2024/06/03 by Xinchun Yu, Yu, Xinchun, Shuangqing Wei +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Information Theory (cs.IT) #Mathematical Approximation and Integration #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2406.00939
openalex publication_date 2024/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work establishes computable bounds between f-divergences for probability measures within a generalized quasi-ε(M,m)-neighborhood framework. We make the following key contributions. (1) a unified characterization of local distributional proximity beyond structural constraints is provided, which encompasses discrete/continuous cases through parametric flexibility. (2) First-order differentiable f-divergence classification with Taylor-based inequalities is established, which generalizes χ2-divergence results to broader function classes. (3) We provide tighter reverse Pinsker's inequalities than existing ones, bridging asymptotic analysis and computable bounds. The proposed framework demonstrates particular efficacy in goodness-of-fit test asymptotics while maintaining computational tractability.