Graphical Multi-Task Learning

We investigate multi-task learning in a setting where relationships between tasks are modeled by a graph structure. Most existing methods treat all pairs of tasks as being equally related, which can be hurt performance when the true structure of task relationships is more complex. Our method uses regularization to encourage models for task pairs to be similar whenever they are connected in the network. This idea was first proposed by Evgeniou, Micchelli and Pontil, who pointed out that the multi-task problem can be reduced to a single-task learning problem with a modified kernel constructed from the graph Laplacian. We extend their work to fully incorporate non-linear kernels and make a practical modification to the kernel that performs better in practice. We also present the first empirical evaluation of graphical multi-task learning on one synthetic and two real applications to demonstrate its value over methods that treat tasks relationships symmetrically.