Neighborhood Selection with Application to Social Networks

• Activity Number: 184 - SPEED: Variable Selection and Networks
• Type: Contributed
• Date/Time: Monday, July 31, 2017 : 11:35 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Nana Wang* and Wolfgang Polonik
• Companies: and University of California, Davis
• Keywords: dependence ; networks ; graphical model ; Lasso-based selectors ; Dantzig-type selectors

Abstract

The topic of this talk is modeling and analyzing depdendence in stochastic networks, which has not received much attention in the literature so far. We propose a latent variable block model that allows the analysis of dependence between blocks via the analysis of a latent graphical model. Our approach is based on the idea underlying the neighborhood selection scheme put forward by Meinshausen and Bühlmann. However, because of the latent nature of our model, estimates have to be used in lieu of the unobserved variable. This leads to a novel analysis of graphical models under uncertainty, in the spirit of Rosenbaum and Tsybakov (2010), or Belloni, Rosenbaum and Tsybakov (2016). Lasso-based selectors, and a class of Dantzig-type selectors are studied.