{"ID":2845360,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.04422","arxiv_id":"2511.04422","title":"On the Equivalence of Regression and Classification","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.","short_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 linear...","url_abs":"https://arxiv.org/abs/2511.04422","url_pdf":"https://arxiv.org/pdf/2511.04422v1","authors":"[\"Jayadeva\",\"Naman Dwivedi\",\"Hari Krishnan\",\"N. M. Anoop Krishnan\"]","published":"2025-11-06T14:54:25Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"cs.CV\"]","methods":"[]","has_code":false}