This paper studies the variable selection problem in high dimensional linear regression, where there are multiple response vectors, and they share the same or similar subsets of predictor variables to be selected from a large set of candidate variables. In the literature, this problem is called multi-task learning, support union recovery or simultaneous sparse coding in different contexts. In this paper, we propose a Bayesian method for solving this problem by introducing two nested sets of binary indicator variables. In the first set of indicator variables, each indicator is associated with a predictor variable or a regressor, indicating whether this variable is active for any of the response vectors. In the second set of indicator variables, each indicator is associated with both a predicator variable and a response vector, indicating whether this variable is active for the particular response vector. The problem of variable selection can then be solved by sampling from the posterior distributions of the two sets of indicator variables. We develop the Gibbs sampling algorithm for posterior sampling and demonstrate the performances of the proposed method for both simulated and real data sets.
|Number of pages||15|
|Journal||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Publication status||Published - 2014 Jan 1|
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)