2025/12/03 by Ortiz, Inocencio, Gómez-Guerrero, Santiago, Schaerer, Christian E.
#20M32 #54E40 #54H99 #94A17 #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2512.04020
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.