Functional multi-layer perceptron: a non-linear tool for functional data analysis.
In this paper, we study a natural extension of multi-layer perceptrons (MLP) to functional inputs. We show that fundamental results for classical MLP can be extended to functional MLP. We obtain universal approximation results that show the expressive power of functional MLP is comparable to that of numerical MLP. We obtain consistency results, which imply that the estimation of optimal parameters for functional MLP is statistically well defined. We finally show on simulated and real world data that the proposed model performs in a very satisfactory way.
Rossi
Fabrice
F
CEREMADE, UMR CNRS 7534, Université Paris-IX Dauphine, Place du Maréchal de Lattre de Tassigny, 75016 Paris, France. fabrice.rossi@inria.fr
Conan-Guez
Brieuc
B
D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D015233:Models, Statistical; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology; D017711:Nonlinear Dynamics; D009626:Terminology as Topic