GP-based kernel evolution for L2-Regularization Networks

In kernel-based learning methods, a crucial design parameter is given by the choice of the kernel function to be used. Although there is, in theory, an infinite range of potential candidates, a handful of kernels covers the majority of actual applications. Partly, this is due to the difficulty of choosing an optimal kernel function in absence of a-priori information. In this respect, Genetic Programming (GP) techniques have shown interesting capabilities of learning non-trivial kernel functions that outperform commonly used ones. However, experiments have been restricted to the use of Support Vector Machines (SVMs), and have not addressed some problems that are specific to GP implementations, such as diversity maintenance. In these respects, the aim of this paper is twofold. First, we present a customized GP-based kernel search method that we apply using an L₂-Regularization Network as the base learning algorithm. Second, we investigate the problem of diversity maintenance in the context of kernel evolution, and test an adaptive criterion for maintaining it in our algorithm. For the former point, experiments show a gain in accuracy for our method against fine-tuned standard kernels. For the latter, we show that diversity is decreasing critically fast during the GP iterations, but this decrease does not seems to affect performance of the algorithm.