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.

Sequential Estimation of Temporally Evolving Latent Space Network Models

“…The latter has been addressed via approximations (see Raftery et al (2012) and Rastelli et al (2018)), though it is not straightforward to adapt this approach within the context of SMC. Alternatively, the modelling approach taken in Fosdick et al (2019), in which the nodes are partitioned into communities and the within-community connection probabilities are modelled via a latent space, may allow us to consider networks with larger N . In this setting, regions of independence in the latent space may allow us to develop a more scalable approach by partitioning the state space (for example, as in Rebeschini and van Handel (2015)).…”

Continuous Latent Position Models for Instantaneous Interactions

“…Other relevant and interesting works that revolve around the distance models in either static or dynamic settings include Gollini and Murphy (2014) and Salter-Townshend and McCormick (2017) for multi-view networks, Sewell and Chen (2016) for dynamic weighted networks, and Gormley and Murphy (2007) and Sewell and Chen (2015a) for networks of rankings. We also mention Raftery et al (2012), Fosdick et al (2019), Rastelli et al (2018), and Tafakori et al (2019) which introduce original and closely related modeling or computational ideas.…”

Model-based clustering for multidimensional social networks

“…An extension to the framework of latent position cluster model is that by Gormley & Murphy (2010), which combines it with a mixture of experts framework. Fosdick et al (2018) attempt to bridge stochastic block models and latent position cluster models, using the so-called Latent Space Stochastic Blockmodel. In this framework, within cluster probabilities are modelled via a latent space model, while between cluster interactions are expressed as in stochastic block models.…”