Incorporating fuzzy prior knowledge into Relevance Vector Machine regression

Although supervised learning has been widely used to tackle problems of function approximation and regression estimation, prior knowledge fails to be incorporated into the data-driven approach because the form of input-output data pairs are not applied. To overcome this limitation, focusing on the fusion between rough fuzzy system and very rare samples of input-output pairs with noise, this paper presents a simple but effective re-sampling algorithm based on piecewise differential interpolation and it is integrated with the sparse Bayesian learning framework for fuzzy model fused Relevance Vector Machine (RVM) regression. By using resampling algorithm encoded derivative regularization, the prior knowledge is translated into a pseudo training dataset, which finally is trained by the adaptive Gaussian kernel RVM to obtain more sparse solution. A preliminary empirical study shows that combining prior knowledge with training examples can dramatically improve the regression performance, particularly when the training dataset is limited.