Adaptive Multi-task Sparse Learning with an Application to fMRI Study

In this paper, we consider the multi-task sparse learning problem under the assumption that the dimensionality diverges with the sample size. The traditional l1/l2 multi-task lasso does not enjoy the oracle property unless a rather strong condition is enforced. Inspired by adaptive lasso, we propose a multi-stage procedure, adaptive multi-task lasso, to simultaneously conduct model estimation and variable selection across different tasks. Motivated by adaptive elastic-net, we further propose the adaptive multi-task elastic-net by adding another quadratic penalty to address the problem of collinearity. When the number of tasks is fixed, under weak assumptions, we establish the asymptotic oracle property for the proposed adaptive multi-task sparse learning methods including both adaptive multitask lasso and elastic-net. In addition to the desirable asymptotic property, we show by simulations that adaptive sparse learning methods also achieve much improved finite sample performance. A...

• Type: Journal
• Year: 2012
• Where: SDM
• Authors: Xi Chen, Jingrui He, Rick Lawrence, Jaime G. Carbonell
• Keywords: Data Mining, Model Estimation, Quadratic Penalty, SDM 2012, Semantic Basis