An algebraic generalization of the entropy and its application to statistics
Year: 2026
Type: article
Abstract: We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality, and relate our approach to the theory of scoring rules. Many supporting examples illustrate our approach and give new perspectives on established notions, such as the likelihood, the Kullback-Leibler divergence, the uncorrelatedness of random variables, the scalar product itself, the Tichonov regularization and the mutual information.
Source: Journal of Applied Statistics
Author: Martin Schlather
Institution: University of Mannheim
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4394708807