On topological and algebraic structures of categorical random variables
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914453036990464 |
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| author | Ortiz, Inocencio Gómez-Guerrero, Santiago Schaerer, Christian E. |
| author_facet | Ortiz, Inocencio Gómez-Guerrero, Santiago Schaerer, Christian E. |
| contents | Based on entropy and symmetrical uncertainty (SU), we define a metric for categorical random variables and show that this metric can be promoted into an appropriate quotient space of categorical random variables. Moreover, we also show that there is a natural commutative monoid structure in the same quotient space, which is compatible with the topology induced by the metric, in the sense that the monoid operation is continuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04020 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On topological and algebraic structures of categorical random variables Ortiz, Inocencio Gómez-Guerrero, Santiago Schaerer, Christian E. Information Theory 94A17, 54E40, 20M32, 54H99 Based on entropy and symmetrical uncertainty (SU), we define a metric for categorical random variables and show that this metric can be promoted into an appropriate quotient space of categorical random variables. Moreover, we also show that there is a natural commutative monoid structure in the same quotient space, which is compatible with the topology induced by the metric, in the sense that the monoid operation is continuous. |
| title | On topological and algebraic structures of categorical random variables |
| topic | Information Theory 94A17, 54E40, 20M32, 54H99 |
| url | https://arxiv.org/abs/2512.04020 |