Examples of such interaction data include commenting a post on an online social network, exchanging an email, or meeting in a coffee shop. An important challenge is to understand the underlying structure that underpins these interactions. To do so, it is important to develop statistical network models with interpretable parameters, that capture the properties which are observed in real social interaction data.

One important aspect to capture is the *community structure* of the interactions. Individuals are often affiliated to some latent communities (e.g. work, sport, etc.), and their affiliations determine their interactions: they are more likely to interact with individuals sharing the same interests than to individuals affiliated with different communities. An other important aspect is *reciprocity*. Many events are responses to recent events of the opposite direction. For example, if Helen sends an email to Mary, then Mary is more likely to send an email to Helen shortly afterwards. A number of papers have proposed statistical models to capture both community structure and reciprocity in temporal interaction data [@Blundell2012; @Dubois2013; @Linderman2014]. They use models based on Hawkes processes for capturing reciprocity and stochastic block-models or latent feature models for capturing community structure.

In addition to the above two properties, 