Solving Sparse \& High-Dimensional-Output Regression via Compression

• URL: http://arxiv.org/abs/2410.15762v1
• Date: Mon, 21 Oct 2024 08:21:25 GMT
• Title: Solving Sparse \& High-Dimensional-Output Regression via Compression
• Authors: Renyuan Li, Zhehui Chen, Guanyi Wang,
• Abstract summary: Multi-Output Regression (MOR) has been widely used in scientific data analysis for decision-making. The increasing dimensionality of the outputs poses significant challenges regarding interpretability and computational scalability for modern MOR applications. This paper proposes a Sparse & High-dimensional-Output REgression model by incorporating additional sparsity requirements to resolve the output interpretability. 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.
• Score: 2.7596444457918263
• License:
• Abstract: 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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