|
Abstract:
|
Variable selection and network estimation have been popular tools for identifying key variables associated with a response variable of interest in settings involving non-negligible dependency structures among variables. However, the ability to identify relevant variables in a high dimensional setting while accounting for conditional dependencies 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. At both levels, variables work together to accomplish certain tasks, hence the dependency structure. Our main interest is to simultaneously explore variable selection and identify dependency structures among both higher and lower-level variables. Given data from heterogeneous classes, we propose a multi-level nonparametric kernel machine approach, utilizing both MCMC and Variational Inference to jointly identify multi-level variables as well as build the network. The Variational Inference approach is novel in its utilization of the sampled dependency structure as the observed variable rather than the response. In addition to th
|
