New Upper bounds for KL-divergence Based on Integral Norms
<|reference_start|>New Upper bounds for KL-divergence Based on Integral Norms: In this paper, some new upper bounds for KL-divergence based on $L^1, L^2$ and $L^\infty$ norms of density functions are discussed. Our findings unveil that the convergence in KL-divergence sense sandwiches between the convergence of density functions in terms of $L^1$ and $L^2$ norms. Furthermore, we endeavor to apply our newly derived upper bounds to the analysis of the rate theorem of the entropic conditional central limit theorem.<|reference_end|>
@article{yao2024new,
    title={New Upper bounds for KL-divergence Based on Integral Norms},
    author={Liuquan Yao, Songhao Liu},
    journal={arXiv preprint arXiv:2409.00934},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.00934},
    primaryClass={math.PR cs.IT math.IT}
}