Graphical Models via Univariate Exponential Family Distributions

摘要

Undirected graphical models, or Markov networks, are a popularclass of statistical models, used in a wide variety ofapplications. Popular instances of this class include Gaussiangraphical models and Ising models. In many settings, however, itmight not be clear which subclass of graphical models to use,particularly for non-Gaussian and non-categorical data. In thispaper, we consider a general sub-class of graphical models wherethe node-wise conditional distributions arise from exponentialfamilies. This allows us to derive multivariate graphicalmodel distributions from univariate exponential familydistributions, such as the Poisson, negative binomial, andexponential distributions. Our key contributions include a classof M-estimators to fit these graphical model distributions; andrigorous statistical analysis showing that these M-estimatorsrecover the true graphical model structure exactly, with highprobability. We provide examples of genomic and proteomicnetworks learned via instances of our class of graphical modelsderived from Poisson and exponential distributions. color="gray">