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Abstract:
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Variable selection and network estimation have been popular tools for identifying key variables associated with a response variable of interest while accounting for underlying dependency structures among variables. However, the ability to identify such variables and investigate conditional dependencies among them within a multi-level structure is still limited. The case under examination is a two-level structure where some variables are considered as higher-level variables and other, lower level variables, nested within them. Higher-level variables are not isolated; instead, they work together to accomplish certain tasks. Therefore, our main interest is to simultaneously explore variable selection and dependency structures among higher and lower-level variables. Given data from heterogeneous classes, we propose a multi-level nonparametric kernel machine approach to jointly identify multi-level variables as well as build the network, such that common variables and network structures, are shared across classes during the Bayesian estimation procedure, while retaining unique structures for each class. We demonstrate the advantages of our approach using genetic pathway based analysis.
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