On topological and algebraic structures of categorical random variables
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.
Fields of Study & Subjects
Advanced Algebra and Logic
Statistical Mechanics and Entropy
Multi-Criteria Decision Making
Publication details
- Journal / source
- Communications in Mathematics
- Volume
- Volume 34 (2026), Issue 2...
- Publication date
- 1 April 2026
- Language
- EN