  Volterra series are especially useful for nonlinear system identification,
also thanks to their capability to approximate a broad range of input-output
maps. However, their identification from a finite set of data is hard, due to
the curse of dimensionality. Recent approaches have shown how regularized
kernel-based methods can be useful for this task. In this paper, we propose a
new regularization network for Volterra models identification. It relies on a
new kernel given by the product of basic building blocks. Each block contains
some unknown parameters that can be estimated from data using marginal
likelihood optimization. In comparison with other algorithms proposed in the
literature, numerical experiments show that our approach allows to better
select the monomials that really influence the system output, much increasing
the prediction capability of the model.
