This paper introduces a novel approach for multi-task regression that connects Kernel Machines (KMs) and Extreme Learning Machines (ELMs) through the exploitation of the Random Fourier Features (RFFs) approximation of the RBF kernel. In this sense, one of the contributions of this paper shows that for the proposed models, the KM and the ELM formulations can be regarded as two sides of the same coin. These proposed models, termed RFF-BLR, stand on a Bayesian framework that simultaneously addresses two main design goals. On the one hand, it fits multitask regressors based on KMs endowed with RBF kernels. On the other hand, it enables the introduction of a common-across-tasks prior that promotes multioutput sparsity in the ELM view. This Bayesian approach facilitates the simultaneous consideration of both the KM and ELM perspectives enabling (i) the optimisation of the RBF kernel parameter $\gamma$ within a probabilistic framework, (ii) the optimisation of the model complexity, and (iii) an efficient transfer of knowledge across tasks. The experimental results show that this framework can lead to significant performance improvements compared to the state-of-the-art methods in multitask nonlinear regression.

翻译：本文提出了一种新颖的多任务回归方法，通过利用随机傅里叶特征（RFFs）对径向基函数核（RBF核）的近似，将核机器（KMs）与极限学习机（ELMs）联系起来。在此意义上，本文的贡献之一表明，对于所提出的模型，KM和ELM的公式可以视为一枚硬币的两面。这些被称为RFF-BLR的模型基于贝叶斯框架，同时实现了两个主要设计目标。一方面，它基于具有RBF核的KM拟合多任务回归器；另一方面，它引入了跨任务共享的先验，在ELM视角下促进了多输出的稀疏性。这种贝叶斯方法便于同时考虑KM与ELM的视角，从而能够：（i）在概率框架内优化RBF核参数$\gamma$，（ii）优化模型复杂度，（iii）实现跨任务的高效知识迁移。实验结果表明，与多任务非线性回归的现有最优方法相比，该框架能显著提升性能。