Poisson Graphical Models With Rich Dependence Structures

Pradeep Ravikumar, University of Texas at Austin

Undirected graphical models, such as Gaussian, Ising, and discrete/multinomial graphical models, are widely used in a variety of applications for modeling distributions over a large number of variables. These standard instances, however, are ill-suited to modeling count data, which are increasingly ubiquitous in climate studies, and spatial incidence data, as well as other big-data settings such as genomic sequencing data, user-ratings data, and site visits. Existing proposals for distributions for multivariate count data have a crucial caveat: the dependence structures they model are largely restrictive, with solely negative or positive dependencies in some cases.

Can we devise multivariate distributions that can capture rich dependence structures between count-valued variables? We address this question via a series of multivariate extensions of the univariate Poisson distribution, providing a new class of Poisson graphical models. We also provide tractable schemes with guarantees for learning our class of Poisson graphical models from data, and demonstrate the performance of our methods by learning simulated networks as well as a network from microRNA-Sequencing data.

Joint work with Eunho Yang, Genevera Allen, Zhandong Liu, David Inouye, Inderjit Dhillon.

Link to Recording: https://www.youtube.com/watch?v=SfkOU29cs04

Link to Presentation: CI2016 Ravikumar