Adaptive spherical Gaussian kernel for fast relevance vector machine regression

As a popular and competent kernel function in kernel based machine learning techniques, conventional Gaussian kernel has unified kernel width with each of basis functions, which make impliedly a basic assumption: the response signal represents below certain frequency and the noise represents above such certain frequency. However, in many case, this assumption does not hold. To overcome this limitation, a novel adaptive spherical Gaussian kernel is utilized for nonlinear regression, and the stagewise optimization algorithm for maximizing Bayesian evidence in sparse Bayesian learning framework is proposed for model selection. Extensive empirical study shows its effectiveness and flexibility of model on representing regression problem with higher levels of sparsity and higher performance than classical RVM. The attractive ability of this approach is to automatically choose the right kernel widths locally fitting RVs from the training dataset, which could keep right level smoothing at each scale of signal.