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The differential approximation method to determine a scale parameter interval for a multi-scale Gaussian kernel RVM regression

A scale parameter of a Gaussian kernel relevance vector machine (RVM) directly determine a result of the RVM regression. Because this scale parameter interval is from zero to positive infinite, it is difficult to choose the proper scale parameter for the Gaussian kernel function. This paper introduces a differential approximation method (DAM) to determine a scale parameter interval for a Gaussian kernel function. We acquired a very small scale parameter interval by utilizing the DAM from a training set. After training the multi-scale Gaussian kernel RVM, we easily searched the proper scale parameter values for Gaussian kernels in the scale parameter interval by a simple search algorithm. The results of experiments indicate the DAM can determine the proper scale parameter interval. The result of RVM predictor in the test set is very excellent.