Hierarchical Models for Relational Event Sequences

Interaction within small groups can often be represented as a sequence of events, where each event involves a sender and a recipient. Recent methods for modeling network data in continuous time model the rate at which individuals interact conditioned on the previous history of events as well as actor covariates. We present a hierarchical extension for modeling multiple such sequences, facilitating inferences about event-level dynamics and their variation across sequences. The hierarchical approach allows one to share information across sequences in a principled manner---we illustrate the efficacy of such sharing through a set of prediction experiments. After discussing methods for adequacy checking and model selection for this class of models, the method is illustrated with an analysis of high school classroom dynamics

Analysis of Partially Observed Networks via Exponential-family Random Network Models

Exponential-family random network (ERN) models specify a joint representation of both the dyads of a network and nodal characteristics. This class of models allow the nodal characteristics to be modelled as stochastic processes, expanding the range and realism of exponential-family approaches to network modelling. In this paper we develop a theory of inference for ERN models when only part of the network is observed, as well as specific methodology for missing data, including non-ignorable mechanisms for network-based sampling designs and for latent class models. In particular, we consider data collected via contact tracing, of considerable importance to infectious disease epidemiology and public health

Mixed membership stochastic blockmodels

Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate models no longer hold. In this paper, we describe a latent variable model of such data called the mixed membership stochastic blockmodel. This model extends blockmodels for relational data to ones which capture mixed membership latent relational structure, thus providing an object-specific low-dimensional representation. We develop a general variational inference algorithm for fast approximate posterior inference. We explore applications to social and protein interaction networks.Comment: 46 pages, 14 figures, 3 table