Non-linear Functional Modeling using Neural Networks

04/19/2021
by   Aniruddha Rajendra Rao, et al.
0

We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two variations of our framework: a functional neural network with continuous hidden layers, called the Functional Direct Neural Network (FDNN), and a second version that utilizes basis expansions and continuous hidden layers, called the Functional Basis Neural Network (FBNN). Both are designed explicitly to exploit the structure inherent in functional data. To fit these models we derive a functional gradient based optimization algorithm. The effectiveness of the proposed methods in handling complex functional models is demonstrated by comprehensive simulation studies and real data examples.

READ FULL TEXT

page 5

page 9

research
07/29/2021

Modern Non-Linear Function-on-Function Regression

We introduce a new class of non-linear function-on-function regression m...
research
12/07/2021

A generalization gap estimation for overparameterized models via the Langevin functional variance

This paper discusses the estimation of the generalization gap, the diffe...
research
01/14/2023

Functional Neural Networks: Shift invariant models for functional data with applications to EEG classification

It is desirable for statistical models to detect signals of interest ind...
research
04/18/2019

On the validity of memristor modeling in the neural network literature

An analysis of the literature shows that there are two types of non-memr...
research
10/14/2022

Latent process models for functional network data

Network data are often sampled with auxiliary information or collected t...
research
02/18/2020

Learning Parities with Neural Networks

In recent years we see a rapidly growing line of research which shows le...
research
02/22/2020

Regression with Deep Learning for Sensor Performance Optimization

Neural networks with at least two hidden layers are called deep networks...

Please sign up or login with your details

Forgot password? Click here to reset