Spatial Temporal Exponential-Family Point Process Models for the Evolution of Social Systems

TL;DR

This paper introduces a novel class of exponential-family point process models that capture the coevolution of social structure and individual behavior over time, using a latent social space and Markov dynamics.

Contribution

It develops a new modeling framework combining latent social spaces with temporal Markov processes, providing analytic inference methods and practical computational tools.

Findings

Successfully modeled adolescent friendship networks over time.

Demonstrated the model's ability to analyze social behavior evolution.

Provided a scalable inference and simulation framework.

Abstract

We develop a class of exponential-family point processes based on a latent social space to model the coevolution of social structure and behavior over time. Temporal dynamics are modeled as a discrete Markov process specified through individual transition distributions for each actor in the system at a given time. We prove that these distributions have an analytic closed form under certain conditions and use the result to develop likelihood-based inference. We provide a computational framework to enable both simulation and inference in practice. Finally, we demonstrate the value of these models by analyzing alcohol and drug use over time in the context of adolescent friendship networks.