Neighborhood selection with application to social networks

TL;DR

This paper develops a novel approach for modeling dependence in social networks using latent variable block models and neighborhood selection, addressing uncertainty with Lasso and Dantzig-type estimators.

Contribution

It introduces a new analysis framework for graphical models with latent variables, extending neighborhood selection methods to uncertain, social network data.

Findings

Effective estimation of dependence structures in social networks.

Extension of neighborhood selection to latent variable models.

Comparison of Lasso and Dantzig-type selectors under uncertainty.

Abstract

The topic of this paper is modeling and analyzing dependence in stochastic social networks. Using a latent variable block model allows the analysis of dependence between blocks via the analysis of a latent graphical model. Our approach to the analysis of the graphical model then is based on the idea underlying the neighborhood selection scheme put forward by Meinshausen and B\"{u}hlmann (2006). However, because of the latent nature of our model, estimates have to be used in lieu of the unobserved variables. This leads to a novel analysis of graphical models under uncertainty, in the spirit of Rosenbaum et al. (2010), or Belloni et al. (2017). Lasso-based selectors, and a class of Dantzig-type selectors are studied.