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abstract: 'We propose a novel class of network models for temporal dyadic interaction data. Our objective is to capture important features often observed in social interactions: sparsity, degree heterogeneity, community structure and reciprocity. We use mutually-exciting Hawkes processes to model the interactions between each (directed) pair of individuals. The intensity of each process allows interactions to arise as responses to opposite interactions (reciprocity), or due to shared interests between individuals (community structure). For sparsity and degree heterogeneity, we build the non time dependent part of the intensity function on compound random measures following [@Todeschini2016]. We conduct experiments on real-world temporal interaction data and show that the proposed model outperforms competing approaches for link prediction, and leads to interpretable parameters.'
author:
- |
    Xenia  Miscouridou$^{\mathbf{1}}$, François Caron$^{\mathbf{1}}$, Yee Whye Teh$^{\mathbf{1,2}}$\
    $^{1}$Department of Statistics, University of Oxford\
    $^{2}$DeepMind\
    `{miscouri, caron, y.w.teh}@stats.ox.ac.uk`\
bibliography:
- '../biblio.bib'
title: 'Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data'
---

Introduction
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There is a growing interest in modelling and understanding temporal dyadic interaction data. Temporal interaction data take the form of time-stamped triples $(t,i,j)$ indicating that an interaction occurred between individuals $i$ and $j$ at time $t$. Interactions may be directed or undirected. 