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Main Authors: Li, Renyuan, Chen, Zhehui, Wang, Guanyi
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2410.15762
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author Li, Renyuan
Chen, Zhehui
Wang, Guanyi
author_facet Li, Renyuan
Chen, Zhehui
Wang, Guanyi
contents Multi-Output Regression (MOR) has been widely used in scientific data analysis for decision-making. Unlike traditional regression models, MOR aims to simultaneously predict multiple real-valued outputs given an input. However, the increasing dimensionality of the outputs poses significant challenges regarding interpretability and computational scalability for modern MOR applications. As a first step to address these challenges, this paper proposes a Sparse \& High-dimensional-Output REgression (SHORE) model by incorporating additional sparsity requirements to resolve the output interpretability, and then designs a computationally efficient two-stage optimization framework capable of solving SHORE with provable accuracy via compression on outputs. Theoretically, we show that the proposed framework is computationally scalable while maintaining the same order of training loss and prediction loss before-and-after compression under arbitrary or relatively weak sample set conditions. Empirically, numerical results further validate the theoretical findings, showcasing the efficiency and accuracy of the proposed framework.
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id arxiv_https___arxiv_org_abs_2410_15762
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Solving Sparse \& High-Dimensional-Output Regression via Compression
Li, Renyuan
Chen, Zhehui
Wang, Guanyi
Machine Learning
Optimization and Control
Multi-Output Regression (MOR) has been widely used in scientific data analysis for decision-making. Unlike traditional regression models, MOR aims to simultaneously predict multiple real-valued outputs given an input. However, the increasing dimensionality of the outputs poses significant challenges regarding interpretability and computational scalability for modern MOR applications. As a first step to address these challenges, this paper proposes a Sparse \& High-dimensional-Output REgression (SHORE) model by incorporating additional sparsity requirements to resolve the output interpretability, and then designs a computationally efficient two-stage optimization framework capable of solving SHORE with provable accuracy via compression on outputs. Theoretically, we show that the proposed framework is computationally scalable while maintaining the same order of training loss and prediction loss before-and-after compression under arbitrary or relatively weak sample set conditions. Empirically, numerical results further validate the theoretical findings, showcasing the efficiency and accuracy of the proposed framework.
title Solving Sparse \& High-Dimensional-Output Regression via Compression
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2410.15762