Yongtao Guan

Research output: Contribution to journalArticlepeer-review


Modeling event patterns is a central task in a wide range of disciplines. In applications such as studying human activity patterns, events often arrive clustered with sporadic and long periods of inactivity. Such heterogeneity in event patterns poses challenges for existing point process models. In this article, we propose a new class of clustered point processes that alternate between active and inactive states. The proposed model is flexible, highly interpretable, and can provide useful insights into event patterns. A composite likelihood approach and a composite EM estimation procedure are developed for efficient and numerically stable parameter estimation. We study both the computational and statistical properties of the estimator including convergence, consistency, and asymptotic normality. The proposed method is applied to Donald Trump’s Twitter data to investigate if and how his behaviors evolved before, during, and after the presidential campaign. Additionally, we analyze large-scale social media data from Sina Weibo and identify interesting groups of users with distinct behaviors.

Original languageEnglish (US)
JournalJournal of Business and Economic Statistics
StateAccepted/In press - 2022
Externally publishedYes


  • Clustered point processes
  • Composite EM algorithm
  • Composite likelihood
  • Nonoverlapping clusters
  • Social media

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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