Efficient Multitask Feature and Relationship Learning

TL;DR

This paper introduces an efficient method for multitask learning that jointly learns task and feature relationships, improving speed and generalization over existing approaches.

Contribution

It proposes a novel formulation and a fast coordinate-wise optimization algorithm for learning task and feature covariances in multitask learning.

Findings

The new algorithm is significantly faster than existing methods.

The nonlinear extension achieves better generalization.

The approach addresses issues of ill-posed optimization in prior methods.

Abstract

We consider a multitask learning problem, in which several predictors are learned jointly. Prior research has shown that learning the relations between tasks, and between the input features, together with the predictor, can lead to better generalization and interpretability, which proved to be useful for applications in many domains. In this paper, we consider a formulation of multitask learning that learns the relationships both between tasks and between features, represented through a task covariance and a feature covariance matrix, respectively. First, we demonstrate that existing methods proposed for this problem present an issue that may lead to ill-posed optimization. We then propose an alternative formulation, as well as an efficient algorithm to optimize it. Using ideas from optimization and graph theory, we propose an efficient coordinate-wise minimization algorithm that has a closed form solution for each block subproblem. Our experiments show that the proposed optimization method is orders of magnitude faster than its competitors. We also provide a nonlinear extension that is able to achieve better generalization than existing methods.