Structured feature selection and task relationship inference for multi-task learning

Multi-task learning (MTL) aims to enhance the generalization performance of supervised regression or classification by learning multiple related tasks simultaneously. In this paper, we aim to extend the current MTL techniques to high dimensional data sets with structured input and structured output (SISO), where the SI means the input features are structured and the SO means the tasks are structured. We investigate a completely ignored problem in MTL with SISO data: the interplay of structured feature selection and task relationship modeling. We hypothesize that combining the structure information of features and task relationship inference enables us to build more accurate MTL models. Based on the hypothesis, we have designed an efficient learning algorithm, in which we utilize a task covariance matrix related to the model parameters to capture the task relationship. In addition, we design a regularization formulation for incorporating the structured input features in MTL. We have developed an efficient iterative optimization algorithm to solve the corresponding optimization problem. Our algorithm is based on the accelerated first order gradient method in conjunction with the projected gradient scheme. Using two real-world data sets, we demonstrate the utility of the proposed learning methods.