Like their inhabitants, countries interact with one another: they consult, negotiate, trade, threaten, and fight. These interactions are seldom uncoordinated. Rather, they are connected by a fabric of overlapping communities, such as security coalitions, treaties, trade cartels, and military alliances. A single country can belong to multiple communities, reflecting its many overlapping identities, and can engage in both within- and between-community interactions, depending on the capacity in which it is acting. In this talk, I will introduce two tensor decomposition models for modeling interaction events of the form "country i took action a toward country j at time t." The first model (Bayesian Poisson CP decomposition) discovers coherent threads of events, characterized by sender countries, receiver countries, action types, and time steps; the second model (Bayesian Poisson Tucker decomposition) discovers latent country--community memberships, including the number of latent communities, as well as directed community--community interaction networks that are specific to "topics" of similar action types. I will demonstrate that these models infer interpretable latent structures that conform to and inform our knowledge of international relations. Many existing models for discrete data (such as networks and text) are special cases of these models, including infinite relational models, stochastic block models, and latent Dirichlet allocation. As a result, Bayesian Poisson tensor decomposition is a general framework for
analyzing and understanding discrete data sets in the social sciences.