# On the Equivalence of Regression and Classification

arXiv: https://arxiv.org/abs/2511.04422 · HTML: https://mlsanity.com/paper/2511.04422/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 0 of its 7 references that are in the map.
- First posted on arXiv 6 Nov 2025.

## Abstract (arXiv)

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.