APPLICATION AND PERFORMANCE COMPARISON OF MULTI-OUTPUT MACHINE LEARNING FOR NUMERICAL-NUMERICAL AND NUMERICAL-CATEGORICAL OUTPUTS

Aug 2, 2026

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Multi-Output Machine Learning extends traditional machine learning to predict multiple output variables simultaneously by modeling interdependencies among outputs. It serves as a decision support approach because real-world decisions often depend on several factors, making it more time-efficient, easier to maintain, and more practical under data limitations, supporting cost savings in big-data settings. This study evaluates Multivariate Regression Tree, Multivariate Random Forest, and Multi-Output Neural Network. Tree and forest variants modify splitting via Mahalanobis distance, while the neural network improves accuracy through shared and private hidden-layer topology changes. Results show an error trade-off between outputs for tree and forest single-output comparisons, whereas the multi-output neural network improves both outputs. The work further introduces Mixed Multi-Output Machine Learning for numerical and categorical targets, using logistic-regression logit values to widen prediction beyond the 0–1 interval.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Introduction

Motivation for multi-output learning

Prior work and related studies

Challenge of mixed numerical and categorical outputs

Proposed approach using logistic regression

APPLICATION AND PERFORMANCE COMPARISON OF MULTI-OUTPUT MACHINE LEARNING FOR NUMERICALNUMERICAL AND NUMERICAL-CATEGORICAL OUTPUTS Karin Joan 1, Robyn Irawan2, Benny Yong3* 1,2,3Center for Mathematics and Society, Faculty of Science, Parahyangan Catholic University Jln. Ciumbuleuit No. 94, Bandung, 40141, Indonesia Corresponding author’s e-mail: * [benny_y@unpar.ac.id](benny_y@unpar.ac.id) Article History: Received: 30th November 2024 Revised: 2nd February 2025 Accepted: 8th March 2025 Published: 1st April 2025 Keywords: Logistic Regression; Multi-Output Machine Learning; Multivariate Regression Tree; Multivariate Random Forest; Multi-Output Neural Network. ABSTRACT Multi-Output Machine Learning is an advancement of traditional machine learning, designed to predict multiple output variables simultaneously while considering the relationships between these output variables. Multi-Output Machine Learning is essential as a decision support tool because decision-making in many problems generally considers multiple factors. The use of Multi-Output Machine Learning is more advantageous than conventional machine learning in terms of time efficiency, addressing data limitations, and ease of maintenance. These benefits will significantly impact cost savings for industries utilizing Big Data. The models used in this research include Multivariate Regression Tree, Multivariate Random Forest, and Multi-Output Neural Network. The Multivariate Regression Tree and Multivariate Random Forest are developed by modifying the splitting function using Mahalanobis distance. The topological changes introducing shared and private hidden layers are the key development of the Multi-Output Neural Network. The prediction results indicated a trade-off in error between two output variables when comparing the Multivariate Regression Tree and Multivariate Random Forest with their single output counterparts. Meanwhile, the Multi-Output Neural Network model successfully improved the prediction results for both output variables. This research also introduces Mixed Multi-Output Machine Learning, which can predict numerical and categorical output variables. The Mixed Multi-Output Machine Learning model utilizes the logit values from the Logistic Regression model to extend the range of prediction results beyond the 0 to 1 interval. Multi-Output Neural Network is the sole model that roduces predictions with relatively small errors and high accuracy values This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-ShareAlike 4.0 International License. How to cite this article: K. Joan, R. Irawan and B. Yong.,“APPLICATION AND PERFORMANCE COMPARISON OF MULTI-OUTPUT MACHINE LEARNING FOR NUMERICAL-NUMERICAL AND NUMERICAL-CATEGORICAL OUTPUTS,” BAREKENG: J. Math. & App., vol. 19, iss. 2, pp. 1421-1432, June, 2025. Copyright © 2025 Author(s) Journal homepage: [https://ojs3.unpatti.ac.id/index.php/barekeng/](https://ojs3.unpatti.ac.id/index.php/barekeng/) Journal e-mail: [barekeng.math@yahoo.com](barekeng.math@yahoo.com); [barekeng.journal@mail.unpatti.ac.id](barekeng.journal@mail.unpatti.ac.id) Research Article ∙ Open Access 1. INTRODUCTION Decision-making is one of the most crucial parts of every business flow to achieve set targets. Decisions are usually made by considering multiple factors based on data. For example, the success of a digital marketing campaign on social media can be measured by program awareness and the revenue generated by the campaign. Machine learning has significantly aided the decision-making process [1] . However, traditional machine learning (hereinafter called single-output machine learning) can only predict one variable, whether a numerical or categorical output. Therefore, multi-output machine learning has been developed from single-output machine learning to predict multiple outputs simultaneously. Using multioutput machine learning offers ben

FAQs

What problem does Multi-Output Machine Learning address?

It predicts multiple output variables at the same time while considering relationships among those outputs, supporting decisions that depend on multiple factors.

How do Multivariate Regression Tree and Multivariate Random Forest differ from their single-output counterparts?

They modify the splitting function using Mahalanobis distance to account for multiple outputs during training.

How does the Multi-Output Neural Network improve prediction for both output variables?

It introduces shared and private hidden layers through a topological change, enabling better joint modeling and reducing errors for both outputs.

Aug 2, 2026

Upload by Quinn