A Survey of Statistical Network Models
Now Publishers Inc, Jan 29, 2010 - Computers - 120 pages
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.
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Motivation and DataSet Examples
Static Network Models
adjacency matrix algorithm analyze asymptotics Barabási Bayesian blocks Carnegie Mellon University clustering Computer Science context continuous-time continuous-time Markov process D. M. Blei data set DCFM degree distribution directed graphs duplication-attachment model dyad dynamic models dynamic network e-mail E. M. Airoldi edge-oriented empirical Enron Erdös–Rényi Erdös–Rényi–Gilbert model ERGM estimation example exchangeable graph model exponential family exponential random graph function giant component inference Journal K. M. Carley latent positions latent space model Leinhardt likelihood function M. S. Handcock machine learning Markov chain Mathematical maximum likelihood MCMC mixed membership network analysis network data network structure node-specific nodes observed p1 model pairs of nodes papers parameters power-law preferential attachment probability random graph models reciprocation Research S. E. Fienberg sampling scale-free small-world models snapshots Snijders social networks static statistical network modeling statistical physics stochastic blockmodel structural equivalence sufficient statistics theory tion undirected University