On Graphical Models via Univariate Exponential Family Distributions

摘要

Undirected graphical models, or Markov networks, are a popular class ofstatistical models, used in a wide variety of applications. Popular instancesof this class include Gaussian graphical models and Ising models. In manysettings, however, it might not be clear which subclass of graphical models touse, particularly for non-Gaussian and non-categorical data. In this paper, weconsider a general sub-class of graphical models where the node-wiseconditional distributions arise from exponential families. This allows us toderive multivariate graphical model distributions from univariate exponentialfamily distributions, such as the Poisson, negative binomial, and exponentialdistributions. Our key contributions include a class of M-estimators to fitthese graphical model distributions; and rigorous statistical analysis showingthat these M-estimators recover the true graphical model structure exactly,with high probability. We provide examples of genomic and proteomic networkslearned via instances of our class of graphical models derived from Poisson andexponential distributions.