Semi-parametric vertex set prediction for dynamic networks using latent tree models

Abstract

Dynamic networks may be viewed as arising from a process of change in the vertex set and/or edge set of a network, with joint edge/vertex evolution being common in observational settings. In this latter case, recent work has shown that the accuracy of vertex set prediction substantially affects the ability of dynamic network models to correctly predict features of the edge structure (Almquist and Butts, 2011). Past research has applied dynamic logistic regression to scalably model joint edge/vertex dynamics; this approach, however, is unable to capture potentially important sources of dependence within the vertex set (e.g., subgroups who tend to be jointly present or absent due to endogenous social relations). Recent developments in latent tree models suggest their use as a mechanism for modeling dependence in vertex co-presence; these models can easily represent types of dependence expected in typical settings (e.g., subgroup structure, selective pairing), and can be efficiently inferred even for very large graphs. Here, we introduce a semi-parametric approach to the problem of vertex set prediction in dynamic networks, combining a parametric model for covariate effects with anon-parametric latent tree structure. We illustrate this approach on a classic data set involving interactions among windsurfers on a California beach (Freeman et al., 1988).