Efficient Multitask Feature and Relationship Learning
This work addresses multitask learning for applications requiring improved generalization and interpretability, but it is incremental as it builds on prior formulations with algorithmic improvements.
The paper tackles the multitask learning problem by jointly learning relationships between tasks and features, identifying an ill-posed optimization issue in existing methods and proposing an alternative formulation with an efficient algorithm. The results show the proposed method is orders of magnitude faster than competitors and achieves better generalization in a nonlinear extension.
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.