Adaptive Graph Laplacian for Convex Multi-Task Learning SVM

Multi-Task Learning (MTL) aims at solving different tasks simultaneously to obtain better models. Some Support Vector Machines (SVMs) formulations for the MTL context involve the combination of common and task-independent models, where we can also use an homogeneous graph over the tasks to impose pairwise connections between the independent models. The graph weight matrix is usually taken as a uniform (i.e., maximum entropy) one that connects equally every pair of tasks. If we take instead the identity matrix (i.e., the one of minimum entropy), then no connections are considered. In MTL situations where the real tasks or the relationships among them are unknown, these two rigid approaches can be detrimental to the learning process. In order to identify the true underlying tasks and their structure, we propose here a Convex Adaptive Graph Laplacian MTL SVM, where the task models and the graph that reflects their relationships are learned in a sequential and collaborative way. We illustrate on four different synthetic scenarios the task structure identification capacities of this approach and how it can lead to better models.