Multivariate Scale mixtures for joint sparse regularization in multi-task learning

In this paper we address the problem of learning shared sparse representation across several tasks. Assuming that the tasks share a common set of relevant features across all tasks is highly restrictive. This acts as a motivation to look for a generalized model which will be able to learn any correlation structure present between the tasks. We propose a generalized scale mixture distribution, the Multivariate Power Exponential Scale Mixture (M-PESM), as a joint sparsity promoting prior and derive a unified framework which consists of many of the popular Multitask Learning algorithms. Our proposed unified model also has the ability to learn any present correlation structure between tasks which leads to a more robust framework.