Monotone Classification with Relative Approximations
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911474898698240 |
|---|---|
| author | Tao, Yufei |
| author_facet | Tao, Yufei |
| contents | In monotone classification, the input is a multi-set $P$ of points in $\mathbb{R}^d$, each associated with a hidden label from $\{-1, 1\}$. The goal is to identify a monotone function $h$, which acts as a classifier, mapping from $\mathbb{R}^d$ to $\{-1, 1\}$ with a small {\em error}, measured as the number of points $p \in P$ whose labels differ from the function values $h(p)$. The cost of an algorithm is defined as the number of points having their labels revealed. This article presents the first study on the lowest cost required to find a monotone classifier whose error is at most $(1 + ε) \cdot k^*$ where $ε\ge 0$ and $k^*$ is the minimum error achieved by an optimal monotone classifier -- in other words, the error is allowed to exceed the optimal by at most a relative factor. Nearly matching upper and lower bounds are presented for the full range of $ε$. All previous work on the problem can only achieve an error higher than the optimal by an absolute factor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10775 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monotone Classification with Relative Approximations Tao, Yufei Machine Learning In monotone classification, the input is a multi-set $P$ of points in $\mathbb{R}^d$, each associated with a hidden label from $\{-1, 1\}$. The goal is to identify a monotone function $h$, which acts as a classifier, mapping from $\mathbb{R}^d$ to $\{-1, 1\}$ with a small {\em error}, measured as the number of points $p \in P$ whose labels differ from the function values $h(p)$. The cost of an algorithm is defined as the number of points having their labels revealed. This article presents the first study on the lowest cost required to find a monotone classifier whose error is at most $(1 + ε) \cdot k^*$ where $ε\ge 0$ and $k^*$ is the minimum error achieved by an optimal monotone classifier -- in other words, the error is allowed to exceed the optimal by at most a relative factor. Nearly matching upper and lower bounds are presented for the full range of $ε$. All previous work on the problem can only achieve an error higher than the optimal by an absolute factor. |
| title | Monotone Classification with Relative Approximations |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.10775 |