Convex Graph Laplacian Multi-Task Learning SVM

Multi-Task Learning (MTL) goal is to achieve a better generalization by using data from different sources. MTL Support Vector Machines (SVMs) embrace this idea in two main ways: by using a combination of common and task-specific parts, or by fitting individual models adding a graph Laplacian regularization that defines different degrees of task relationships. The first approach is too rigid since it imposes the same relationship among all tasks. The second one does not have a clear way of sharing information among the different tasks. In this paper, we propose a model that combines both approaches. It uses a convex combination of a common model and of task specific models, where the relationships between these specific models are determined through a graph Laplacian regularization. We write the primal problem of this formulation and derive its dual problem, which is shown to be equivalent to a standard SVM dual using a particular kernel choice. Empirical results over different regression and classification problems support the usefulness of our proposal.