Generalization Bounds of Regularization Algorithm with Gaussian Kernels

In many practical applications, the performance of a learning algorithm is not actually affected only by an unitary factor just like the complexity of hypothesis space, stability of the algorithm and data quality. This paper addresses in the performance of the regularization algorithm associated with Gaussian kernels. The main purpose is to provide a framework of evaluating the generalization performance of the algorithm conjointly in terms of hypothesis space complexity, algorithmic stability and data quality. The new bounds on generalization error of such algorithm measured by regularization error and sample error are established. It is shown that the regularization error has polynomial decays under some conditions, and the new bounds are based on uniform stability of the algorithm, covering number of hypothesis space and data information simultaneously. As an application, the obtained results are applied to several special regularization algorithms, and some new results for the special algorithms are deduced.