Bounds on f-Divergences between Distributions within Generalized Quasi-$\varepsilon$-Neighborhood
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909729757855744 |
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| author | Yu, Xinchun Wei, Shuangqing Zhang, Xiao-Ping |
| author_facet | Yu, Xinchun Wei, Shuangqing Zhang, Xiao-Ping |
| contents | This work establishes computable bounds between f-divergences for probability measures within a generalized quasi-$\varepsilon_{(M,m)}$-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 $χ^2$-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_00939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounds on f-Divergences between Distributions within Generalized Quasi-$\varepsilon$-Neighborhood Yu, Xinchun Wei, Shuangqing Zhang, Xiao-Ping Information Theory This work establishes computable bounds between f-divergences for probability measures within a generalized quasi-$\varepsilon_{(M,m)}$-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 $χ^2$-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. |
| title | Bounds on f-Divergences between Distributions within Generalized Quasi-$\varepsilon$-Neighborhood |
| topic | Information Theory |
| url | https://arxiv.org/abs/2406.00939 |