New Upper bounds for KL-divergence Based on Integral Norms

2024/09/02 by Yao, Liuquan, Liu, Songhao
#28D20 #60F05 #68P30 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2409.00934

Abstract

In this paper, some new upper bounds for Kullback-Leibler divergence(KL-divergence) based on L¹, L² and L^∞ 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 L¹ and L² 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.

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