it is important to capture the global properties of the interaction data. Interaction data are often *sparse*: only a small fraction of the pairs of nodes actually interact. Additionally, they typically exhibit high degree (number of interactions per node) *heterogeneity*: some individuals have a large number of interactions, whereas most individuals have very few, therefore resulting in empirical degree distributions being heavy-tailed. As shown by @Karrer2011, @Gopalan2013 and @Todeschini2016, failing to account explicitly for degree heterogeneity in the model can have devastating consequences on the estimation of the latent structure.

Recently, two classes of statistical models, based on random measures, have been proposed to capture sparsity and power-law degree distribution in network data. The first one is the class of models based on exchangeable random measures [@Caron2017; @Veitch2015; @Herlau2015; @Borgs2016; @Todeschini2016; @Palla2016; @Janson2017]. The second one is the class of edge-exchangeable models [@Crane2015; @Crane2017; @Cai2016; @Williamson2016; @Janson2017a; @Ng2017]. Both classes of models can handle both sparse and dense networks and, although the two constructions are different, connections have been highlighted between the two approaches [@Cai2016; @Janson2017a].

The objective of this paper is to propose a class of statistical models for temporal dyadic interaction data that can capture all the desired 