Multiresolution Network Models

ABSTRACT

Many existing statistical and machine learning tools for social network analysis focus on a single level of analysis. Methods designed for clustering optimize a global partition of the graph, whereas projection-based approaches (e.g., the latent space model in the statistics literature) represent in rich detail the roles of individuals. Many pertinent questions in sociology and economics, however, span multiple scales of analysis. Further, many questions involve comparisons across disconnected graphs that will, inevitably be of different sizes, either due to missing data or the inherent heterogeneity in real-world networks. We propose a class of network models that represent network structure on multiple scales and facilitate comparison across graphs with different numbers of individuals. These models differentially invest modeling effort within subgraphs of high density, often termed communities, while maintaining a parsimonious structure between said subgraphs. We show that our model class is projective, highlighting an ongoing discussion in the social network modeling literature on the dependence of inference paradigms on the size of the observed graph. We illustrate the utility of our method using data on household relations from Karnataka, India. Supplementary material for this article is available online.

KEYWORDS:

• Latent space
• Multiscale
• Projectivity
• Social network
• Stochastic blockmodel

Funding

This work was partially supported by the National Science Foundation under grant number SES-1461495 to Fosdick and grant number SES-1559778 to McCormick. McCormick is also supported by grant number K01 HD078452 from the National Institute of Child Health and Human Development (NICHD). This material is based upon work supported by, or in part by, the U. S. Army Research Laboratory and the U. S. Army Research Office under contract/grant number W911NF-12-1-0379. Murphy and Ng are supported by the Science Foundation Ireland funded Insight Research Centre (SFI/12/RC/2289). The authors would also like to thank the Isaac Newton Institute Program on Theoretical Foundations for Statistical Network Analysis workshop on Bayesian Models for Networks, supported by EPSRC grant number EP/K032208/1.