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arXiv · 2512.04020

On topological and algebraic structures of categorical random variables

Inocencio Ortiz·Santiago Gómez-Guerrero·Christian E. Schaerer
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Abstract

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.

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Inocencio Ortiz, Santiago Gómez-Guerrero, Christian E. Schaerer. 2025-12-03. On topological and algebraic structures of categorical random variables. https://doi.org/10.46298/cm.17035

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