# Deep Learning with Functional Inputs

@article{Thind2020DeepLW, title={Deep Learning with Functional Inputs}, author={Barinder Thind and Kevin Multani and Jiguo Cao}, journal={ArXiv}, year={2020}, volume={abs/2006.09590} }

We present a methodology for integrating functional data into deep densely connected feed-forward neural networks. The model is defined for scalar responses with multiple functional and scalar covariates. A by-product of the method is a set of dynamic functional weights that can be visualized during the optimization process. This visualization leads to greater interpretability of the relationship between the covariates and the response relative to conventional neural networks. The model is… Expand

#### Figures, Tables, and Topics from this paper

#### 2 Citations

FuncNN: An R Package to Fit Deep Neural Networks Using Generalized Input Spaces

- Computer Science, Mathematics
- ArXiv
- 2020

Several functions are introduced that provide users an avenue to easily build models, generate predictions, and run cross-validations and the ultimate contribution is a package that provides a set of general modelling and diagnostic tools for data problems in which there exist both functional and scalar covariates. Expand

Neural Networks as Functional Classifiers

- Computer Science, Mathematics
- ArXiv
- 2020

This work extends notable deep learning methodologies to the domain of functional data for the purpose of classification problems and demonstrates the effectiveness of the method in a number of classification applications such as classification of spectrographic data. Expand

#### References

SHOWING 1-10 OF 39 REFERENCES

Functional multi-layer perceptron: a non-linear tool for functional data analysis

- Mathematics, Computer Science
- Neural Networks
- 2005

This paper studies a natural extension of multi-layer perceptrons (MLP) to functional inputs and obtains universal approximation results that show the expressive power of functional MLP is comparable to that of numerical MLP. Expand

Functional Regression

- Mathematics
- 2014

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions… Expand

Semi-functional partial linear regression

- Mathematics
- 2006

This note deals with the problem of predicting some real-valued response variable in the situation where some among the explanatory variables are functional. More precisely, a new model is introduced… Expand

Adam: A Method for Stochastic Optimization

- Computer Science, Mathematics
- ICLR
- 2015

This work introduces Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments, and provides a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Expand

Dropout: a simple way to prevent neural networks from overfitting

- Computer Science
- J. Mach. Learn. Res.
- 2014

It is shown that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets. Expand

Deep Residual Learning for Image Recognition

- Computer Science
- 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
- 2016

This work presents a residual learning framework to ease the training of networks that are substantially deeper than those used previously, and provides comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. Expand

Generalized functional linear models

- Mathematics
- 2004

We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained… Expand

ImageNet classification with deep convolutional neural networks

- Computer Science
- Commun. ACM
- 2012

A large, deep convolutional neural network was trained to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes and employed a recently developed regularization method called "dropout" that proved to be very effective. Expand

Statistical Computing in Functional Data Analysis: The R Package fda.usc

- Computer Science
- 2012

This paper is devoted to the R package fda.usc which includes some utilities for functional data analysis. This package carries out exploratory and descriptive analysis of functional data analyzing… Expand

Nonparametric Functional Data Analysis: Theory And Practice

- Mathematics, Computer Science
- Technometrics
- 2007

The present book applies kernel regression techniques to functional data problems such as functional regression or classification, where the predictor is a function and nonparametric statisticians should feel very much at home with the approach taken in this book. Expand