  We present a novel methodology to jointly perform multi-task learning and
infer intrinsic relationship among tasks by an interpretable and sparse graph.
Unlike existing multi-task learning methodologies, the graph structure is not
assumed to be known a priori or estimated separately in a preprocessing step.
Instead, our graph is learned simultaneously with model parameters of each
task, thus it reflects the critical relationship among tasks in the specific
prediction problem. We characterize graph structure with its weighted adjacency
matrix and show that the overall objective can be optimized alternatively until
convergence. We also show that our methodology can be simply extended to a
nonlinear form by being embedded into a multi-head radial basis function
network (RBFN). Extensive experiments, against six state-of-the-art
methodologies, on both synthetic data and real-world applications suggest that
our methodology is able to reduce generalization error, and, at the same time,
reveal a sparse graph over tasks that is much easier to interpret.
