Clustered Multi-Task Learning: A Convex Formulation
Laurent jacob, Francis Bach and Jean-Philippe Vert
In: NIPS 2008(2009).
In multi-task learning several related tasks are considered simultaneously, with
the hope that by an appropriate sharing of information across tasks, each task may
benefit from the others. In the context of learning linear functions for supervised
classification or regression, this can be achieved by including a priori information
about the weight vectors associated with the tasks, and how they are expected
to be related to each other. In this paper, we assume that tasks are clustered into
groups, which are unknown beforehand, and that tasks within a group have similar
weight vectors. We design a new spectral norm that encodes this a priori assumption,
without the prior knowledge of the partition of tasks into groups, resulting
in a new convex optimization formulation for multi-task learning. We show in
simulations on synthetic examples and on the IEDB MHC-I binding dataset, that
our approach outperforms well-known convex methods for multi-task learning, as
well as related non-convex methods dedicated to the same problem.