Stochastic Block Transition Models for Dynamic Networks

There has been great interest in recent years on statistical models for dynamic networks. In this paper, I propose a stochastic block transition model (SBTM) for dynamic networks that is inspired by the well-known stochastic block model (SBM) for static networks and previous dynamic extensions of the SBM. Unlike most existing dynamic network models, it does not make a hidden Markov assumption on the edge-level dynamics, allowing the presence or absence of edges to directly influence future edge probabilities while retaining the interpretability of the SBM. I derive an approximate inference procedure for the SBTM and demonstrate that it is significantly better at reproducing durations of edges in real social network data.Comment: To appear in proceedings of AISTATS 201

A Dynamic Additive and Multiplicative Effects Model with Application to the United Nations Voting Behaviors

We introduce a regression model for a series of networks that are correlated over time. Our model is a dynamic extension of the additive and multiplicative effects network model (AMEN) of Hoff (2019) In addition to incorporating a temporal structure, the model accommodates two types of missing data thus allows the size of the network to vary over time. We demonstrate via simulations the necessity of various components of the model. We apply the model to the United Nations General Assembly voting data from 1983 to 2014 (Voeten (2013)) to answer interesting research questions regarding to international voting behaviors. In addition to finding important factors that could explain the voting behaviors, the model-estimated additive effects, multiplicative effects, and their movements reveal meaningful foreign policy positions and alliances of various countries

A survey of statistical network models

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference

A Latent Space Approach to Dynamic Embedding of Co-occurrence Data

We consider dynamic co-occurrence data, such as author-word links in papers published in successive years of the same conference. For static co-occurrence data, researchers often seek an embedding of the entities (authors and words) into a lowdimensional Euclidean space. We generalize a recent static co-occurrence model, the CODE model of Globerson et al. (2004), to the dynamic setting: we seek coordinates for each entity at each time step. The coordinates can change with time to explain new observations, but since large changes are improbable, we can exploit data at previous and subsequent steps to find a better explanation for current observations. To make inference tractable, we show how to approximate our observation model with a Gaussian distribution, allowing the use of a Kalman filter for tractable inference. The result is the first algorithm for dynamic embedding of co-occurrence data which provides distributional information for its coordinate estimates. We demonstrate our model both on synthetic data and on author-word data from the NIPS corpus, showing that it produces intuitively reasonable embeddings. We also provide evidence for the usefulness of our model by its performance on an authorprediction task.