Multi-Task Learning with Gaussian Matrix Generalized Inverse Gaussian Model

In this paper, we study the multi-task learning problem with a new perspective of considering the structure of the residue error matrix and the low-rank approximation to the task covariance matrix simultaneously. In particular, we first introduce the Matrix Generalized Inverse Gaussian (MGIG) prior and define a Gaussian Matrix Generalized Inverse Gaussian (GMGIG) model for low-rank approximation to the task covariance matrix. Through combining the GMGIG model with the residual error structure assumption, we propose the GMGIG regression model for multi-task learning. To make the computation tractable, we simultaneously use variational inference and sampling techniques. In particular, we propose two sampling strategies for computing the statistics of the MGIG distribution. Experiments show that this model is superior to the peer methods in regression and prediction.