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

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.

http://www.sciencedirect.com/science/journal/08936080

Cited by in corpus (22)

• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Support vector machine for functional data classification
• The Random Feature Model for Input-Output Maps between Banach Spaces
• Representation of Functional Data in Neural Networks
• A hidden process regression model for functional data description. Application to curve discrimination
• Deep Learning with Functional Inputs
• Functional archetype and archetypoid analysis
• Multilayer Perceptron with Functional Inputs: an Inverse Regression Approach
• Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs
• Operator Learning Using Random Features: A Tool for Scientific Computing
• Remaining Useful Life Estimation Using Functional Data Analysis
• Neural Networks for Scalar Input and Functional Output
• Neural Networks for Complex Data
• Theoretical Properties of Projection Based Multilayer Perceptrons with Functional Inputs
• A Practitioner's Guide to Kolmogorov-Arnold Networks
• Consistency of functional learning methods based on derivatives
• Classification supervisée en grande dimension. Application à l'agrément de conduite automobile
• FuncNN: An R Package to Fit Deep Neural Networks Using Generalized Input Spaces
• Deep Time Series Models for Scarce Data
• Neural Networks as Functional Classifiers
• A Functional Perspective on Learning Symmetric Functions with Neural Networks
• A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems