On the Equivalence of Regression and Classification

• URL: http://arxiv.org/abs/2511.04422v1
• Date: Thu, 06 Nov 2025 14:54:25 GMT
• Title: On the Equivalence of Regression and Classification
• Authors: Jayadeva, Naman Dwivedi, Hari Krishnan, N. M. Anoop Krishnan,
• Abstract summary: We show that a regression problem with $M$ samples lying on a hyperplane has a one-to-one with a linearly separable classification task with $2M$ samples.<n>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.
• Score: 7.718380841006887
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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