Corpus ID: 236493495

Modern Non-Linear Function-on-Function Regression

@article{Rao2021ModernNF,
  title={Modern Non-Linear Function-on-Function Regression},
  author={Aniruddha Rajendra Rao and Matthew L. Reimherr},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.14151}
}
  • Aniruddha Rajendra Rao, M. Reimherr
  • Published 2021
  • Computer Science, Mathematics
  • ArXiv
We introduce a new class of non-linear function-on-function regression models for functional data using neural networks. We propose a framework using a hidden layer consisting of continuous neurons, called a continuous hidden layer, for functional response modeling and give two model fitting strategies, Functional Direct Neural Network (FDNN) and Functional Basis Neural Network (FBNN). Both are designed explicitly to exploit the structure inherent in functional data and capture the complex… Expand

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References

SHOWING 1-10 OF 51 REFERENCES
Non-linear Functional Modeling using Neural Networks
TLDR
A new class of non-linear models for functional data based on neural networks designed explicitly to exploit the structure inherent in functional data are introduced and a functional gradient based optimization algorithm is derived. Expand
Optimal Prediction for Additive Function-on-Function Regression
As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models,Expand
Function-on-function quadratic regression models
TLDR
Methods to estimate the coefficient functions, predict unknown response and test significance of the quadratic term are developed in functional principal component regression paradigm and asymptotic theories for these approaches are established. Expand
Functional additive regression
We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving aExpand
Additive Function-on-Function Regression
  • Janet S. Kim, A. Staicu, A. Maity, R. Carroll, David Ruppert
  • Mathematics, Medicine
  • Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
  • 2018
TLDR
A computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function is developed to study additive function-on-function regression. Expand
Continuously additive models for nonlinear functional regression
We introduce continuously additive models, which can be viewed as extensions of additive regression models with vector predictors to the case of infinite-dimensional predictors. This approachExpand
Functional Additive Models
In commonly used functional regression models, the regression of a scalar or functional response on the functional predictor is assumed to be linear. This means that the response is a linear functionExpand
Structured functional additive regression in reproducing kernel Hilbert spaces.
  • H. Zhu, F. Yao, H. Zhang
  • Mathematics, Medicine
  • Journal of the Royal Statistical Society. Series B, Statistical methodology
  • 2014
TLDR
A new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces is proposed and takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. Expand
Continuously dynamic additive models for functional data
TLDR
This article proposes the continuously dynamic additive model (CDAM), in which both the predictor and response are random functions, and characterize this model through a time-dependent smooth surface that reflects the underlying nonlinear dynamic relationships between functional predictor and functional response. Expand
Single and multiple index functional regression models with nonparametric link
Fully nonparametric methods for regression from functional data have poor accuracy from a statistical viewpoint, reflecting the fact that their convergence rates are slower than nonparametric ratesExpand
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