On the Equivalence of Regression and Classification
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918188771442688 |
|---|---|
| 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 |