Bayesian learning of feature spaces for multitasks problems

This paper presents a Bayesian framework to construct non-linear, parsimonious, shallow models for multitask regression. The proposed framework relies on the fact that Random Fourier Features (RFFs) enables the approximation of an RBF kernel by an extreme learning machine whose hidden layer is formed by RFFs. The main idea is to combine both dual views of a same model under a single Bayesian formulation that extends the Sparse Bayesian Extreme Learning Machines to multitask problems. From the kernel methods point of view, the proposed formulation facilitates the introduction of prior domain knowledge through the RBF kernel parameter. From the extreme learning machines perspective, the new formulation helps control overfitting and enables a parsimonious overall model (the models that serve each task share a same set of RFFs selected within the joint Bayesian optimisation). The experimental results show that combining advantages from kernel methods and extreme learning machines within the same framework can lead to significant improvements in the performance achieved by each of these two paradigms independently.