  Traditionally, multitask learning (MTL) assumes that all the tasks are
related. This can lead to negative transfer when tasks are indeed incoherent.
Recently, a number of approaches have been proposed that alleviate this problem
by discovering the underlying task clusters or relationships. However, they are
limited to modeling these relationships at the task level, which may be
restrictive in some applications. In this paper, we propose a novel MTL
formulation that captures task relationships at the feature-level. Depending on
the interactions among tasks and features, the proposed method construct
different task clusters for different features, without even the need of
pre-specifying the number of clusters. Computationally, the proposed
formulation is strongly convex, and can be efficiently solved by accelerated
proximal methods. Experiments are performed on a number of synthetic and
real-world data sets. Under various degrees of task relationships, the accuracy
of the proposed method is consistently among the best. Moreover, the
feature-specific task clusters obtained agree with the known/plausible task
structures of the data.
