Multitask learning (MTL) leverages task-relatedness to enhance performance.
With the emergence of multimodal data, tasks can now be referenced by multiple
indices. In this paper, we employ high-order tensors, with each mode
corresponding to a task index, to naturally represent tasks referenced by
multiple indices and preserve their structural relations. Based on this
representation, we propose a general framework of low-rank MTL methods with
tensorized support vector machines (SVMs) and least square support vector
machines (LSSVMs), where the CP factorization is deployed over the coefficient
tensor. Our approach allows to model the task relation through a linear
combination of shared factors weighted by task-specific factors and is
generalized to both classification and regression problems. Through the
alternating optimization scheme and the Lagrangian function, each subproblem is
transformed into a convex problem, formulated as a quadratic programming or
linear system in the dual form. In contrast to previous MTL frameworks, our
decision function in the dual induces a weighted kernel function with a
task-coupling term characterized by the similarities of the task-specific
factors, better revealing the explicit relations across tasks in MTL.
Experimental results validate the effectiveness and superiority of our proposed
methods compared to existing state-of-the-art approaches in MTL. The code of
implementation will be available at this https URL

多任务学习中使用高阶张量表示任务间的结构关系，并通过线性组合共享因子、特定因子来模拟任务关联，提出通用的基于低秩的多任务学习方法，证实了该方法在多任务学习中的有效性和优越性。