Regularisation by Convolution in Symmetric-α-Stable function networks

In previous work, Regularisation by Convolution was proposed to improve the generalisation on regression of Gaussian Radial Basis Function Networks [Molina and Niranjan, 1997]. In this paper, we demonstrate that the same technique can be applied to a more general family of RBF networks called Symmetric-α-Stable function networks (SαS networks) which contains the Gaussian and Cauchy functions as particular cases. We also demonstrate that Regularisation by Convolution can be applied to sigmoidallike function networks obtained by integration of SαS kernels. We illustrate the performance of Regularisation by Convolution on Wahba's toy problem and the probability density estimation of ink in ancient manuscript letters (British library Beowulf manuscript).