Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis

TL;DR

This paper introduces a functional extension of Multi-Layer Perceptrons (MLP), demonstrating their universal approximation capabilities and statistical consistency, with promising results on simulated and real data.

Contribution

It extends classical MLP theory to functional data, establishing universal approximation and consistency results for functional MLPs.

Findings

Functional MLPs have comparable expressive power to classical MLPs.

The estimation of parameters in functional MLPs is statistically consistent.

The model performs well on both simulated and real-world datasets.

Abstract

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.