Gaussian Graphical Models: An Exploration and Application of Learning Conditional Independence

Abstract

This paper is an application and exploration of how precision matrices signify conditional independence between Gaussian random variables, and what this conditional independence means for the simplification of probabilistic graphical models. We worked with atmospheric data from the National Center for Atmospheric Research (Skamarock, William C., et al., 2012) to determine conditional independence between Gaussian mean variables. We also generated variables from an ordinary differential equation system and looked at the resulting precision matrices. This research details one potential avenue to create precision matrices and probabilistic graphical models from a set of Gaussian random variables, then determine conditional independence. It also explores the setup for a problem relating precision matrices to an oscillating system of ordinary differential equations, and potential applications of this method.</p