  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.
