# American Institute of Mathematical Sciences

July  2014, 19(5): 1335-1354. doi: 10.3934/dcdsb.2014.19.1335

## Latent self-exciting point process model for spatial-temporal networks

 1 USC Information Sciences Institute, Marina del Rey, CA 90292, United States 2 USC Information Sciences Institute, United States 3 University of California, Los Angeles, United States 4 University of California, Irvine, United States

Received  December 2012 Revised  April 2013 Published  April 2014

We propose a latent self-exciting point process model that describes geographically distributed interactions between pairs of entities. In contrast to most existing approaches that assume fully observable interactions, here we consider a scenario where certain interaction events lack information about participants. Instead, this information needs to be inferred from the available observations. We develop an efficient approximate algorithm based on variational expectation-maximization to infer unknown participants in an event given the location and the time of the event. We validate the model on synthetic as well as real-world data, and obtain very promising results on the identity-inference task. We also use our model to predict the timing and participants of future events, and demonstrate that it compares favorably with baseline approaches.
Citation: Yoon-Sik Cho, Aram Galstyan, P. Jeffrey Brantingham, George Tita. Latent self-exciting point process model for spatial-temporal networks. Discrete & Continuous Dynamical Systems - B, 2014, 19 (5) : 1335-1354. doi: 10.3934/dcdsb.2014.19.1335
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