Creation of Specific-to-Problem Kernel Functions for Function Approximation

Although there is a large diversity in the literature related to kernel methods, there are only a few works which do not use kernels based on Radial Basis Functions (RBF) for regression problems. The reason for that is that they present very good generalization capabilities and smooth interpolation. This paper studies an initial framework to create specific-to-problem kernels for application to regression models. The kernels are created without prior knowledge about the data to be approximated by means of a Genetic Programming algorithm. The quality of a kernel is evaluated independently of a particular model, using a modified version of a non parametric noise estimator. For a particular problem, performances of generated kernels are tested against common ones using weighted k-nn in the kernel space. Results show that the presented method produces specific-to-problem kernels that outperform the common ones for this particular case. Parallel programming is utilized to deal with large computational costs.