Learning, Regularization and Ill-Posed Inverse Problems
Lorenzo Rosasco, Andrea Caponnetto, Ernesto De Vito, Umberto De Giovannini and Francesca Odone
In: nips 2004, 13-18 2004, vancouver canada.
Many works have shown that strong connections relate learning from
examples to regularization techniques for ill-posed inverse problems.
Nevertheless by now there was no formal evidence neither that
learning from examples could be seen as an inverse problem nor
that theoretical results in learning theory could be
independently derived using tools from regularization theory.
In this paper we provide a positive answer
to both questions. Indeed, considering the square loss, we
translate the learning problem in the language of regularization
theory and show that consistency results and optimal
regularization parameter choice can be derived by the discretization
of the corresponding inverse problem.