From Kernel Methods to Neural Networks: A Unifying Variational Formulation

Understand

The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning.

• In this paper, we present a unifying regularization functional that depends on an operator and on a generic Radon-domain norm.
• We establish the existence of a minimizer and give the parametric form of the solution(s) under very mild assumptions.
• When the norm is Hilbertian, the proposed formulation yields a solution that involves radial-basis functions and is compatible with the classical methods of machine learning.