Efficient Estimation for Longitudinal Networks via Adaptive Merging

Longitudinal network, also known as temporal network or continuous-time dynamic network, consists of a sequence of temporal edges among multiple nodes, where the temporal edges may be observed between each node pair in real time (Holme and Saramäki, 2012). It provides a flexible framework for modeling dynamic interactions between multiple objects and how network structure evolves over time (Aggarwal and Subbian, 2014). For instances, in online social platform such as Facebook, users send likes to the posts of their friends recurrently at different time (Perry-Smith and Shalley, 2003; Snijders et al., 2010); in international politics, countries may have conflict with others at one time but become allies at others (Cranmer and Desmarais, 2011; Kinne, 2013). Similar longitudinal networks have also been frequently encountered in biological science (Voytek and Knight, 2015; Avena-Koenigsberger et al., 2018) and ecological science (Ulanowicz, 2004; De Ruiter et al., 2005). One of the key challenges in estimating longitudinal network resides in its scarce temporal edges, as the interactions between node pairs are instantaneous and come in a streaming fashion (Holme and Saramäki, 2012), and thus the observed network at each given time point can be extremely sparse. This makes longitudinal network substantially different from discrete-time dynamic network (Kim et al., 2018), where multiple snapshots of networks are collected each with much more observed edges.