This archive is distributed in association with the INFORMS Journal on Computing under the MIT License.
The software and data in this repository are a snapshot of the software and data that were used in the research reported on in the paper Function-on-Function Gaussian Process with Application in Robust Parameter Design by Jingru Huang, Haijie Xu, Yifei Gao, and Chen Zhang.
To cite the contents of this repository, please cite both the paper and this repo, using their respective DOIs.
https://doi.org/10.1287/ijoc.2024.0751
https://doi.org/10.1287/ijoc.2024.0751.cd
Below is the BibTex for citing this snapshot of the repository.
@misc{FFGP,
author = {Huang, Jingru and Xu, Haijie and Gao, Yifei and Zhang, Chen},
publisher = {INFORMS Journal on Computing},
title = {Function-on-Function Gaussian Process with Application in Robust Parameter Design},
year = {2025},
doi = {10.1287/ijoc.2024.0751.cd},
url = {https://github.com/INFORMSJoC/2024.0751},
note = {Available for download at https://github.com/INFORMSJoC/2024.0751},
}
As data sensing technology advances, functional data has become increasingly popular in complex systems. Function-on-function regression models, where both input and output variables are functional data, have attracted increasing attention in research. However, all the existing models have limitations that cannot qualify prediction uncertainty. To fill this gap, we propose a novel function-on-function Gaussian process (FFGP). It employs a detachable structure based on the operator-valued kernel to represent the covariance between functional inputs and output. Compared with existing Gaussian process models, FFGP can model functional data directly in the continuous space, and a scalar-valued operator-covariance is defined to qualify the output uncertainty. We further apply FFGP to robust parameter design by proposing an expected loss function to measure the functional output bias and uncertainty given a functional input. Then, an effective and scalable functional gradient descent algorithm (FRGD) is proposed to identify the optimal functional input that minimizes the loss function.
This project contains three folders: data, results, src.
data: contains the datasets used in the paper.results: contains the experimental results reported in the paper.src: contains the source code and scripts for experimental comparisons.
- R 4.5.1 or higher
- Required R Packages:
cubature,lava,mcGlobaloptim,DiceKriging,nloptr,MASS,mcmc,geoR,lhs,numDeriv,magrittr,FRegSigCom,proxy,R.matlab,writexl
To reproduce the results reported in the paper, please run the corresponding scripts in the src folder. For example, to generate the numerical results for Table 2 in Section 5 of the main paper, run the corresponding script Table_2.R in src.
Please refer to the README.md file in each folder for detailed descriptions.
All experiments were conducted on a desktop computer running a 64-bit Windows operating system, equipped with an AMD Ryzen Threadripper 3990X CPU (2.90 GHz) and 256 GB of RAM. All algorithms were implemented in R.