Title: Neighborhood selection with application to social networks,
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
Bühlmann (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.