Genetic complex multiple kernel for relevance vector regression

Relevance vector machine (RVM) is a state-of-the-art technique for regression and classification, as a sparse Bayesian extension version of the support vector machine. The selection of a kernel and associated parameter is a critical step of RVM application. The real-world application and recent researches have emphasized the requirement to multiple kernel learning, in order to boost the fitting accuracy by adapting better the characteristics of the data. This paper presents a data-driven evolutionary approach, called Genetic Complex Multiple Kernel Relevance Vector Regression (GCMK RVR), which combines genetic programming(GP) and relevance vector regression to evolve an optimal or near-optimal complex multiple kernel function. Each GP chromosome is a tree that encodes the mathematical expression of a complex multiple kernel function. Numerical experiments on several benchmark datasets show that the RVR involving this GCMK perform better than not only the widely used simple kernel, Polynomial, Gaussian RBF and Sigmoid kernel, but also the convex linear multiple kernel function.