Clustered Multi-Task Learning: A Convex Formulation

TL;DR

This paper introduces a convex multi-task learning method that automatically identifies task clusters, improving prediction accuracy by leveraging shared structure without prior knowledge of task groupings.

Contribution

It proposes a novel spectral norm-based convex formulation for clustered multi-task learning that does not require pre-specified task groupings.

Findings

Outperforms existing convex multi-task learning methods in simulations

Achieves better results on the IEDB MHC-I dataset

Effectively identifies task clusters without prior partition knowledge

Abstract

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.