Poisson Graphical Models

• Activity Number: 102
• Type: Invited
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Pradeep Ravikumar*+ and Eunho Yang and Genevera Allen and Zhandong Liu
• Companies: University of Texas at Austin and University of Texas at Austin and Rice University/Baylor College of Medicine and Baylor College of Medicine
• Keywords: Poisson ; GraphicalModels

Abstract

Standard instance of undirected graphical models, such as Gaussian graphical models, and Ising models, are ill-suited to modeling count data such as genomic sequencing data, user-ratings data from mental health studies, etc. Existing classes of Poisson graphical models, which arise as the joint distributions that correspond to Poisson distributed node-conditional distributions, have a major drawback: they can only model negative conditional dependencies. We consider the task of modifying the Poisson graphical model distribution so that it can capture a rich dependence structure between count-valued variables. We begin by discussing two strategies for truncating the Poisson distribution and show that only one of these leads to a valid joint distribution; even this model, however, has limitations on the types of variables and dependencies that may be modeled. To address this, we further propose two novel variants of the Poisson distribution and their corresponding joint graphical model distributions. We demonstrate the performance of our methods by learning simulated networks as well as networks from microRNA-Sequencing data and user-ratings data from mental health studies.