| The topic of this work is modeling and analyzing dependence in stochastic social networks. In a latent variable block model, we present an approach for analyzing the dependence between blocks via the analysis of a latent graphical model by using the idea of neighborhood selection in graphical models (Meinshausen and Buhlmann (2006)). Lasso-based selectors, and a class of Dantzig-type selectors are studied. 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).;The second part of this work extends the iid setting of the first part to a dependent setup. This leads to the analysis of latent dynamic graphical models under uncertainty. Here the concept of locally stationary VAR(p) graphical models comes into play. Due to the assumed local stationarity we now use kernel-based versions of our selectors to analyze the dependence structure of the networks. |
