On the Equivalence of Regression and Classification

Fuente: arXiv
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Hauptverfasser: Jayadeva, Dwivedi, Naman, Krishnan, Hari, Krishnan, N. M. Anoop
Format: Preprint
Veröffentlicht: 2025
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author Jayadeva
Dwivedi, Naman
Krishnan, Hari
Krishnan, N. M. Anoop
author_facet Jayadeva
Dwivedi, Naman
Krishnan, Hari
Krishnan, N. M. Anoop
contents A formal link between regression and classification has been tenuous. Even though the margin maximization term $\|w\|$ is used in support vector regression, it has at best been justified as a regularizer. We show that a regression problem with $M$ samples lying on a hyperplane has a one-to-one equivalence with a linearly separable classification task with $2M$ samples. We show that margin maximization on the equivalent classification task leads to a different regression formulation than traditionally used. Using the equivalence, we demonstrate a ``regressability'' measure, that can be used to estimate the difficulty of regressing a dataset, without needing to first learn a model for it. We use the equivalence to train neural networks to learn a linearizing map, that transforms input variables into a space where a linear regressor is adequate.
format Preprint
id arxiv_https___arxiv_org_abs_2511_04422
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the Equivalence of Regression and Classification
Jayadeva
Dwivedi, Naman
Krishnan, Hari
Krishnan, N. M. Anoop
Machine Learning
Artificial Intelligence
Computer Vision and Pattern Recognition
68T05, 68T10, 68Q32
I.2.6; I.5.1; I.5.2
A formal link between regression and classification has been tenuous. Even though the margin maximization term $\|w\|$ is used in support vector regression, it has at best been justified as a regularizer. We show that a regression problem with $M$ samples lying on a hyperplane has a one-to-one equivalence with a linearly separable classification task with $2M$ samples. We show that margin maximization on the equivalent classification task leads to a different regression formulation than traditionally used. Using the equivalence, we demonstrate a ``regressability'' measure, that can be used to estimate the difficulty of regressing a dataset, without needing to first learn a model for it. We use the equivalence to train neural networks to learn a linearizing map, that transforms input variables into a space where a linear regressor is adequate.
title On the Equivalence of Regression and Classification
topic Machine Learning
Artificial Intelligence
Computer Vision and Pattern Recognition
68T05, 68T10, 68Q32
I.2.6; I.5.1; I.5.2
url https://arxiv.org/abs/2511.04422