In this thesis, we consider a Bayesian bi-level variable selection problem in high-dimensional regressions. In many practical situations, it is natural to assign group membership to each predictor. Examples include that genetic variants can be grouped at the gene level and a covariate from different tasks naturally forms a group. Thus, it is of interest to select important groups as well as important members from those groups. The existing methods based on Markov Chain Monte Carlo (MCMC) are often computationally intensive and not scalable to large data sets. To address this problem, we consider variational inference for bi-level variable selection (BIVAS). In contrast to the commonly used mean-field approximation, we propose a hierarchical factorization to approximate the posterior distribution, by utilizing the structure of bi-level variable selection. Moreover, we develop a computationally efficient and fully parallelizable algorithm based on this variational approximation. We further extend the developed method to model data sets from multi-task learning. The comprehensive numerical results from both simulation studies and real data analysis demonstrate the advantages of BIVAS for variable selection, parameter estimation and computational efficiency over existing methods. The BIVAS software with support of parallelization is implemented in R package `bivas' available at https://github.com/mxcai/bivas.
|Date of Award||17 May 2018|
|Supervisor||Heng PENG (Supervisor)|
- Bayesian statistical decision theory
- Data mining
- Regression analysis.