Complexity of regularization RBF networks

We attempt to unify and compare a class of algorithms for learning input-output (I/O) functions f from examples. Our general approach involves parsing information about f into a priori and a posteriori information, with each represented by a probability measure on the space F of candidate functions. A consequence is that complexities of different approximation algorithms for the same problems are possible to be compared, and optimal algorithms to be identified. We illustrate this by formulating an information complexity theory for regularization radial basis function (RBF) networks. We show the ε-complexity of approximating f using regularization is equivalent to the ε-complexity of approximating f using any consistent Bayesian approach. In particular, a Gaussian prior distribution may be assumed for correct computation of all complexities