Nonlinear functional regression: a functional RKHS approach

Hachem Kadri, Emmanuel Duflos, Philippe Preux, Stéphane Canu, Manuel Davy ; JMLR W&CP 9:374-380, 2010.

Abstract

This paper deals with functional regression, in which the input attributes as well as the response are functions. To deal with this problem, we develop a functional reproducing kernel Hilbert space approach; here, a kernel is an operator acting on a function and yielding a function. We demonstrate basic properties of these functional RKHS, as well as a representer theorem for this setting; we investigate the construction of kernels; we provide some experimental insight.