Work

Jensen-$$\phi $$-entropy, g-mean mixture distributions and optimal information: application to binary models

Year: 2026

Type: article

Abstract: This paper has two main objectives. First, we introduce a Jensen-type extension of the $$\phi $$ ϕ -entropy, which naturally generalizes the classical Jensen–Shannon divergence and explores its connections with Bregman divergence. Several theoretical results are established that highlight the interplay between these entropy and divergence measures, particularly in the context of mixture distributions. Second, we propose the g-mean mixture distribution, a general class of statistical models that encompasses many classical mixtures, such as arithmetic, geometric, and $$(\alpha ,\lambda )$$ ( α , λ ) -mixtures, as special cases. We show that this class arises as the optimal solution to a family of optimization problems formulated in terms of Bregman divergence. Finally, we apply the Jensen- $$\phi $$ ϕ -entropy to two binary models as an alternative to classical estimation methods, demonstrating promising empirical performance and potential for further theoretical investigation.

Source: Computational and Applied Mathematics

DOI: 10.1007/s40314-026-03730-4

Authors: Omid Kharazmi, Elena Castilla

Institutions: Vali Asr University of Rafsanjan, Universidad Rey Juan Carlos

Language: English

Topic: Bayesian Methods and Mixture Models

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funder: Universidad Rey Juan Carlos