Multi-Task Multiple Kernel Relationship Learning

Abstract: This paper presents a novel multitask multiple kernel learning framework that efficiently learns the kernel weights leveraging the relationship across multiple tasks. The idea is to automatically infer this task relationship in the \textit{RKHS} space corresponding to the given base kernels. The problem is formulated as a regularization-based approach called \textit{Multi-Task Multiple Kernel Relationship Learning} (\textit{MK-MTRL}), which models the task relationship matrix from the weights learned from latent feature spaces of task-specific base kernels. Unlike in previous work, the proposed formulation allows one to incorporate prior knowledge for simultaneously learning several related tasks. We propose an alternating minimization algorithm to learn the model parameters, kernel weights and task relationship matrix. In order to tackle large-scale problems, we further propose a two-stage \textit{MK-MTRL} online learning algorithm and show that it significantly reduces the computational time, and also achieves performance comparable to that of the joint learning framework. Experimental results on benchmark datasets show that the proposed formulations outperform several state-of-the-art multitask learning methods.