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Title: Multilevel multiclass Gaussian graphical model Authors:  Inyoung Kim - Virginia Tech (United States) [presenting]
Abstract: Gaussian graphical models have been a popular tool to investigate conditional dependency structure between random variables by estimating sparse precision matrices. The estimated precision matrices could be mapped into networks for visualization. However, investigating the conditional dependency structure when there exists the two-level structure among variables is still limited; some variables are considered as higher level variables while others are nested in these higher-level variables; the latter are called lower-level variables. For instance, genes are grouped into pathways for particular functions, so that pathways are the higher-level variables and genes within pathways are the lower level variables. Higher-level variables are not isolated; instead, they work together to accomplish certain tasks. Therefore, simultaneously exploring conditional dependency structures among higher level variables and among lower level variables are of our main interest. Given two level data from heterogeneous classes, we propose a method to jointly estimate the two level Gaussian graphical models across multiple classes, so that common structures in terms of the two level conditional dependency are shared during the estimation procedure, yet unique structures for each class are retained as well. Our proposed approach is achieved by first introducing higher-level variable factors within classes, and then introducing common factors across classes.