Divergence and deformed exponential family
Abstract
The Kullback--Leibler divergence together with exponential families establishes the foundation of information geometry and is widely generalized. Among the generalization, we focus on the $(h,τ)$-divergence and $(h,τ)$-exponential families. We present a sufficient condition for the $(h,τ)$-divergence to induce a Hessian structure on an $(h,τ)$-exponential family. We also define the $(h,τ)$-dependence of random variables and prove a kind of the law of large numbers.
Fields of Study & Subjects
Statistical Mechanics and Entropy
Mathematical Inequalities and Applications
Wireless Communication Security Techniques
Publication details
- Journal / source
- Journal of Mathematical Analysis and Applications
- Volume
- 567
- Issue
- 1
- Pages
- 131088–131088
- Publication date
- 23 September 2026
- Language
- EN