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A study on nonlinear multivariate regression using fully connected deep neural network
Journal of the Korean Data & Information Science Society 2022;33:785-99
Published online September 30, 2022;
© 2022 Korean Data and Information Science Society.

Seokwon Han1 · Sungwan Bang2

1Training and Doctrine Command(TRADOC), ROK Army
2Department of Mathmatics, Korea Military Academy
Correspondence to: This work was supported by (21-MS-24) research fund of Korea Military Academy (Hwarangdae Research Institute) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT)(NRF-2022R1F1A1061622).
1 Protection simulation logic officer, Training and Doctrine Command(TRADOC), ROK Army, Jaun-ro, Yuseong-gu, Daejeon, Korea.
2 Professor, Department of Mathematics, Korea Military Academy, 574, Hwarang-ro, Nowon-gu, Seoul, Korea. E-mail:
Received May 6, 2022; Revised July 20, 2022; Accepted July 25, 2022.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
The focus of recent studies about multivariate regression analysis is to consider the correlation of response variables, and to model the complex relationship between explanatory variables and response variables. Most studies related to multivariate regression analysis rarely solve both of these problems. Deep neural networks (DNNs) are suitable for multivariate regression analysis as simply increasing the number of nodes in the output layer can increase the number of response variables in the model, and adding hidden layers can model the complex relationship between explanatory and response variables. DNNs have recently been used in various fields based on its excellent predictive power and accuracy, but there are insufficient cases of applying it to multivariate regression analysis. Therefore, we propose a simultaneous estimation method of a nonlinear multivariate regression model by applying a fully connected deep neural network, the basic structure of neural networks, to multivariate regression analysis, and it was confirmed through simulation that the proposed model performed better than the existing regression models learned each response variable independently.
Keywords : Fully connected deep neural network, multi-task learning, multivariate regression, nonlinear regression function.