New Upper bounds for KL-divergence Based on Integral Norms
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909371459436544 |
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| author | Yao, Liuquan Liu, Songhao |
| author_facet | Yao, Liuquan Liu, Songhao |
| contents | In this paper, some new upper bounds for Kullback-Leibler divergence(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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00934 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New Upper bounds for KL-divergence Based on Integral Norms Yao, Liuquan Liu, Songhao Probability Information Theory 60F05, 28D20, 68P30 In this paper, some new upper bounds for Kullback-Leibler divergence(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. |
| title | New Upper bounds for KL-divergence Based on Integral Norms |
| topic | Probability Information Theory 60F05, 28D20, 68P30 |
| url | https://arxiv.org/abs/2409.00934 |