Are You Going to the Party: Depends, Who Else is Coming?: [Learning Hidden Group Dynamics via Conditional Latent Tree Models]

Scalable probabilistic modeling and prediction in high dimensional multivariate time-series, such as dynamic social networks with co-evolving nodes and edges, is a challenging problem, particularly for systems with hidden sources of dependence and/or homogeneity. Here, we address this problem through the discovery of hierarchical latent groups. We introduce a family of Conditional Latent Tree Models (CLTM), in which tree-structured latent variables incorporate the unknown groups. The latent tree itself is conditioned on observed covariates such as seasonality, historical activity, and node attributes. We propose a statistically efficient framework for learning both the hierarchical tree structure and the parameters of the CLTM. We demonstrate competitive performance on two real world datasets, one from the students' attempts at answering questions in a psychology MOOC and the other from Twitter users participating in an emergency management discussion and interacting with one another. In addition, our modeling framework provides valuable and interpretable information about the hidden group structures and their effect on the evolution of the time series.