2025/12/25 by Hiroshi Matsuzoe, Matsuzoe, Hiroshi, Asuka Takatsu +1
Engineering · Mathematics · Physics and Astronomy · #53B12 #62B11 #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Inequalities and Applications #Probability (math.PR) #Statistical Mechanics and Entropy #Wireless Communication Security Techniques
paper · doi:10.48550/arxiv.2512.21532
openalex publication_date 2025/12/25 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28
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.