Bounds on f-Divergences between Distributions within Generalized Quasi-$\varepsilon$-Neighborhood
<|reference_start|>Bounds on f-Divergences between Distributions within Generalized Quasi-$\varepsilon$-Neighborhood: A general reverse Pinsker's inequality is derived to give an upper bound on f-divergences in terms of total variational distance when two distributions are close measured under our proposed generalized local information geometry framework. In addition, relationships between two f-divergences equipped with functions that are third order differentiable are established in terms of the lower and upper bounds of their ratio, when the underlying distributions are within a generalized quasi-$\varepsilon$-neighborhood.<|reference_end|>
@article{yu2024bounds,
    title={Bounds on f-Divergences between Distributions within Generalized
  Quasi-$\varepsilon$-Neighborhood},
    author={Xinchun Yu, Shuangqing Wei, Shao-Lun Huang, and Xiao-Ping Zhang},
    journal={arXiv preprint arXiv:2406.00939},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.00939},
    primaryClass={cs.IT math.IT}
}