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Multi-task learning is a learning paradigm that improves the performance of "related" tasks through their joint learning. To do this each task answers the question "Which other task should I share with"? This task relatedness can be complex - a task may be related to one set of tasks based on one subset of features and to other tasks based on other subsets. Existing multi-task learning methods do not explicitly model this reality, learning a single-faceted task relationship over all the features. This degrades performance by forcing a task to become similar to other tasks even on their unrelated features. Addressing this gap, we propose a novel multi-task learning model that leams multi-faceted task relationship, allowing tasks to collaborate differentially on different feature subsets. This is achieved by simultaneously learning a low dimensional sub-space for task parameters and inducing task groups over each latent subspace basis using a novel combination of L1 and pairwise L∞ norms. Further, our model can induce grouping across both positively and negatively related tasks, which helps towards exploiting knowledge from all types of related tasks. We validate our model on two synthetic and five real datasets, and show significant performance improvements over several state-of-the-art multi-task learning techniques. Thus our model effectively answers for each task: What shall I share and with whom

What shall I share and with Whom? - A Multi-Task Learning Formulation using Multi-Faceted Task Relationships