Multilevel Gaussian Graphical Models Conditional on Covariates
[edit]
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:42164225, 2020.
Abstract
We address the problem of learning the structure of a highdimensional Gaussian graphical model conditional on covariates, when each sample belongs to groups at multiple levels of hierarchy. The existing statistical methods for learning covariateconditioned Gaussian graphical models focused on learning the aggregate behavior of inputs and outputs in a singlelayer network. We propose a statistical model called multilevel conditional Gaussian graphical models for modeling multilevel output networks influenced by both individuallevel and grouplevel inputs. We describe a decomposition of our model into a product of two components, one for sum variables and the other for difference variables derived from the original variables. This decomposition leads to an efficient learning algorithm for both complete data and incomplete data with randomly missing individual observations, as the expensive repeated computation of the partition function can be avoided. We demonstrate our method on simulated data and realworld data in finance and genomics.
Related Material


